%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%%     author          = "Nicholas J. Higham",
%%%     version         = "2.33",
%%%     date            = "17 November 2023",
%%%     time            = "13:06:30 MST",
%%%     filename        = "acc-stab-num-alg-2ed.bib",
%%%     address         = "Department of Mathematics
%%%                        University of Manchester
%%%                        Manchester M13 9PL
%%%                        England",
%%%     telephone       = "+44 (0)161 275 5800",
%%%     FAX             = "+44 (0)161 275 5819",
%%%     checksum        = "33498 19700 71755 745778"
%%%     email           = "higham at ma.man.ac.uk (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "bibliography, numerical analysis, N. J. Higham",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of publications cited
%%%                        in the second edition of the book ``Accuracy
%%%                        and Stability of Numerical Algorithms'', SIAM
%%%                        (2002).
%%%
%%%                        At version 2.33, the year coverage looked
%%%                        like this:
%%%
%%%                             1841 (   1)    1895 (   0)    1949 (   3)
%%%                             1842 (   0)    1896 (   0)    1950 (   1)
%%%                             1843 (   0)    1897 (   0)    1951 (   4)
%%%                             1844 (   0)    1898 (   0)    1952 (   2)
%%%                             1845 (   0)    1899 (   0)    1953 (   4)
%%%                             1846 (   0)    1900 (   0)    1954 (   5)
%%%                             1847 (   0)    1901 (   0)    1955 (   5)
%%%                             1848 (   0)    1902 (   0)    1956 (   3)
%%%                             1849 (   0)    1903 (   0)    1957 (   3)
%%%                             1850 (   1)    1904 (   0)    1958 (   3)
%%%                             1851 (   1)    1905 (   0)    1959 (   8)
%%%                             1852 (   0)    1906 (   0)    1960 (   4)
%%%                             1853 (   0)    1907 (   0)    1961 (   7)
%%%                             1854 (   0)    1908 (   0)    1962 (  14)
%%%                             1855 (   0)    1909 (   0)    1963 (  13)
%%%                             1856 (   0)    1910 (   0)    1964 (   9)
%%%                             1857 (   0)    1911 (   0)    1965 (  18)
%%%                             1858 (   0)    1912 (   0)    1966 (  17)
%%%                             1859 (   0)    1913 (   0)    1967 (  16)
%%%                             1860 (   0)    1914 (   0)    1968 (  16)
%%%                             1861 (   0)    1915 (   0)    1969 (  14)
%%%                             1862 (   0)    1916 (   0)    1970 (  16)
%%%                             1863 (   0)    1917 (   0)    1971 (  25)
%%%                             1864 (   0)    1918 (   0)    1972 (  16)
%%%                             1865 (   0)    1919 (   0)    1973 (  19)
%%%                             1866 (   0)    1920 (   0)    1974 (  31)
%%%                             1867 (   0)    1921 (   0)    1975 (  19)
%%%                             1868 (   0)    1922 (   1)    1976 (  29)
%%%                             1869 (   0)    1923 (   0)    1977 (  26)
%%%                             1870 (   0)    1924 (   1)    1978 (  15)
%%%                             1871 (   0)    1925 (   0)    1979 (  28)
%%%                             1872 (   0)    1926 (   0)    1980 (  27)
%%%                             1873 (   0)    1927 (   0)    1981 (  27)
%%%                             1874 (   0)    1928 (   0)    1982 (  21)
%%%                             1875 (   0)    1929 (   1)    1983 (  34)
%%%                             1876 (   0)    1930 (   0)    1984 (  29)
%%%                             1877 (   0)    1931 (   1)    1985 (  31)
%%%                             1878 (   0)    1932 (   1)    1986 (  24)
%%%                             1879 (   0)    1933 (   0)    1987 (  38)
%%%                             1880 (   0)    1934 (   1)    1988 (  38)
%%%                             1881 (   1)    1935 (   0)    1989 (  41)
%%%                             1882 (   0)    1936 (   2)    1990 (  51)
%%%                             1883 (   0)    1937 (   0)    1991 (  56)
%%%                             1884 (   1)    1938 (   1)    1992 (  71)
%%%                             1885 (   0)    1939 (   0)    1993 (  46)
%%%                             1886 (   0)    1940 (   1)    1994 (  53)
%%%                             1887 (   0)    1941 (   1)    1995 (  44)
%%%                             1888 (   0)    1942 (   1)    1996 (  25)
%%%                             1889 (   0)    1943 (   2)    1997 (  47)
%%%                             1890 (   0)    1944 (   0)    1998 (  36)
%%%                             1891 (   0)    1945 (   1)    1999 (  25)
%%%                             1892 (   0)    1946 (   1)    2000 (  23)
%%%                             1893 (   0)    1947 (   2)    2001 (  33)
%%%                             1894 (   1)    1948 (   7)    2002 (   7)
%%%                             19xx (   9)
%%%
%%%                             Article:        899
%%%                             Book:           198
%%%                             InBook:           1
%%%                             InCollection:    22
%%%                             InProceedings:   98
%%%                             MastersThesis:    1
%%%                             Misc:             5
%%%                             PhdThesis:        8
%%%                             Proceedings:      3
%%%                             TechReport:      41
%%%                             Unpublished:     12
%%%
%%%                             Total entries: 1288
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%     }
%%% ====================================================================
%%%
%%% The URL (Uniform Resource Locator) of this file is
%%%
%%%   URL = "http://www.ma.man.ac.uk/~higham/asna/acc-stab-num-alg-2ed.bib"
%%%
%%% with an edited copy in the BibNet Project archive at
%%%
%%%    https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.*
%%%

@Preamble{
          "\def \noopsort#1{}"
        # "\def \l{\char32l}"
        # "\def \v#1{{\accent20 #1}} \let\^^_=\v"
        # "\def \hbk{hardback}"
        # "\def \pbk{paperback}"
        # "\ifx \undefined \mathrm  \let \mathrm  = \relax \fi"
        # "\ifx \undefined \textup  \let \textup  = \relax \fi"
        # "\ifx \undefined \upshape \let \upshape = \relax \fi"
}

%%% ====================================================================
%%% Journal abbreviations:

@String{j-ACM                   = "J. Assoc. Comput. Mach."}

@String{j-ACM-SIGSOFT           = "ACM Sigsoft"}

@String{j-ACTA-MATH             = "Acta Mathematica"}

@String{j-ACTA-NUMERICA         = "Acta Numerica"}

@String{j-AHC                   = "Annals of the History of Computing"}

@String{j-ALGORITHMICA          = "Algorithmica"}

@String{j-AM-J-MATH             = "American Journal of Mathematics"}

@String{j-AMER-STAT             = "The American Statistician"}

@String{j-AMM                   = "Amer. Math. Monthly"}

@String{j-ANAL-CHEM             = "Analytical Chemistry"}

@String{j-ANN-MATH-STAT         = "Annals of mathematical statistics"}

@String{j-ANN-NUM-MATH          = "Annals of Numerical Mathematics"}

@String{j-ANN-PROBAB            = "Annals of Probability"}

@String{j-ANN-STAT              = "Ann. Statist."}

@String{j-APP-MATH-COMP         = "Appl. Math. Comput."}

@String{j-APP-MATH-LETT         = "Applied Mathematics Letters"}

@String{j-APP-NUM-MATH          = "Appl. Numer. Math."}

@String{j-APPL-MATH-LETT        = "Applied Mathematics Letters"}

@String{j-APPROX                = "J. Approximation Theory"}

@String{j-ART-INTELL            = "Artificial Intelligence"}

@String{j-ASA                   = "J. Amer. Statist. Assoc."}

@String{j-ASTRON-J              = "Astronomical Journal"}

@String{j-Adv-Comp-Math         = "Adv. in Comput. Math."}

@String{j-BAMS                  = "Bull. Amer. Math. Soc."}

@String{j-BIOGRAPH-MEMOIRS-FELLOWS-ROY-SOC = "Biographical Memoirs of Fellows
                                  of the Royal Society"}

@String{j-BIT                   = "BIT"}

@String{j-BRITISH-J-CANCER      = "British Journal of Cancer"}

@String{j-BULL-AUSTRAL-MATH-SOC = "Bulletin of the Australian Mathematical
                                  Society"}

@String{j-BULL-GEODESIQUE       = "Bulletin G\'eod\'esique (Toulouse)"}

@String{j-BULL-LOND-MATH-SOC    = "Bulletin of the London Mathematical
                                  Society"}

@String{j-BYTE                  = "BYTE Magazine"}

@String{j-C-R-ACAD-SCI          = "Comptes Rendus de l'Acad{\'e}mie des
                                  Sciences"}

@String{j-CACM                  = "Comm. ACM"}

@String{j-CAN-MATH-BULL         = "Canadian mathematical bulletin = Bulletin
                                  canadien de math{\'e}matiques"}

@String{j-CELEST-MECH-DYN-ASTR  = "Celestial Mechanics and Dynamical
                                  Astronomy"}

@String{j-CMJ                   = "College Mathematics Journal"}

@String{j-COMP-J                = "Comput. J."}

@String{j-COMP-LANG-MAG         = "Computer Language Magazine"}

@String{j-COMP-MATH-APPL        = "Computers Math. Applic."}

@String{j-COMP-PHYS-COMM        = "Computer Physics Communications"}

@String{j-COMP-SURV             = "ACM Computing Surveys"}

@String{j-COMPUT-GRAPH-STAT     = "Journal of Computational and Graphical
                                  Statistics"}

@String{j-COMPUTER              = "Computer"}

@String{j-COMPUTING             = "Computing"}

@String{j-COMPUTING             = "Computing: Archiv f{\"u}r informatik und
                                  numerik"}

@String{j-CSE                   = "Computing in Science and Engineering"}

@String{j-DDJ                   = "Dr. Dobb's Journal of Software Tools"}

@String{j-DEMONSTRATIO-MATHEMATICA = "Demonstratio Mathematica"}

@String{j-DISCRETE-COMPUT-GEOM  = "Discrete and Computational Geometry"}

@String{j-DUKE-MATH-J           = "Duke Mathematical Journal"}

@String{j-EL                    = "Electronics Letters"}

@String{j-ELA                   = "The Electronic Journal of Linear Algebra"}

@String{j-ETNA                  = "Electron. Trans. Numer. Anal."}

@String{j-EUROMATH-BULL         = "Euromath Bulletin"}

@String{j-FOCM                  = "Found. Comput. Math."}

@String{j-HIST-MATH             = "Historia Mathematica"}

@String{j-IBM-JRD               = "IBM Journal of Research and Development"}

@String{j-IBM-SYS-J             = "IBM Systems Journal"}

@String{j-IEEE-AC               = "IEEE Trans. Automat. Control"}

@String{j-IEEE-AHC              = "IEEE Annals of the History of Computing"}

@String{j-IEEE-ASSP             = "IEEE Trans. Acoust., Speech, Signal
                                  Processing"}

@String{j-IEEE-C                = "IEEE Trans. Comput."}

@String{j-IEEE-MG               = "IEEE Trans. Magnetics"}

@String{j-IEEE-MICRO            = "IEEE Micro"}

@String{j-IEEE-PC               = "IEEE Trans. Prof. Commun."}

@String{j-IEEE-SE               = "IEEE Trans. Software Engrg."}

@String{j-IEEE-SP               = "IEEE Trans. Signal Processing"}

@String{j-IEEE-TRANS-AEROSP-ELECTRON-SYST = "IEEE Transactions on Aerospace
                                  and Electronic Systems"}

@String{j-IJC                   = "Internat. J. Control"}

@String{j-IJNME                 = "Internat. J. Numer. Methods Eng."}

@String{j-IJSA                  = "Internat. J. Supercomputer Appl."}

@String{j-IMA-BULL              = "IMA Bulletin"}

@String{j-IMAJNA                = "IMA J. Numer. Anal."}

@String{j-INFPL                 = "Inform. Process. Lett."}

@String{j-INT-J-HIGH-SPEED-COMPUTING = "International Journal of High Speed
                                  Computing"}

@String{j-INTEL-TECH-J          = "Intel Technology Journal"}

@String{j-J-ECON-LIT            = "Journal of economic literature"}

@String{j-J-INF-PROCESS         = "Journal of Information Processing"}

@String{j-J-INFO-PROC-CYBERNETICS-EIK = "Journal of Information Processing and
                                  Cybernetics: EIK"}

@String{j-J-MATH-ANAL-APPL      = "Journal of Mathematical Analysis and
                                  Applications"}

@String{j-J-RES-NATL-BUR-STAND-B = "Journal of Research of the National Bureau
                                  of Standards. Section B, Mathematics
                                  and Mathematical Physics"}

@String{j-J-SUPERCOMPUTING      = "The Journal of Supercomputing"}

@String{j-JAMS                  = "J. Amer. Math. Soc."}

@String{j-JCAM                  = "J. Comput. Appl. Math."}

@String{j-JCOMP-PHYS            = "J. Comput. Phys."}

@String{j-JIMA                  = "J. Inst. Maths. Applics."}

@String{j-JMAA                  = "J. Math. Anal. and Appl."}

@String{j-JNLAA                 = "Journal of Numerical Linear Algebra with
                                  Applications"}

@String{j-JOTA                  = "J. Optimization Theory and Applications"}

@String{j-JSV                   = "Journal of Sound and Vibration"}

@String{j-JUCS                  = "Journal of Universal Computer Science"}

@String{j-LAA                   = "Linear Algebra Appl."}

@String{j-LMA                   = "Linear and Multilinear Algebra"}

@String{j-MATH-COMP             = "Math. Comp."}

@String{j-MATH-CONTROL-SIGNALS-SYST = "Mathematics of control, signals, and
                                  systems: MCSS"}

@String{j-MATH-GAZ              = "Mathematical Gazette"}

@String{j-MATH-PROG             = "Math. Programming"}

@String{j-MATH-PROG-STUDY       = "Mathematical Programming Study"}

@String{j-MATH-REV              = "Mathematical Reviews"}

@String{j-MATH-SCAND            = "Mathematica Scandinavica"}

@String{j-MATH-STOS             = "Math. Stos."}

@String{j-MATH-TABLES-OTHER-AIDS-COMPUT = "Mathematical Tables and Other Aids
                                  to Computation"}

@String{j-MATH-TODAY            = "Mathematics Today"}

@String{j-MATHEMATICA-J         = "Mathematica Journal"}

@String{j-MATHWORKS-NEWSLETTER  = "The MathWorks Newsletter"}

@String{j-MTAC                  = "M.T.A.C."}

@String{j-NA-DIGEST             = "NA Digest"}

@String{j-NAMS                  = "Notices Amer. Math. Soc."}

@String{j-NEW-SCIENTIST         = "New Scientist"}

@String{j-NFAO                  = "Numerical Functional Analysis and
                                  Optimization"}

@String{j-NLAA                  = "Numerical Linear Algebra with Applications"}

@String{j-NUM-ALG               = "Numerical Algorithms"}

@String{j-NUM-LIN-ALG-APPL      = "Numerical Linear Algebra with Applications"}

@String{j-NUM-MATH              = "Numer. Math."}

@String{j-NY-TIMES              = "New York Times"}

@String{j-Nature                = "Nature"}

@String{j-PAC-J-MATH            = "Pacific Journal of Mathematics"}

@String{j-PAR-COMP              = "Parallel Comput."}

@String{j-PHIL-MAGAZINE         = "Philosophical Magazine"}

@String{j-PROC-AMER-PHIL-SOC    = "Proceedings of the {American Philosophical
                                  Society} held at {Philadelphia} for
                                  promoting useful knowledge"}

@String{j-PROC-AMS              = "Proc. Amer. Math. Soc."}

@String{j-PROC-CAMBRIDGE-PHIL-SOC = "Proceedings of the Cambridge
                                  Philosophical Society. Mathematical and
                                  physical sciences"}

@String{j-PROC-CONTROL-AUTOMATION = "Process Control and Automation"}

@String{j-PROC-IEEE             = "Proceedings of the IEEE"}

@String{j-PROC-LONDON-MATH-SOC-3 = "Proceedings of the London Mathematical
                                  Society. Third Series"}

@String{j-PROC-R-SOC-EDINB      = "Proceedings of the Royal Society of
                                  Edinburgh"}

@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI = "Proceedings of the Royal
                                  Society of London. Series A, Mathematical
                                  and physical sciences"}

@String{j-PSYCHO                = "Psychometrika"}

@String{j-QJMAM                 = "Quart. J. Mech. Appl. Math."}

@String{j-QUART-J-MATH          = "Quarterly Journal of Mathematics"}

@String{j-REE                   = "The Radio and Electronic Engineer"}

@String{j-SCI-AMER              = "Scientific American"}

@String{j-SCI-PROG              = "Scientific Programming"}

@String{j-SCIENCE               = "Science"}

@String{j-SCL                   = "Systems and Control Letters"}

@String{j-SIAD                  = "SIAM J. Alg. Discrete Methods"}

@String{j-SIAM                  = "J. Soc. Indust. Appl. Math."}

@String{j-SIAM-J-DISCR-MATH     = "SIAM Journal on Discrete Mathematics"}

@String{j-SIAM-NEWS             = "SIAM News"}

@String{j-SIAMA                 = "SIAM J. Appl. Math."}

@String{j-SICOMP                = "SIAM J. Comput."}

@String{j-SICOPT                = "SIAM J. Control Optim."}

@String{j-SIDM                  = "SIAM J. Disc. Math."}

@String{j-SIGNUM                = "ACM SIGNUM Newsletter"}

@String{j-SIGPLAN               = "ACM SIG{\-}PLAN Notices"}

@String{j-SIMA                  = "SIAM J. Math. Anal."}

@String{j-SIMAX                 = "SIAM J. Matrix Anal. Appl."}

@String{j-SINUM                 = "SIAM J. Numer. Anal."}

@String{j-SIOPT                 = "SIAM J. Optim."}

@String{j-SIREV                 = "SIAM Rev."}

@String{j-SISC                  = "SIAM J. Sci. Comput."}

@String{j-SISSC                 = "SIAM J. Sci. Statist. Comput."}

@String{j-SOVIET-PHYS-DOKL      = "Soviet Physics---Doklady"}

@String{j-SPE                   = "Soft{\-}ware\emdash Prac{\-}tice and
                                  Experience"}

@String{j-STUDIES-APPL-MATH     = "Studies in Applied Mathematics"}

@String{j-TOMS                  = "ACM Trans. Math. Software"}

@String{j-TOPLAS                = "ACM Transactions on Programming Languages
                                  and Systems"}

@String{j-TPLS                  = "ACM Trans. Program. Lang. Syst."}

@String{j-TRANS-AMER-INST-ELEC-ENG = "Transactions of the American Institute
                                  of Electrical Engineers"}

@String{j-USSR-COMP-MATH-MATH-PHYS = "U.S.S.R. Computational Mathematics and
                                  Mathematical Physics"}

@String{j-WALL-ST-J             = "Wall Street Journal"}

@String{j-ZAMM                  = "Z. Angew. Math. Mech."}

@String{j-ZAMP                  = "Z. Angew. Math. Phys."}

%%% ====================================================================
%%% Type abbreviations:

@String{t-NAREP                 = "Numerical Analysis Report"}

%%% ====================================================================
%%% Departments/Institutions and their addresses:

@String{inst-ATT                = "AT\&T Bell Laboratories"}

@String{inst-ATT:adr            = "Murray Hill, NJ, USA"}

@String{inst-Bell               = "Bell Laboratories"}

@String{inst-Belladr            = "Murray Hill, NJ, USA"}

@String{inst-Berkeley           = "University of California"}

@String{inst-Berkeley-CS        = "Department of Computer Science, University
                                  of California"}

@String{inst-Berkeley-Math      = "Department of Mathematics, University of
                                  California"}

@String{inst-Berkeley:adr       = "Berkeley, CA, USA"}

@String{inst-CERFACS            = "CERFACS"}

@String{inst-CERFACS:adr        = "Toulouse, France"}

@String{inst-CS-Lucent          = "Computing Sciences Research Center, Bell
                                  Laboratories"}

@String{inst-CS-Lucent:adr      = "Murray Hill, NJ"}

@String{inst-CS-U-KY            = "Department of Mathematics, University of
                                  Kentucky"}

@String{inst-CS-U-KY:adr        = "Lexington, KY, USA"}

@String{inst-CS-U-MARYLAND      = "Department of Computer Science, University
                                  of Maryland"}

@String{inst-CS-U-MARYLAND:adr  = "College Park, MD, USA"}

@String{inst-CS-U-STANFORD      = "Department of Computer Science, Stanford
                                  University"}

@String{inst-CS-U-Tenn          = "Department of Computer Science, University
                                  of Tennessee"}

@String{inst-CS-U-Tenn:adr      = "Knoxville, TN, USA"}

@String{inst-CS-U-Umea          = "Institute of Information Processing,
                                  University of Ume{\aa}"}

@String{inst-CS-U-Umea:adr      = "Ume{\aa}, Sweden"}

@String{inst-Cornell            = "Cornell University"}

@String{inst-Cornell:adr        = "Ithaca, NY, USA"}

@String{inst-DAMTP              = "Department of Applied Mathematics and
                                  Theoretical Physics, University of
                                  Cambridge"}

@String{inst-DAMTP:adr          = "Cambridge, UK"}

%%% L'Institut National Polytechnique De Toulouse, D\'{e}partment Informatique N7 - IRIT
@String{inst-ENSEEIHT           = "Dept. Informatique et Maths Appls.,
                                  ENSEEIHT-IRIT"}

@String{inst-ENSEEIHT:adr       = "31071 Toulouse Cedex, France"}

@String{inst-HARWELL            = "{AERE} {Harwell} Laboratory"}

@String{inst-HARWELL:adr        = "Chilton, Oxon, England"}

@String{inst-IAN                = "Istituto di Analisi Numerica del CNR"}

@String{inst-IAN:adr            = "Pavia, Italy"}

@String{inst-IMA                = "Institute for Mathematics and Its
                                  Applications, University of Minnesota"}

@String{inst-IMA-UK             = "The Institute of Mathematics and Its
                                  Applications"}

@String{inst-IMA-UK:adr         = "Southend-On-Sea, Essex, UK"}

@String{inst-IMA:adr            = "Minneapolis, MN, USA"}

@String{inst-M-Utrecht          = "Department of Mathematics, Utrecht
                                  University"}

@String{inst-M-Utrecht:adr      = "Utrecht, Netherlands"}

@String{inst-MCCM               = "Manchester Centre for Computational
                                  Mathematics"}

@String{inst-MCCM:adr           = "Manchester, England"}

%%% Numerical Analysis Reports: ISSN 1360-1725

@String{inst-MCS-Argonne        = "Mathematics and Computer Science Division,
                                  Argonne National Laboratory"}

@String{inst-MCS-Argonne:adr    = "Argonne, IL, USA"}

@String{inst-Math-U-Strath      = "Department of Mathematics, University of
                                  Strathclyde"}

@String{inst-Math-U-Strath:adr  = "Glasgow, Scotland"}

@String{inst-Math-UCLA          = "Department of Mathematics, University of
                                  California"}

@String{inst-Math-UCLA:adr      = "Los Angeles, USA"}

@String{inst-Math-UCSD          = "Department of Mathematics, University of
                                  California"}

@String{inst-Math-UCSD:adr      = "San Diego, USA"}

@String{inst-NAG                = "NAG Ltd."}

@String{inst-NAG:adr            = "Oxford, UK"}

@String{inst-NASA-Ames          = "NASA Ames Research Center"}

@String{inst-NASA-Ames:adr      = "Moffett Field, CA, USA"}

@String{inst-NPL                = "National Physical Laboratory"}

@String{inst-NPL:adr            = "Teddington, UK"}

@String{inst-OR-U-STANFORD      = "Department of Operations Research, Stanford
                                  University"}

@String{inst-ORNL               = "Oak Ridge National Laboratory"}

@String{inst-ORNL:adr           = "Oak Ridge, TN, USA"}

@String{inst-OUCL               = "Numerical Analysis Group, Oxford University
                                  Computing Laboratory"}

@String{inst-OUCL:adr           = "Oxford, UK"}

@String{inst-RAL                = "Atlas Centre, Rutherford Appleton
                                  Laboratory"}

@String{inst-RAL:adr            = "Didcot, Oxon, UK"}

@String{inst-RICE-CAM           = "Department of Computational and Applied
                                  Mathematics"}

@String{inst-RICE-CAM:adr       = "Rice University, Houston, TX, USA"}

@String{inst-TU-Chemnitz        = "Fak. f. Mathematik, Technische
                                  Universit{\"a}t Chemnitz-Zwickau"}

@String{inst-TU-Chemnitz:adr    = "Chemnitz, FRG"}

@String{inst-U-Bremen-ZT        = "Zentrum f{\"u}r Technomathematik,
                                  Universit{\"a}t Bremen"}

@String{inst-U-Bremen-ZT:adr    = "Bremen, Germany"}

@String{inst-U-Dundee           = "Department of Mathematics and Computer
                                  Science, University of Dundee"}

@String{inst-U-Dundee:adr       = "Dundee, Scotland"}

@String{inst-U-Manchester       = "University of Manchester"}

@String{inst-U-Manchester:adr   = "Manchester, England"}

@String{inst-U-STANFORD:adr     = "Stanford, CA, USA"}

%%% ====================================================================
%%% Publishers and their addresses:

@String{pub-ACADEMIC            = "Academic Press"}
@String{pub-ACADEMIC:adr        = "New York, NY, USA"}

@String{pub-ACM                 = "ACM Press"}
@String{pub-ACM:adr             = "New York"}

@String{pub-ADAM-HILGER         = "Adam Hilger Ltd."}
@String{pub-ADAM-HILGER:adr     = "Bristol, UK"}

@String{pub-AMS                 = "American Mathematical Society"}
@String{pub-AMS:adr             = "Providence, RI, USA"}

@String{pub-AP                  = "Academic Press"}
@String{pub-AP:adr-B            = "Boston, MA, USA"}
@String{pub-AP:adr-L            = "London"}
@String{pub-AP:adr-NY           = "New York"}
@String{pub-AP:adr-S            = "San Diego, CA, USA"}

@String{pub-AW                  = "Ad{\-d}i{\-s}on-Wes{\-l}ey"}
%%% @String{pub-AW:adr              = "Reading, Massachusetts"}
@String{pub-AW:adr              = "Reading, MA, USA"}

@String{pub-AWLongman           = "Addison Wesley Longman"}
@String{pub-AWLongman:adr       = "Harlow, Essex, UK"}

@String{pub-BH                  = "Birkh{\"{a}}user"}
@String{pub-BH:adr              = "Boston, MA, USA"}
@String{pub-BH:adr-Basel        = "Basel, Switzerland"}

@String{pub-Blaisdell           = "Blaisdell"}
@String{pub-Blaisdell:adr-MA    = "Waltham, MA, USA"}
@String{pub-Blaisdell:adr-NY    = "New York"}

@String{pub-BrooksCole          = "Brooks/Cole"}
@String{pub-BrooksCole:adr      = "Pacific Grove, CA, USA"}

@String{pub-CH                  = "Chapman and Hall"}
@String{pub-CH:adr-L            = "London"}
@String{pub-CH:adr-NY           = "New York"}

@String{pub-CHCRC               = "Chapman and Hall/CRC"}

@String{pub-CLARENDON           = "Clarendon Press"}
@String{pub-CLARENDON:adr       = "Oxford, UK"}

@String{pub-CRC                 = "CRC Press"}
@String{pub-CRC:adr             = "Boca Raton, FL, USA"}

@String{pub-CUP                 = "Cambridge University Press"}
@String{pub-CUP:adr             = "Cambridge, UK"}

@String{pub-DCH                 = "D. C. Heath"}
@String{pub-DCH:adr             = "Lexington, MA, USA"}

@String{pub-DEKKER              = "Marcel Dekker, Inc."}
@String{pub-DEKKER:adr          = "New York, NY, USA"}

@String{pub-Dover               = "Dover"}
@String{pub-Dover:adr           = "New York"}

@String{pub-EH                  = "Ellis Horwood"}
@String{pub-EH:adr              = "New York"}

@String{pub-ELS                 = "Elsevier"}
@String{pub-ELS:adr             = "Amsterdam, The Netherlands"}

@String{pub-ELSNH               = "Elsevier/North-Hol{\-}land"}
@String{pub-ELSNH:adr           = "Amsterdam, The Netherlands"}

@String{pub-Freeman             = "W. H. Freeman"}
@String{pub-Freeman:adr         = "New York"}

@String{pub-Gruyter             = "Walter de Gruyter"}
@String{pub-Gruyter:adr         = "Berlin"}

@String{pub-HMSO                = "Her Majesty's Stationary Office"}
@String{pub-HMSO:adr            = "London"}

@String{pub-HRW                 = "Holt, Rinehart and Winston"}
@String{pub-HRW:adr             = "New York"}

@String{pub-Harvard             = "Harvard University Press"}
@String{pub-Harvard:adr         = "Cambridge, MA, USA"}

@String{pub-IEC                 = "International Electrotechnical Commission"}
@String{pub-IEC:adr             = "Geneva, Switzerland"}

@String{pub-JH                  = "Johns Hopkins University Press"}
@String{pub-JH:adr              = "Baltimore, MD, USA"}

@String{pub-JOHNS-HOPKINS       = "The Johns Hopkins University Press"}
@String{pub-JOHNS-HOPKINS:adr   = "Baltimore, MD, USA"}

@String{pub-Kluwer              = "Kluwer Academic Publishers"}
@String{pub-Kluwer:adr          = "Dordrecht, The Netherlands"}
@String{pub-Kluwer:adr-NY       = "New York"}

@String{pub-Longman-ST          = "Longman Scientific and Technical"}
@String{pub-Longman-ST:adr      = "Essex, UK"}

@String{pub-MAA                 = "Mathematical Association of America"}
@String{pub-MAA:adr             = "Washington, D.C."}

@String{pub-MD                  = "Marcel Dekker"}
@String{pub-MD:adr              = "New York"}

@String{pub-MH                  = "Mc{\-}Graw-Hill"}
@String{pub-MH:adr              = "New York"}

@String{pub-MIT                 = "MIT Press"}
@String{pub-MIT:adr             = "Cambridge, MA, USA"}

@String{pub-NH                  = "North-Hol{\-}land"}
@String{pub-NH:adr              = "Amsterdam, The Netherlands"}

@String{pub-OUP                 = "Oxford University Press"}
@String{pub-OUP:adr-NY          = "New York"}

@String{pub-PH                  = "Pren{\-}tice-Hall"}

@String{pub-PUP                 = "Princeton University Press"}
@String{pub-PUP:adr             = "Princeton, NJ, USA"}

@String{pub-Penguin             = "Penguin"}
@String{pub-Penguin:adr-H       = "Harmondsworth, UK"}
@String{pub-Penguin:adr-L       = "London"}
@String{pub-Penguin:adr-NY      = "New York"}

@String{pub-Peters              = "A K Peters"}
@String{pub-Peters:adr          = "Wellesley, Massachusetts"}

@String{pub-Plenum              = "Plenum Press"}
@String{pub-Plenum:adr          = "New York"}
%%% @String{pub-PH:adr              = "Englewood Cliffs, NJ 07632, USA"}
@String{pub-PH2:adr             = "Upper Saddle River, NJ, USA"}
@String{pub-PH:adr              = "Englewood Cliffs, NJ, USA"}

@String{pub-PHI                 = "Pren{\-}tice-Hall International"}
@String{pub-PHI:adr             = "Englewood Cliffs, NJ, USA"}

@String{pub-SIAM                = "Society for Industrial and Applied
                                  Mathematics"}
@String{pub-SIAM:adr            = "Philadelphia, PA, USA"}

@String{pub-Springer            = "Spring{\-}er-Ver{\-}lag"}
@String{pub-Springer:adr-B      = "Berlin"}
@String{pub-Springer:adr-NY     = "New York"}

@String{pub-SV                  = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg,
                                  Germany~/ London, UK~/ etc."}

@String{pub-WS                  = "World Scientific"}
@String{pub-WS:adr              = "Singapore"}

@String{pub-Wellesley           = "Wellesley-Cambridge Press"}
@String{pub-Wellesley:adr       = "Wellesley, MA, USA"}

@String{pub-Wiley               = "Wiley"}
@String{pub-Wiley:adr           = "New York"}
@String{pub-Wiley:adr-C         = "Chichester, UK"}

@String{pub-reidel              = "D. Reidel"}
@String{pub-reidel:adr          = "Dordrecht, Holland"}

%%% ====================================================================
%%% Bibliography entries, sorted by label:

@Article{Aasen:1971:RSM,
  author =       "Jan Ole Aasen",
  title =        "On the Reduction of a Symmetric Matrix to Tridiagonal
                 Form",
  journal =      j-BIT,
  volume =       "11",
  pages =        "233--242",
  year =         "1971",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Alpert:1993:WLB,
  author =       "B. Alpert and G. Beylkin and R. Coifman and V.
                 Rokhlin",
  title =        "Wavelet-Like Bases for the Fast Solution of
                 Second-Kind Integral Equations",
  journal =      j-SISC,
  volume =       "14",
  number =       "1",
  pages =        "159--184",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Anderson:1992:GQF,
  author =       "E. Anderson and Z. Bai and J. Dongarra",
  title =        "Generalized {QR} Factorization and Its Applications",
  journal =      j-LAA,
  volume =       "162--164",
  pages =        "243--271",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Abdelmalek:1971:REA,
  author =       "Nabih N. Abdelmalek",
  title =        "Round Off Error Analysis for {Gram--Schmidt} Method
                 and Solution of Linear Least Squares Problems",
  journal =      j-BIT,
  volume =       "11",
  pages =        "345--368",
  year =         "1971",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Ahac:1988:SFM,
  author =       "Alan A. Ahac and John J. Buoni and D. D. Olesky",
  title =        "Stable {$LU$} Factorization of {$H$}-Matrices",
  journal =      j-LAA,
  volume =       "99",
  pages =        "97--110",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{acm87,
  key =          "ACM Press",
  title =        "{ACM Turing} Award Lectures: {The} First Twenty Years,
                 1966--1985",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xviii + 483",
  year =         "1987",
  ISBN =         "0-201-54885-2",
  ISBN-13 =      "978-0-201-54885-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Acton:1970:NMW,
  author =       "Forman S. Acton",
  title =        "Numerical Methods That Work",
  publisher =    "Harper and Row",
  address =      "New York",
  pages =        "xviii + 541",
  year =         "1970",
  ISBN =         "0-88385-450-3",
  ISBN-13 =      "978-0-88385-450-1",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted by Mathematical Association of America,
                 Washington, D.C., with new preface and additional
                 problems, 1990",
}

@Book{Acton:1996:RCM,
  author =       "Forman S. Acton",
  title =        "Real Computing Made Real: {Preventing} Errors in
                 Scientific and Engineering Calculations",
  publisher =    pub-PUP,
  address =      pub-PUP:adr,
  pages =        "xv + 259",
  year =         "1996",
  ISBN =         "0-691-03663-2",
  ISBN-13 =      "978-0-691-03663-2",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Adams:1967:SCP,
  author =       "Duane A. Adams",
  title =        "A Stopping Criterion for Polynomial Root Finding",
  journal =      j-CACM,
  volume =       "10",
  number =       "10",
  pages =        "655--658",
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Arioli:1989:SSL,
  author =       "M. Arioli and J. W. Demmel and I. S. Duff",
  title =        "Solving Sparse Linear Systems with Sparse Backward
                 Error",
  journal =      j-SIMAX,
  volume =       "10",
  number =       "2",
  pages =        "165--190",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Arioli:1989:ASA,
  author =       "M. Arioli and I. S. Duff and P. P. M. de Rijk",
  title =        "On the Augmented System Approach to Sparse
                 Least-Squares Problems",
  journal =      j-NUM-MATH,
  volume =       "55",
  pages =        "667--684",
  year =         "1989",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Arioli:1992:SCI,
  author =       "Mario Arioli and Iain S. Duff and Daniel Ruiz",
  title =        "Stopping Criteria for Iterative Solvers",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "138--144",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Almacany:1984:DCA,
  author =       "M. Almacany and C. B. Dunham and J. Williams",
  title =        "Discrete {Chebyshev} Approximation by Interpolating
                 Rationals",
  journal =      j-IMAJNA,
  volume =       "4",
  pages =        "467--477",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Aggarwal:1979:REM,
  author =       "Vijay B. Aggarwal and James W. Burgmeier",
  title =        "A Round-Off Error Model With Applications to
                 Arithmetic Expressions",
  journal =      j-SICOMP,
  volume =       "8",
  number =       "1",
  pages =        "60--72",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ashcraft:1998:ASI,
  author =       "Cleve Ashcraft and Roger G. Grimes and John G. Lewis",
  title =        "Accurate Symmetric Indefinite Linear Equation
                 Solvers",
  journal =      j-SIMAX,
  volume =       "20",
  number =       "2",
  pages =        "513--561",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Alonso:1997:BEA,
  author =       "P. Alonso and M. Gasca and J. M. Pe{\~n}a",
  title =        "Backward Error Analysis of {Neville} Elimination",
  journal =      j-APP-NUM-MATH,
  volume =       "23",
  pages =        "193--204",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ahlberg:1963:CPS,
  author =       "J. H. Ahlberg and E. N. Nilson",
  title =        "Convergence Properties of the Spline Fit",
  journal =      j-SIAM,
  volume =       "11",
  number =       "1",
  pages =        "95--104",
  year =         "1963",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InCollection{Ewing:1991:PHP,
  editor =       "John H. Ewing and F. W. Gehring",
  key =          "Albers, Donald J.",
  booktitle =    "{Paul Halmos}: {Celebrating} 50 Years of Mathematics",
  title =        "{Paul Halmos} By Parts (Interviews by {Donald J.
                 Albers})",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "3--32",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Alefeld:1983:IIC,
  author =       "G{\"o}ltz Alefeld and J{\"u}rgen Herzberger",
  title =        "Introduction to Interval Computations",
  publisher =    pub-AP,
  address =      pub-AP:adr-NY,
  pages =        "xviii + 333",
  year =         "1983",
  ISBN =         "0-12-049820-0",
  ISBN-13 =      "978-0-12-049820-8",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Althoen:1987:GJR,
  author =       "Steven C. Althoen and Renate Mclaughlin",
  title =        "{Gauss--Jordan} Reduction: {A} Brief History",
  journal =      j-AMM,
  volume =       "94",
  number =       "2",
  pages =        "130--142",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Alt:1981:CBC,
  author =       "H. Alt and J. van Leeuwen",
  title =        "The Complexity of Basic Complex Operations",
  journal =      j-COMPUTING,
  volume =       "27",
  pages =        "205--215",
  year =         "1981",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Amodio:1994:BEA,
  author =       "Pierluigi Amodio and Francesca Mazzia",
  title =        "Backward Error Analysis of Cyclic Reduction for the
                 Solution of Tridiagonal Systems",
  journal =      j-MATH-COMP,
  volume =       "62",
  number =       "206",
  pages =        "601--617",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Anderson:1971:SAT,
  author =       "T. W. Anderson",
  title =        "The Statistical Analysis of Time Series",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  pages =        "xiv + 704",
  year =         "1971",
  ISBN =         "0-471-02900-9",
  ISBN-13 =      "978-0-471-02900-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Anderson:1991:RTS,
  author =       "Edward Anderson",
  title =        "Robust Triangular Solves for Use in Condition
                 Estimation",
  type =         "Technical Report",
  number =       "CS-91-142",
  institution =  inst-CS-U-Tenn,
  address =      inst-CS-U-Tenn:adr,
  pages =        "35",
  month =        aug,
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "LAPACK Working Note 36",
}

@Article{Anderson:1999:DAF,
  author =       "I. J. Anderson",
  title =        "A Distillation Algorithm for Floating-Point
                 Summation",
  journal =      j-SISC,
  volume =       "20",
  number =       "5",
  pages =        "1797--1806",
  year =         "1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ando:1987:TPM,
  author =       "T. Ando",
  title =        "Totally Positive Matrices",
  journal =      j-LAA,
  volume =       "90",
  pages =        "165--219",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Andrew:1990:ESV,
  author =       "Alan L. Andrew",
  title =        "Eigenvalues and Singular Values of Certain Random
                 Matrices",
  journal =      j-JCAM,
  volume =       "30",
  pages =        "165--171",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Anonymous:1922:CC,
  author =       "Anonymous",
  title =        "Le {Commandant Cholesky}",
  journal =      j-BULL-GEODESIQUE,
  pages =        "159--161",
  year =         "1922",
  CODEN =        "BGDQAG",
  ISSN =         "0007-4632",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Translation by Richard W. Cottle (``Major
                 {Cholesky}'') appears in
                 \cite[Appendix]{Maindonald:1984:SC} and in NA Digest,
                 Volume 90, Issue 7, 1990",
  fjournal =     "Bulletin G\'eod\'esique (Toulouse)",
  journal-URL =  "http://link.springer.com/journal/190",
}

@Article{Anda:1994:FPR,
  author =       "Andrew A. Anda and Haesun Park",
  title =        "Fast Plane Rotations with Dynamic Scaling",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "1",
  pages =        "162--174",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Anderson:1987:GRO,
  author =       "T. W. Anderson and I. Olkin and L. G. Underhill",
  title =        "Generation of Random Orthogonal Matrices",
  journal =      j-SISSC,
  volume =       "8",
  number =       "4",
  pages =        "625--629",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Computer:1988:ANM,
  author =       "Apple Computer",
  title =        "Apple Numerics Manual",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Computer:1994:IMP,
  author =       "Apple Computer",
  title =        "Inside {Macintosh}: {PowerPC} Numerics",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  year =         "1994",
  ISBN =         "0-201-40728-0",
  ISBN-13 =      "978-0-201-40728-0",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InCollection{Alvarado:1993:HPS,
  author =       "Fernando L. Alvarado and Alex Pothen and Robert S.
                 Schreiber",
  editor =       "J. Alan George and John R. Gilbert and Joseph W. H.
                 Liu",
  booktitle =    "Graph Theory and Sparse Matrix Computations",
  title =        "Highly Parallel Sparse Triangular Solution",
  volume =       "56",
  publisher =    pub-Springer # ", " # pub-Springer:adr-NY,
  pages =        "141--158",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "IMA Volumes in Mathematics and Its Applications",
}

@TechReport{Arioli:2000:SCC,
  author =       "Mario Arioli",
  title =        "A Stopping Criterion for the Conjugate Gradient
                 Algorithm in a Finite Element Method Framework",
  type =         "Technical Report",
  number =       "1179",
  institution =  "Istituto di Analisi Numerica - C.N.R.",
  address =      "Pavia, Italy",
  pages =        "12",
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Arnold:1984:GEA,
  author =       "William F. Arnold and Alan J. Laub",
  title =        "Generalized Eigenproblem Algorithms and Software for
                 Algebraic {Riccati} Equations",
  journal =      j-PROC-IEEE,
  volume =       "72",
  number =       "12",
  pages =        "1746--1754",
  year =         "1984",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}

@Article{Arioli:1985:EAA,
  author =       "M. Arioli and A. Laratta",
  title =        "Error Analysis of an Algorithm for Solving an
                 Underdetermined Linear System",
  journal =      j-NUM-MATH,
  volume =       "46",
  pages =        "255--268",
  year =         "1985",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Arioli:1986:EAA,
  author =       "M. Arioli and A. Laratta",
  title =        "Error Analysis of Algorithms for Computing the
                 Projection of a Point onto a Linear Manifold",
  journal =      j-LAA,
  volume =       "82",
  pages =        "1--26",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Arioli:1992:SCC,
  author =       "Mario Arioli and Francesco Romani",
  title =        "Stability, Convergence, and Conditioning of Stationary
                 Iterative Methods of the Form {$x^{(i+1)} = P x^{(i)} +
                 q$} for the Solution of Linear Systems",
  journal =      j-IMAJNA,
  volume =       "12",
  pages =        "21--30",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ashenhurst:1965:EEC,
  author =       "R. L. Ashenhurst and N. Metropolis",
  title =        "Error Estimation in Computer Calculation",
  journal =      j-AMM,
  volume =       "72",
  number =       "2",
  pages =        "47--58",
  year =         "1965",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  part =         "II",
}

@Article{Asplund:1959:IMW,
  author =       "Edgar Asplund",
  title =        "Inverses of Matrices {$\{a_{ij}\}$} Which Satisfy
                 {$a_{ij}=0$} For {$j>i+p$}",
  journal =      j-MATH-SCAND,
  volume =       "7",
  pages =        "57--60",
  year =         "1959",
  CODEN =        "MTSCAN",
  ISSN =         "0025-5521 (print), 1903-1807 (electronic)",
  ISSN-L =       "0025-5521",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Mathematica Scandinavica",
}

@Misc{Atanasoff:1940:CMS,
  author =       "John V. Atanasoff",
  title =        "Computing Machine for the Solution of Large Systems of
                 Linear Algebraic Equations",
  howpublished = "Unpublished manuscript, Iowa State College, Ames, IA,
                 USA",
  month =        aug,
  year =         "1940",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted in \cite[pp.~315--335]{Randell:1975:ODC}",
}

@Book{Axelsson:1994:ISM,
  author =       "Owe Axelsson",
  title =        "Iterative Solution Methods",
  publisher =    pub-CUP,
  pages =        "xiii + 654",
  year =         "1994",
  ISBN =         "0-521-44524-8",
  ISBN-13 =      "978-0-521-44524-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Barlow:1985:RED,
  author =       "Jesse L. Barlow and E. H. Bareiss",
  title =        "On Roundoff Error Distributions in Floating Point and
                 Logarithmic Arithmetic",
  journal =      j-COMPUTING,
  volume =       "34",
  pages =        "325--347",
  year =         "1985",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Barlow:1985:PEA,
  author =       "Jesse L. Barlow and E. H. Bareiss",
  title =        "Probabilistic Error Analysis of {Gaussian} Elimination
                 in Floating Point and Logarithmic Arithmetic",
  journal =      j-COMPUTING,
  volume =       "34",
  pages =        "349--364",
  year =         "1985",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@InProceedings{Babuska:1969:NSM,
  author =       "Ivo Babu{\v{s}}ka",
  booktitle =    "Proc. IFIP Congress",
  title =        "Numerical Stability in Mathematical Analysis",
  publisher =    pub-NH # ", " # pub-NH:adr,
  pages =        "11--23",
  year =         "1969",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Information Processing 68",
}

@Article{Bai:1993:SDB,
  author =       "Zhaojun Bai and James W. Demmel",
  title =        "On Swapping Diagonal Blocks in Real {Schur} Form",
  journal =      j-LAA,
  volume =       "186",
  pages =        "73--95",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bai:1993:CGS,
  author =       "Zhaojun Bai and James W. Demmel",
  title =        "Computing the Generalized Singular Value
                 Decomposition",
  journal =      j-SISC,
  volume =       "14",
  number =       "6",
  pages =        "1464--1486",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Bailey:1988:SNA,
  author =       "D. H. Bailey and H. R. P. Ferguson",
  booktitle =    "Proceedings of Supercomputing '88",
  title =        "A {Strassen--Newton} Algorithm for High-Speed
                 Parallelizable Matrix Inversion",
  publisher =    "IEEE Computer Society Press, New York",
  pages =        "419--424",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Barwell:1976:CAS,
  author =       "Victor Barwell and Alan George",
  title =        "A Comparison of Algorithms for Solving Symmetric
                 Indefinite Systems of Linear Equations",
  journal =      j-TOMS,
  volume =       "2",
  number =       "3",
  pages =        "242--251",
  year =         "1976",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Bartels:1992:SSV,
  author =       "Sven G. Bartels and Desmond J. Higham",
  title =        "The Structured Sensitivity of {Vandermonde}-like
                 Systems",
  journal =      j-NUM-MATH,
  volume =       "62",
  pages =        "17--33",
  year =         "1992",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Bailey:1988:EHS,
  author =       "David H. Bailey",
  title =        "Extra High Speed Matrix Multiplication on the
                 {Cray}-2",
  journal =      j-SISSC,
  volume =       "9",
  number =       "3",
  pages =        "603--607",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bailey:1988:CDD,
  author =       "David H. Bailey",
  title =        "The Computation of {$\pi$} to 29,360,000 Decimal
                 Digits Using {Borweins'} Quartically Convergent
                 Algorithm",
  journal =      j-MATH-COMP,
  volume =       "50",
  number =       "181",
  pages =        "283--296",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bailey:1993:AMT,
  author =       "David H. Bailey",
  title =        "Algorithm 719: {Multiprecision} Translation and
                 Execution of {FORTRAN} Programs",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "288--319",
  year =         "1993",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Bailey:1995:FBM,
  author =       "David H. Bailey",
  title =        "A {Fortran} 90-Based Multiprecision System",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "379--387",
  year =         "1995",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Barlow:1987:SGR,
  author =       "Jesse L. Barlow and Ilse C. F. Ipsen",
  title =        "Scaled {Givens} Rotations for the Solution of Linear
                 Least Squares Problems on Systolic Arrays",
  journal =      j-SISSC,
  volume =       "8",
  number =       "5",
  pages =        "716--733",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Baksalary:1979:ME,
  author =       "J. K. Baksalary and R. Kala",
  title =        "The Matrix Equation {$AX-YB=C$}",
  journal =      j-LAA,
  volume =       "25",
  pages =        "41--43",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Baksalary:1980:ME,
  author =       "J. K. Baksalary and R. Kala",
  title =        "The Matrix Equation {$AXB + CYD = E$}",
  journal =      j-LAA,
  volume =       "30",
  pages =        "141--147",
  year =         "1980",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ballester:1967:CDA,
  author =       "C. Ballester and V. Pereyra",
  title =        "On the Construction of Discrete Approximations to
                 Linear Differential Expressions",
  journal =      j-MATH-COMP,
  volume =       "21",
  pages =        "297--302",
  year =         "1967",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Bard:1974:NPE,
  author =       "Yonathan Bard",
  title =        "Nonlinear Parameter Estimation",
  publisher =    pub-AP,
  address =      pub-AP:adr-NY,
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InCollection{Bauer:1971:IPD,
  author =       "F. L. Bauer and C. Reinsch",
  editor =       "J. H. Wilkinson and C. Reinsch",
  booktitle =    "Linear Algebra",
  title =        "Inversion of Positive Definite Matrices by the
                 {Gauss--Jordan} Method",
  volume =       "II",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "45--49",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Contribution I/3",
  series =       "Handbook for Automatic Computation",
  mycrossref =   "Wilkinson:1971:LA",
}

@PhdThesis{Barlow:1981:PEA,
  author =       "Jesse L. Barlow",
  title =        "Probabilistic Error Analysis of Floating Point and
                 {CRD} Arithmetics",
  school =       "Northwestern University",
  address =      "Evanston, IL, USA",
  month =        jun,
  year =         "1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Barlow:1981:DAR,
  author =       "Jesse L. Barlow",
  booktitle =    "Proc. 5th IEEE Symposium on Computer Arithmetic, Ann
                 Arbor, Michigan",
  title =        "On the Distribution of Accumulated Roundoff Error in
                 Floating Point Arithmetic",
  pages =        "100--105",
  year =         "1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{barl86,
  author =       "Jesse L. Barlow",
  title =        "A Note on Monitoring the Stability of Triangular
                 Decomposition of Sparse Matrices",
  journal =      j-SISSC,
  volume =       "7",
  number =       "1",
  pages =        "166--168",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Barlow:1988:EAI,
  author =       "Jesse L. Barlow",
  title =        "Error Analysis and Implementation Aspects of Deferred
                 Correction for Equality Constrained Least Squares
                 Problems",
  journal =      j-SINUM,
  volume =       "25",
  number =       "6",
  pages =        "1340--1358",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Barlow:1991:EAP,
  author =       "Jesse L. Barlow",
  title =        "Error Analysis of a Pairwise Summation Algorithm to
                 Compute the Sample Variance",
  journal =      j-NUM-MATH,
  volume =       "58",
  pages =        "583--590",
  year =         "1991",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Bank:1977:MAE,
  author =       "Randolph E. Bank and Donald J. Rose",
  title =        "Marching Algorithms for Elliptic Boundary Value
                 Problems. {I}: The Constant Coefficient Case",
  journal =      j-SINUM,
  volume =       "14",
  number =       "5",
  pages =        "792--829",
  year =         "1977",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Barrett:1989:FMA,
  author =       "Geoff Barrett",
  title =        "Formal Methods Applied to a Floating-Point Number
                 System",
  journal =      j-IEEE-SE,
  volume =       "15",
  number =       "5",
  pages =        "611--621",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Barrlund:1991:PBD,
  author =       "Anders Barrlund",
  title =        "Perturbation Bounds for the {$LDL^H$} and {$LU$}
                 Decompositions",
  journal =      j-BIT,
  volume =       "31",
  pages =        "358--363",
  year =         "1991",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Barrlund:1994:PBG,
  author =       "Anders Barrlund",
  title =        "Perturbation Bounds for the Generalized {$QR$}
                 Factorization",
  journal =      j-LAA,
  volume =       "207",
  pages =        "251--271",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@MastersThesis{Bartels:1991:TTM,
  author =       "Sven G. Bartels",
  title =        "Two Topics in Matrix Analysis: {Structured}
                 Sensitivity for {Vandermonde}-Like Systems and a
                 Subgradient Method for Matrix Norm Estimation",
  type =         "{M.Sc.} {Thesis}",
  school =       inst-U-Dundee,
  address =      inst-U-Dundee:adr,
  month =        sep,
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Barnett:1968:SAL,
  author =       "S. Barnett and C. Storey",
  title =        "Some Applications of the {Lyapunov} Matrix Equation",
  journal =      j-JIMA,
  volume =       "4",
  pages =        "33--42",
  year =         "1968",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bartels:1972:ASM,
  author =       "R. H. Bartels and G. W. Stewart",
  title =        "Algorithm 432: {Solution} of the Matrix Equation
                 {$AX+XB=C$}",
  journal =      j-CACM,
  volume =       "15",
  number =       "9",
  pages =        "820--826",
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Barron:1960:SSL,
  author =       "D. W. Barron and H. P. F. Swinnerton--Dyer",
  title =        "Solution of Simultaneous Linear Equations Using a
                 Magnetic-Tape Store",
  journal =      j-COMP-J,
  volume =       "3",
  number =       "1",
  pages =        "28--33",
  year =         "1960",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Bauer:1963:OSMa,
  author =       "F. L. Bauer",
  title =        "Optimally Scaled Matrices",
  journal =      j-NUM-MATH,
  volume =       "5",
  pages =        "73--87",
  year =         "1963",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@InProceedings{Bauer:1963:OSMb,
  author =       "F. L. Bauer",
  editor =       "Cicely M. Popplewell",
  booktitle =    "Proc. IFIP Congress 1962",
  title =        "Optimal Scaling of Matrices and the Importance of the
                 Minimal Condition",
  publisher =    pub-NH # ", " # pub-NH:adr,
  pages =        "198--201",
  year =         "1963",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Information Processing 62",
}

@Article{Bauer:1966:GLL,
  author =       "F. L. Bauer",
  title =        "Genauigkeitsfragen bei der {L{\"o}sung} linearer
                 {Gleichungssysteme}",
  journal =      j-ZAMM,
  volume =       "46",
  number =       "7",
  pages =        "409--421",
  year =         "1966",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bauer:1969:ROS,
  author =       "F. L. Bauer",
  title =        "Remarks on Optimally Scaled Matrices",
  journal =      j-NUM-MATH,
  volume =       "13",
  pages =        "1--3",
  year =         "1969",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Bauer:1974:CGR,
  author =       "F. L. Bauer",
  title =        "Computational Graphs and Rounding Errors",
  journal =      j-SINUM,
  volume =       "11",
  number =       "1",
  pages =        "87--96",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Barlow:1992:RDM,
  author =       "Jesse L. Barlow and Udaya B. Vemulapati",
  title =        "Rank Detection Methods for Sparse Matrices",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "4",
  pages =        "1279--1297",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Barlow:1992:NDC,
  author =       "Jesse L. Barlow and Udaya B. Vemulapati",
  title =        "A Note on Deferred Correction for Equality Constrained
                 Least Squares Problems",
  journal =      j-SINUM,
  volume =       "29",
  number =       "1",
  pages =        "249--256",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Barlow:1998:GGE,
  author =       "Jesse L. Barlow and Hongyuan Zha",
  title =        "Growth in {Gaussian} Elimination, Orthogonal Matrices,
                 and the {$2$}-Norm",
  journal =      j-SIMAX,
  volume =       "19",
  number =       "3",
  pages =        "807--815",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Borwein:1989:RME,
  author =       "J. M. Borwein and P. B. Borwein and D. H. Bailey",
  title =        "Ramanujan, Modular Equations, and Approximations to
                 {Pi} or How to Compute One Billion Digits of {Pi}",
  journal =      j-AMM,
  volume =       "96",
  number =       "3",
  pages =        "201--219",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InCollection{Bliss:1992:API,
  author =       "B. Bliss and M.-C. Brunet and E. Gallopoulos",
  editor =       "E. N. Houstis and J. R. Rice and R. Vichnevetsky",
  booktitle =    "Expert Systems for Scientific Computing",
  title =        "Automatic Program Instrumentation with Applications in
                 Performance and Error Analysis",
  publisher =    pub-NH # ", " # pub-NH:adr,
  pages =        "235--260",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Blackford:1997:PEN,
  author =       "L. S. Blackford and A. Cleary and A. Petitet and R. C.
                 Whaley and J. Demmel and I. Dhillon and H. Ren and K.
                 Stanley and J. Dongarra and S. Hammarling",
  title =        "Practical Experience in the Numerical Dangers of
                 Heterogeneous Computing",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "133--147",
  year =         "1997",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Book{Burgisser:1997:ACT,
  author =       "Peter B{\"u}rgisser and Michael Clausen and M. Amin
                 Shokrollahi",
  title =        "Algebraic Complexity Theory",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "xxiii + 618",
  year =         "1997",
  ISBN =         "0-540-60582-7",
  ISBN-13 =      "978-0-540-60582-8",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Blackford:2002:USB,
  author =       "L. Susan Blackford and James Demmel and Jack Dongarra
                 and Iain Duff and Sven Hammarling and Greg Henry and
                 Michael Heroux and Linda Kaufman and Andrew Lumsdaine
                 and Antoine Petitet and Roldan Pozo and Karin Remington
                 and R. Clint Whaley",
  title =        "An updated set of {Basic Linear Algebra Subprograms
                 (BLAS)}",
  journal =      j-TOMS,
  volume =       "28",
  number =       "2",
  pages =        "135--151",
  month =        jun,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/567806.567807",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  abstract =     "This paper expands the specification of a set of
                 kernel routines for linear algebra, historically called
                 the Basic Linear Algebra Subprograms and commonly known
                 as the BLAS.\par

                 Numerical linear algebra, particularly the solution of
                 linear systems of equations, linear least squares
                 problems, eigenvalue problems and singular value
                 problems, is fundamental to most calculations in
                 scientific computing, and is often the computationally
                 intense part of such calculations. Designers of
                 computer programs involving linear algebraic operations
                 have frequently chosen to implement certain low level
                 operations, such as the dot product or the matrix
                 vector product, as separate subprograms. This may be
                 observed both in many published codes and in codes
                 written for specific applications at many computer
                 installations.\par

                 A major aim of the standards defined in this paper is
                 to enable linear algebra libraries (both public domain
                 and commercial) to interoperate efficiently, reliably
                 and easily.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@TechReport{Bai:1997:TMC,
  author =       "Zhaojun Bai and David Day and James Demmel and Jack
                 Dongarra",
  title =        "A Test Matrix Collection for Non-{Hermitian}
                 Eigenvalue Problems (Release 1.0)",
  type =         "Technical Report",
  number =       "CS-97-355",
  institution =  inst-CS-U-Tenn,
  address =      inst-CS-U-Tenn:adr,
  pages =        "45",
  month =        mar,
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "LAPACK Working Note 123",
}

@Article{Bai:1997:SDN,
  author =       "Zhaojun Bai and James W. Demmel and Jack J. Dongarra
                 and Antoine Petitet and Howard Robinson and K.
                 Stanley",
  title =        "The Spectral Decomposition of Nonsymmetric Matrices on
                 Distributed Memory Parallel Computers",
  journal =      j-SISC,
  volume =       "18",
  number =       "5",
  pages =        "1446--1461",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bai:1997:IFP,
  author =       "Zhaojun Bai and James W. Demmel and Ming Gu",
  title =        "Inverse Free Parallel Spectral Divide and Conquer
                 Algorithms for Nonsymmetric Eigenproblems",
  journal =      j-NUM-MATH,
  volume =       "76",
  pages =        "279--308",
  year =         "1997",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@TechReport{Browne:1994:NSR,
  author =       "Shirley V. Browne and Jack J. Dongarra and Stan C.
                 Green and Keith Moore and Thomas H. Rowan and Reed C.
                 Wade",
  title =        "Netlib Services and Resources",
  type =         "Report",
  number =       "ORNL/TM-12680",
  institution =  inst-ORNL,
  address =      inst-ORNL:adr,
  pages =        "42",
  month =        apr,
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bai:1993:CCN,
  author =       "Zhaojun Bai and James W. Demmel and Alan McKenney",
  title =        "On Computing Condition Numbers for the Nonsymmetric
                 Eigenproblem",
  journal =      j-TOMS,
  volume =       "19",
  number =       "2",
  pages =        "202--223",
  year =         "1993",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Bunch:1989:SSA,
  author =       "James R. Bunch and James W. Demmel and Charles F. {Van
                 Loan}",
  title =        "The Strong Stability of Algorithms for Solving
                 Symmetric Linear Systems",
  journal =      j-SIMAX,
  volume =       "10",
  number =       "4",
  pages =        "494--499",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Beckermann:2000:CNR,
  author =       "Bernhard Beckermann",
  title =        "The Condition Number of Real {Vandermonde}, {Krylov}
                 and Positive Definite {Hankel} Matrices",
  journal =      j-NUM-MATH,
  volume =       "85",
  pages =        "553--577",
  year =         "2000",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Bell:1931:RCH,
  author =       "E. T. Bell",
  title =        "Review of ``{Contributions to the History of
                 Determinants}, 1900-1920'', by {Sir Thomas Muir}",
  journal =      j-AMM,
  volume =       "38",
  pages =        "161--164",
  year =         "1931",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Bellman:1970:IMA,
  author =       "Richard Bellman",
  title =        "Introduction to Matrix Analysis",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  edition =      "Second",
  pages =        "xxiii + 403",
  year =         "1970",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted by Society for Industrial and Applied
                 Mathematics, Philadelphia, PA, USA, 1997. ISBN
                 0-89871-399-4",
}

@Book{Bell:1971:CSR,
  author =       "C. Gordon Bell and Allen Newell",
  title =        "Computer Structures: {Readings} and Examples",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Benford:1938:LAN,
  author =       "Frank Benford",
  title =        "The Law of Anomalous Numbers",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "78",
  number =       "4",
  pages =        "551--572",
  month =        mar,
  year =         "1938",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Thu Feb 15 16:28:28 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  note =         "See comments about Benford's biased rounding practices
                 \cite{Diaconis:1979:RP}.",
  URL =          "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
  ZMnumber =     "JFM 64.0555.03; Zbl 0018.26502",
  abstract =     "It has been observed that the first pages of a table
                 of common logarithms show more wear than do the last
                 pages, indicating that more used numbers begin with the
                 digit 1 than with the digit 9. A compilation of some
                 20,000 first digits taken from widely divergent sources
                 shows that there is a logarithmic distribution of first
                 digits when the numbers are composed of four or more
                 digits. An analysis of the numbers from different
                 sources shows that the numbers taken from unrelated
                 subjects, such as a group of newspaper items, show a
                 much better agreement with a logarithmic distribution
                 than do numbers from mathematical tabulations or other
                 formal data. There is here the peculiar fact that
                 numbers that individually are without relationship are,
                 when considered in large groups, in good agreement with
                 a distribution law---hence the name ``Anomalous
                 Numbers.''\par

                 A further analysis of the data shows a strong tendency
                 for bodies of numerical data to fall into geometric
                 series. If the series is made up of numbers containing
                 three or more digits the first digits form a
                 logarithmic series. If the numbers contain only single
                 digits the geometric relation still holds but the
                 simple logarithmic relation no longer applies.\par

                 An equation is given showing the frequencies of first
                 digits in the different orders of numbers 1 to 10, 10
                 to 100, etc.\par

                 The equation also gives the frequency of digits in the
                 second, third + place of a multi-digit number, and it
                 is shown that the same law applies to
                 reciprocals.\par

                 There are many instances showing that the geometric
                 series, or the logarithmic law, has long been
                 recognized as a common phenomenon in factual literature
                 and in the ordinary affairs of life. The wire gauge and
                 drill gauge of the mechanic, the magnitude scale of the
                 astronomer and the sensory response curves of the
                 psychologist are all particular examples of a
                 relationship that seems to extend to all human affairs.
                 The Law of Anomalous Numbers is thus a general
                 probability law of widespread application.",
  acknowledgement = ack-nhfb,
  author-dates = "1883--December 4, 1948",
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From \cite{Logan:1978:FDP}: ``Benford's paper was
                 published in 1938 in a journal of rather limited
                 circulation and not usually read by mathematicians. It
                 so happened that it was immediately followed in the
                 same issue by a physics paper which became of some
                 importance for secret nuclear work during World War II
                 [H. A. Bethe, M. E. Rose, and L. P. Smith, `The
                 Multiple Scattering of Electrons', Proc. Amer. Phil.
                 Soc. 78(4), 573--585 (1938)]. That is why Benford's
                 paper caught the attention of physicists in the early
                 1940's and was much discussed. This led to the notes in
                 Nature by Goudsmit and Furry [3] and Furry and Hurwitz
                 [4] containing an effort to explain Benford's law. We
                 considered it at that time merely a welcome diversion
                 and did not expect that over thirty papers would be
                 devoted to this subject in subsequent years.'' The 2006
                 bibliography \cite{Hurlimann:2006:BLB} cites 325
                 publications about Benford's Law.",
  xxURL =        "http://en.wikipedia.org/wiki/Frank_Benford",
}

@Article{Benoit:1924:NMR,
  author =       "Commandant Benoit",
  title =        "Note sur une m\'ethode de r\'esolution des \'equations
                 normales provenant de l'application de la m\'ethode des
                 moindres carr\'es \`a un syst\`eme d'\'equations
                 lin\'eaires en nombre inf\'erieur \`a celui des
                 inconnues. {Application} de la m\'ethode \`a la
                 r\'esolution d'un syst\`eme d\'efini d'\'equations
                 lin\'eaires \upshape{\char40}{Proc\'ed\'e du Commandant
                 Cholesky}\upshape{\char41}",
  journal =      "Bulletin G\'eod\'esique
                 \upshape{(}Toulouse\upshape{)}",
  volume =       "2",
  pages =        "67--77",
  year =         "1924",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Cited in \cite[Cottle's
                 translation]{Anonymous:1922:CC}",
}

@Book{Berman:1994:NMM,
  author =       "Abraham Berman and Robert J. Plemmons",
  title =        "Nonnegative Matrices in the Mathematical Sciences",
  volume =       "9",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xx + 340",
  year =         "1994",
  DOI =          "https://doi.org/10.1137/1.9781611971262",
  ISBN =         "0-89871-321-8",
  ISBN-13 =      "978-0-89871-321-3",
  LCCN =         "QA188 .B47 1994",
  MRclass =      "15A48 (15-02 60J10 90C33)",
  MRnumber =     "1298430 (95e:15013)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Revised reprint of \cite{Berman:1979:NMM}.",
  series =       "Classics in Applied Mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0708/94037449-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0708/94037449-t.html",
  abstract =     "Here is a valuable text and research tool for
                 scientists and engineers who use or work with theory
                 and computation associated with practical problems
                 relating to Markov chains and queuing networks,
                 economic analysis, or mathematical programming.
                 Originally published in 1979, this new edition adds
                 material that updates the subject relative to
                 developments from 1979 to 1993. Theory and applications
                 of nonnegative matrices are blended here, and extensive
                 references are included in each area. You will be led
                 from the theory of positive operators via the
                 Perron-Frobenius theory of nonnegative matrices and the
                 theory of inverse positivity, to the widely used topic
                 of $M$-matrices. On the way, semigroups of nonnegative
                 matrices and symmetric nonnegative matrices are
                 discussed. Later, applications of nonnegativity and
                 $M$-matrices are given; for numerical analysis the
                 example is convergence theory of iterative methods, for
                 probability and statistics the examples are finite
                 Markov chains and queuing network models, for
                 mathematical economics the example is input-output
                 models, and for mathematical programming the example is
                 the linear complementarity problem. Nonnegativity
                 constraints arise very naturally throughout the
                 physical world. Engineers, applied mathematicians, and
                 scientists who encounter nonnegativity or
                 generalizations of nonegativity in their work will
                 benefit from topics covered here, connecting them to
                 relevant theory. Researchers in one area, such as
                 queuing theory, may find useful the techniques
                 involving nonnegative matrices used by researchers in
                 another area, say, mathematical programming. Exercises
                 and biographical notes are included with each
                 chapter.",
  acknowledgement = ack-njh # " and " # ack-nhfb # " and " # ack-rah,
  tableofcontents = "1: Matrices Which Leave a Cone Invariant \\
                 2: Nonnegative Matrices \\
                 3: Semigroups of Nonnegative Matrices \\
                 4: Symmetric Nonnegative Matrices \\
                 5: Generalized Inverse-Positivity \\
                 6: $M$-Matrices \\
                 7: Iterative Methods for Linear Systems \\
                 8: Finite Markov Chains \\
                 9: Input-Output Analysis in Economics \\
                 10: The Linear Complementarity Problem \\
                 11: Supplement 1979--1993 \\
                 References \\
                 Index",
}

@Article{Benschop:1971:MSE,
  author =       "N. F. Benschop and H. C. Ratz",
  title =        "A Mean Square Estimate of the Generated Roundoff Error
                 in Constant Matrix Iterative Processes",
  journal =      j-ACM,
  volume =       "18",
  number =       "1",
  pages =        "48--62",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Berenbaum:1991:DSM,
  author =       "M. C. Berenbaum",
  title =        "Direct Search Methods in the Optimisation of Cancer
                 Chemotherapy",
  journal =      j-BRITISH-J-CANCER,
  volume =       "61",
  pages =        "101--109",
  year =         "1991",
  CODEN =        "BJCAAI",
  ISSN =         "0007-0920 (print), 1532-1827 (electronic)",
  ISSN-L =       "0007-0920",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "British Journal of Cancer",
}

@Article{Beam:1993:ASB,
  author =       "Richard M. Beam and Robert F. Warming",
  title =        "The Asymptotic Spectra of Banded {Toeplitz} and
                 Quasi-{Toeplitz} Matrices",
  journal =      j-SISC,
  volume =       "14",
  number =       "4",
  pages =        "971--1006",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Boley:1994:FPF,
  author =       "Daniel Boley and Gene H. Golub and Samy Makar and
                 Nirmal Saxena and Edward J. McCluskey",
  title =        "Floating Point Fault Tolerance with Backward Error
                 Assertions",
  journal =      j-IEEE-C,
  volume =       "44",
  number =       "2",
  pages =        "302--311",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Buzbee:1970:DMS,
  author =       "B. L. Buzbee and G. H. Golub and C. W. Nielson",
  title =        "On Direct Methods for Solving {Poisson's} Equations",
  journal =      j-SINUM,
  volume =       "7",
  number =       "4",
  pages =        "627--656",
  year =         "1970",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Bhatia:1997:MA,
  author =       "Rajendra Bhatia",
  title =        "Matrix Analysis",
  volume =       "169",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xii + 347",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4612-0653-8",
  ISBN =         "0-387-94846-5 (print), 1-4612-0653-7 (e-book)",
  ISBN-13 =      "978-0-387-94846-1 (print), 978-1-4612-0653-8
                 (e-book)",
  LCCN =         "QA188 .B485 1996",
  MRclass =      "15-02 (47-02)",
  MRnumber =     "1477662 (98i:15003)",
  MRreviewer =   "R. J. Bumcrot",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
  series =       "Graduate Texts in Mathematics",
  URL =          "http://catdir.loc.gov/catdir/enhancements/fy0818/96032217-d.html;
                 http://www.gbv.de/dms/goettingen/213798093.pdf",
  abstract =     "The aim of this book is to present a substantial part
                 of matrix analysis that is functional analytic in
                 spirit. Much of this will be of interest to graduate
                 students and research workers in operator theory,
                 operator algebras, mathematical physics, and numerical
                 analysis. The book can be used as a basic text for
                 graduate courses on advanced linear algebra and matrix
                 analysis. It can also be used as supplementary text for
                 courses in operator theory and numerical analysis.
                 Among topics covered are the theory of majorization,
                 variational principles of eigenvalues, operator
                 monotone and convex functions, perturbation of matrix
                 functions, and matrix inequalities. Much of this is
                 presented for the first time in a unified way in a
                 textbook. The reader will learn several powerful
                 methods and techniques of wide applicability, and see
                 connections with other areas of mathematics. A large
                 selection of matrix inequalities will make this book a
                 valuable reference for students and researchers who are
                 working in numerical analysis, mathematical physics and
                 operator theory.",
  acknowledgement = ack-nhfb # " and " # ack-rah,
  tableofcontents = "Preface / v \\
                 I A Review of Linear Algebra / 1 \\
                 1.1 Vector Spaces and Inner Product Spaces / 1 \\
                 1.2 Linear Operators and Matrices / 3 \\
                 1.3 Direct Sums / 9 \\
                 1.4 Tensor Products / 12 \\
                 1.5 Symmetry Classes / 16 \\
                 1.6 Problems / 20 \\
                 1.7 Notes and References / 26 \\
                 II Majorisation and Doubly Stochastic Matrices / 28 \\
                 11.1 Basic Notions / 28 \\
                 11.2 Birkhoff's Theorem / 36 \\
                 11.3 Convex and Monotone Functions / 40 \\
                 11.4 Binary Algebraic Operations and Majorisation / 48
                 \\
                 11.5 Problems / 50 \\
                 11.6 Notes and References / 54 \\
                 III Variational Principles for Eigenvalues / 57 \\
                 III.1 The Minimax Principle for Eigenvalues / 57 \\
                 111.2 Weyl's Inequalities / 62 \\
                 111.3 Wielandt's Minimax Principle / 65 \\
                 111.4 Lidskii's Theorems / 68 \\
                 III.5 Eigenvalues of Real Parts and Singular Values /
                 73 \\
                 111.6 Problems / 75 \\
                 111.7 Notes and References / 78 \\
                 IV Symmetric Norms / 84 \\
                 IV.1 Norms on $C^n$ / 84 \\
                 IV.2 Unitarily Invariant Norms on Operators on $C^n$ /
                 91 \\
                 IV.3 Lidskii's Theorem (Third Proof) / 98 \\
                 IV.4 Weakly Unitarily Invariant Norms / 101 \\
                 IV.5 Problems / 107 \\
                 IV.6 Notes and References / 109 \\
                 V Operator Monotone and Operator Convex Functions / 112
                 \\
                 V.1 Definitions and Simple Examples / 112 \\
                 V.2 Some Characterisations / 117 \\
                 V.3 Smoothness Properties / 123 \\
                 V.4 Loewner's Theorems / 131 \\
                 V.5 Problems / 147 \\
                 V.6 Notes and References / 149 \\
                 VI Spectral Variation of Normal Matrices / 152 \\
                 VI.1 Continuity of Roots of Polynomials / 153 \\
                 VI.2 Hermitian and Skew-Hermitian Matrices / 155 \\
                 VI.3 Estimates in the Operator Norm / 159 \\
                 VI.4 Estimates in the Frobenius Norm / 165 \\
                 VI.5 Geometry and Spectral Variation: the Operator Norm
                 / 168 \\
                 VI.6 Geometry and Spectral Variation: wui Norms / 173
                 \\
                 VI.7 Some Inequalities for the Determinant / 181 \\
                 VI.8 Problems / 184 \\
                 VI.9 Notes and References / 190 \\
                 VII Perturbation of Spectral Subspaces of Normal
                 Matrices / 194 \\
                 VII.1 Pairs of Subspaces / 195 \\
                 VII.2 The Equation $A X -X B = Y$ / 203 \\
                 VII.3 Perturbation of Eigenspaces / 211 \\
                 VII.4 A Perturbation Bound for Eigenvalues / 212 \\
                 VII.5 Perturbation of the Polar Factors / 213 \\
                 VII.6 Appendix: Evaluating the (Fourier) constants /
                 216 \\
                 VII.7 Problems / 221 \\
                 VII.8 Notes and References / 223 \\
                 VIII Spectral Variation of Nonnormal Matrices / 226 \\
                 VIII.1 General Spectral Variation Bounds / 227 \\
                 VIII.4 Matrices with Real Eigenvalues / 238 \\
                 VIII.5 Eigenvalues with Symmetries / 240 \\
                 VIII.6 Problems / 244 \\
                 VIII.7 Notes and References / 249 \\
                 IX A Selection of Matrix Inequalities / 253 \\
                 IX.1 Some Basic Lemmas / 253 \\
                 IX.2 Products of Positive Matrices / 255 \\
                 IX.3 Inequalities for the Exponential Function / 258
                 \\
                 IX.4 Arithmetic-Geometric Mean Inequalities / 262 \\
                 IX.5 Schwarz Inequalities / 266 \\
                 IX.6 The Lieb Concavity Theorem / 271 \\
                 IX.7 Operator Approximation / 275 \\
                 IX.8 Problems / 279 \\
                 IX.9 Notes and References / 285 \\
                 X Perturbation of Matrix Functions / 289 \\
                 X.1 Operator Monotone Functions / 289 \\
                 X.2 The Absolute Value / 296 \\
                 X.3 Local Perturbation Bounds / 301 \\
                 X.4 Appendix: Differential Calculus / 310 \\
                 X.5 Problems / 317 \\
                 X.6 Notes and References / 320 \\
                 References / 325 \\
                 Index / 339",
  xxpages =      "xi + 347",
}

@TechReport{Balle:1993:STM,
  author =       "Susanne M. Balle and Per Christian Hansen and Nicholas
                 J. Higham",
  title =        "A {Strassen}-Type Matrix Inversion Algorithm for the
                 {Connection Machine}",
  number =       "CNC/1993/028",
  institution =  "Centre for Novel Computing, " # inst-U-Manchester,
  address =      inst-U-Manchester:adr,
  type =         "Technical Report",
  pages =        "29",
  month =        oct,
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bhatia:1994:VUP,
  author =       "Rajendra Bhatia and Kalyan Mukherjea",
  title =        "Variation of the Unitary Part of a Matrix",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "3",
  pages =        "1007--1014",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bhatia:1997:HWS,
  author =       "Rajendra Bhatia and Peter Rosenthal",
  title =        "How and Why To Solve the Operator Equation {$AX - XB =
                 Y$}",
  journal =      j-BULL-LOND-MATH-SOC,
  volume =       "29",
  pages =        "1--21",
  year =         "1997",
  CODEN =        "LMSBBT",
  ISSN =         "0024-6093 (print), 1469-2120 (electronic)",
  ISSN-L =       "0024-6093",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Bulletin of the London Mathematical Society",
  journal-URL =  "http://blms.oxfordjournals.org/content/by/year",
}

@Article{Brent:1980:AIB,
  author =       "Richard P. Brent and Judith A. Hooper and J. Michael
                 Yohe",
  title =        "An {AUGMENT} Interface for {Brent's} Multiple
                 Precision Arithmetic Package",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "146--149",
  year =         "1980",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Birkhoff:1979:IDT,
  author =       "Garrett Birkhoff and Surender Gulati",
  title =        "Isotropic Distributions of Test Matrices",
  journal =      "J. Appl. Math. Phys. \textup{(}ZAMP\textup{)}",
  volume =       "30",
  pages =        "148--158",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bini:1980:SFA,
  author =       "Dario Bini and Grazia Lotti",
  title =        "Stability of Fast Algorithms for Matrix
                 Multiplication",
  journal =      j-NUM-MATH,
  volume =       "36",
  pages =        "63--72",
  year =         "1980",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Book{Birkhoff:1977:SMA,
  author =       "Garrett Birkhoff and Saunders Mac Lane",
  title =        "A Survey of Modern Algebra",
  publisher =    "Macmillan",
  address =      "New York",
  edition =      "Fourth",
  pages =        "xi + 500",
  year =         "1977",
  ISBN =         "0-02-310070-2",
  ISBN-13 =      "978-0-02-310070-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Bini:1994:PMC,
  author =       "Dario Bini and Victor Y. Pan",
  title =        "Polynomial and Matrix Computations. Volume 1:
                 {Fundamental} Algorithms",
  publisher =    pub-BH,
  address =      pub-BH:adr,
  pages =        "xvi + 415",
  year =         "1994",
  ISBN =         "0-8176-3786-9",
  ISBN-13 =      "978-0-8176-3786-6",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Birkhoff:1975:THN,
  author =       "Garrett Birkhoff",
  title =        "Two {Hadamard} Numbers for Matrices",
  journal =      j-CACM,
  volume =       "18",
  number =       "1",
  pages =        "25--29",
  year =         "1975",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Bischof:1990:ICEa,
  author =       "Christian H. Bischof",
  title =        "Incremental Condition Estimation",
  journal =      j-SIMAX,
  volume =       "11",
  number =       "2",
  pages =        "312--322",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bischof:1987:WRP,
  author =       "Christian H. Bischof and Charles F. {Van Loan}",
  title =        "The {WY} Representation for Products of {Householder}
                 Matrices",
  journal =      j-SISSC,
  volume =       "8",
  number =       "1",
  pages =        "s2--s13",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bjorck:1973:ACV,
  author =       "{\AA}ke Bj{\"o}rck and Tommy Elfving",
  title =        "Algorithms for Confluent {Vandermonde} Systems",
  journal =      j-NUM-MATH,
  volume =       "21",
  pages =        "130--137",
  year =         "1973",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Bjorck:1967:IRLa,
  author =       "{\AA}ke Bj{\"o}rck and Gene H. Golub",
  title =        "Iterative Refinement of Linear Least Squares Solutions
                 by {Householder} Transformation",
  journal =      j-BIT,
  volume =       "7",
  pages =        "322--337",
  year =         "1967",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Bjorck:1967:IRLb,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Iterative Refinement of Linear Least Squares Solutions
                 {I}",
  journal =      j-BIT,
  volume =       "7",
  pages =        "257--278",
  year =         "1967",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Bjorck:1967:SLL,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Solving Linear Least Squares Problems by
                 {Gram--Schmidt} Orthogonalization",
  journal =      j-BIT,
  volume =       "7",
  pages =        "1--21",
  year =         "1967",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Bjorck:1968:IRL,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Iterative Refinement of Linear Least Squares Solutions
                 {II}",
  journal =      j-BIT,
  volume =       "8",
  pages =        "8--30",
  year =         "1968",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Bjorck:1978:CIR,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Comment on the Iterative Refinement of Least-Squares
                 Solutions",
  journal =      j-ASA,
  volume =       "73",
  number =       "361",
  pages =        "161--166",
  year =         "1978",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bjorck:1987:SAM,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Stability Analysis of the Method of Seminormal
                 Equations for Linear Least Squares Problems",
  journal =      j-LAA,
  volume =       "88/89",
  pages =        "31--48",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Bjorck:1990:LSM,
  author =       "{\AA}ke Bj{\"o}rck",
  editor =       "P. G. Ciarlet and J. L. Lions",
  booktitle =    "Handbook of Numerical Analysis",
  title =        "Least Squares Methods",
  volume =       "I: Finite Difference Methods---Solution of Equations
                 in {$R^n$}",
  publisher =    pub-ELSNH,
  address =      pub-ELSNH:adr,
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Bjorck:1990:IRR,
  author =       "{\AA}ke Bj{\"o}rck",
  editor =       "M. G. Cox and S. J. Hammarling",
  booktitle =    "Reliable Numerical Computation",
  title =        "Iterative Refinement and Reliable Computing",
  publisher =    pub-OUP,
  pages =        "249--266",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  mycrossref =   "Cox:1990:RNC",
}

@Article{Bjorck:1991:CWP,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Component-Wise Perturbation Analysis and Error Bounds
                 for Linear Least Squares Solutions",
  journal =      j-BIT,
  volume =       "31",
  pages =        "238--244",
  year =         "1991",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@InProceedings{Bjorck:1992:PSA,
  author =       "{\AA}ke Bj{\"o}rck",
  editor =       "D. F. Griffiths and G. A. Watson",
  booktitle =    "Numerical Analysis \textup{1991}, Proceedings of the
                 \textup{14}th Dundee Conference",
  title =        "Pivoting and Stability in the Augmented System
                 Method",
  volume =       "260",
  publisher =    pub-Longman-ST # ", " # pub-Longman-ST:adr,
  pages =        "1--16",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Pitman Research Notes in Mathematics",
}

@Article{Bjorck:1994:NGS,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Numerics of {Gram--Schmidt} Orthogonalization",
  journal =      j-LAA,
  volume =       "197/198",
  pages =        "297--316",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Bjorck:1996:NML,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Numerical Methods for Least Squares Problems",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xvii + 408",
  year =         "1996",
  ISBN =         "0-89871-360-9",
  ISBN-13 =      "978-0-89871-360-2",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bjorck:1992:LRO,
  author =       "{\AA}ke Bj{\"o}rck and C. C. Paige",
  title =        "Loss and Recapture of Orthogonality in the Modified
                 {Gram--Schmidt} Algorithm",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "176--190",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bjorck:1994:SAL,
  author =       "{\AA}ke Bj{\"o}rck and C. C. Paige",
  title =        "Solution of Augmented Linear Systems Using Orthogonal
                 Factorizations",
  journal =      j-BIT,
  volume =       "34",
  pages =        "1--24",
  year =         "1994",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Bjorck:1970:SVS,
  author =       "{\AA}ke Bj{\"o}rck and Victor Pereyra",
  title =        "Solution of {Vandermonde} Systems of Equations",
  journal =      j-MATH-COMP,
  volume =       "24",
  number =       "112",
  pages =        "893--903",
  year =         "1970",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Unpublished{Boros:1994:FAS,
  author =       "T. Boros and T. Kailath and V. Olshevsky",
  title =        "Fast Algorithms for Solving {Vandermonde} and
                 {Chebyshev--Vandermonde} Systems",
  pages =        "22",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Manuscript",
}

@Article{Bunch:1976:DSM,
  author =       "James R. Bunch and Linda Kaufman and Beresford N.
                 Parlett",
  title =        "Decomposition of a Symmetric Matrix",
  journal =      j-NUM-MATH,
  volume =       "27",
  pages =        "95--109",
  year =         "1976",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@InProceedings{Bailey:1993:MPM,
  author =       "David H. Bailey and Robert Krasny and Richard Pelz",
  editor =       "Richard F. Sincovec and David E. Keyes and Michael R.
                 Leuze and Linda R. Petzold and Daniel A. Reed",
  booktitle =    "Proceedings of the Sixth SIAM Conference on Parallel
                 Processing for Scientific Computing, {Volume I}",
  title =        "Multiple Precision, Multiple Processor Vortex Sheet
                 Roll-Up Computation",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "52--56",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Blanch:1964:NEC,
  author =       "G. Blanch",
  title =        "Numerical Evaluation of Continued Fractions",
  journal =      j-SIREV,
  volume =       "6",
  number =       "4",
  pages =        "383--421",
  year =         "1964",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{BLAST,
  key =          "Basic Linear Algebra Subprograms Technical (BLAST)
                 Forum",
  title =        "{Basic Linear Algebra Subprograms Technical (BLAST)
                 Forum Standard}",
  journal =      "Int. J. High Performance Applications and
                 Supercomputing",
  volume =       "",
  number =       "",
  year =         "2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "To appear",
}

@InProceedings{Bloch:1948:MC,
  author =       "Richard M. Bloch",
  title =        "Mark {I} Calculator",
  crossref =     "harv48",
  pages =        "23--30",
  year =         "1948",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bischof:1990:ICEb,
  author =       "Christian H. Bischof and John G. Lewis and Daniel J.
                 Pierce",
  title =        "Incremental Condition Estimation for Sparse Matrices",
  journal =      j-SIMAX,
  volume =       "11",
  number =       "4",
  pages =        "644--659",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bailey:1991:USA,
  author =       "David H. Bailey and King Lee and Horst D. Simon",
  title =        "Using {Strassen's} Algorithm to Accelerate the
                 Solution of Linear Systems",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "4",
  pages =        "357--371",
  year =         "1991",
  CODEN =        "JOSUED",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@Article{Blue:1978:PFP,
  author =       "James L. Blue",
  title =        "A Portable {Fortran} Program to Find the {Euclidean}
                 Norm of a Vector",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "15--23",
  year =         "1978",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Bowdler:1966:SRC,
  author =       "H. J. Bowdler and R. S. Martin and G. Peters and J. H.
                 Wilkinson",
  title =        "Solution of Real and Complex Systems of Linear
                 Equations",
  journal =      j-NUM-MATH,
  volume =       "8",
  pages =        "217--234",
  year =         "1966",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Also in \cite[pp.~93--110]{Wilkinson:1971:LA},
                 Contribution I/7",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Bjorstad:1992:EMM,
  author =       "P. Bj{\o}rstad and F. Manne and T. S{\o}revik and M.
                 Vajter\v{s}ic",
  title =        "Efficient Matrix Multiplication on {SIMD} Computers",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "386--401",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Bargmann:1946:SLS,
  author =       "V. Bargmann and D. Montgomery and J. von Neumann",
  title =        "Solution of Linear Systems of High Order",
  type =         "Report prepared for {Navy Bureau of Ordnance}",
  year =         "1946",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted in \cite[pp.~421--477]{Taub:1963:JNC}",
}

@Article{Barlow:1988:IME,
  author =       "J. L. Barlow and N. K. Nichols and R. J. Plemmons",
  title =        "Iterative Methods for Equality-Constrained Least
                 Squares Problems",
  journal =      j-SISSC,
  volume =       "9",
  number =       "5",
  pages =        "892--906",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bodewig:1949:RRE,
  author =       "E. Bodewig",
  title =        "Review of ``{Rounding-Off Errors in Matrix
                 Processes}'' by {A. M. Turing}",
  journal =      j-MATH-REV,
  volume =       "10",
  pages =        "405",
  year =         "1949",
  CODEN =        "MAREAR",
  ISSN =         "0025-5629",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Mathematical Reviews",
}

@Article{Bondeli:1994:CRS,
  author =       "S. Bondeli and W. Gander",
  title =        "Cyclic Reduction for Special Tridiagonal Systems",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "1",
  pages =        "321--330",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bohlender:1977:FPC,
  author =       "Gerd Bohlender",
  title =        "Floating-point Computation of Functions with Maximum
                 Accuracy",
  journal =      j-IEEE-C,
  volume =       "C-26",
  number =       "7",
  pages =        "621--632",
  year =         "1977",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bohte:1975:BRE,
  author =       "Z. Bohte",
  title =        "Bounds for Rounding Errors in the {Gaussian}
                 Elimination For Band Systems",
  journal =      j-JIMA,
  volume =       "16",
  pages =        "133--142",
  year =         "1975",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bollen:1984:NSD,
  author =       "Jo A. M. Bollen",
  title =        "Numerical Stability of Descent Methods for Solving
                 Linear Equations",
  journal =      j-NUM-MATH,
  volume =       "43",
  pages =        "361--377",
  year =         "1984",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@InCollection{Bowden:1953:OTM,
  author =       "B. V. Bowden",
  editor =       "B. V. Bowden",
  booktitle =    "Faster than Thought: {A} Symposium on Digital
                 Computing Machines",
  title =        "The Organization of a Typical Machine",
  publisher =    "Pitman",
  address =      "London",
  pages =        "67--77",
  year =         "1953",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Boyd:1974:PMN,
  author =       "David W. Boyd",
  title =        "The Power Method for {$\ell^p$} Norms",
  journal =      j-LAA,
  volume =       "9",
  pages =        "95--101",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Boyer:1989:HM,
  author =       "Carl B. Boyer",
  title =        "A History of Mathematics",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  edition =      "Second",
  pages =        "xviii + 762",
  year =         "1989",
  ISBN =         "0-471-50357-6",
  ISBN-13 =      "978-0-471-50357-6",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Revised by Uta C. Merzbach",
}

@Article{Boyle:1994:AFS,
  author =       "Jeff Boyle",
  title =        "An Application of {Fourier} Series to the Most
                 Significant Digit Problem",
  journal =      j-AMM,
  volume =       "101",
  number =       "11",
  pages =        "879--886",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Boisvert:1997:MMW,
  author =       "Ronald F. Boisvert and Roldan Pozo and Karin Remington
                 and Richard F. Barrett and Jack J. Dongarra",
  editor =       "Ronald F. Boisvert",
  booktitle =    "Quality of Numerical Software: {Assessment} and
                 Enhancement",
  title =        "{Matrix Market}: {A Web} Resource for Test Matrix
                 Collections",
  publisher =    pub-CH # ", " # pub-CH:adr-L,
  pages =        "125--136",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Beaton:1976:ARS,
  author =       "Albert E. Beaton and Donald B. Rubin and John L.
                 Barone",
  title =        "The Acceptability of Regression Solutions: {Another}
                 Look at Computational Accuracy",
  journal =      j-ASA,
  volume =       "71",
  number =       "353",
  pages =        "158--168",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Brent:1970:EAA,
  author =       "R. P. Brent",
  title =        "Error Analysis of Algorithms for Matrix Multiplication
                 and Triangular Decomposition Using {Winograd's}
                 Identity",
  journal =      j-NUM-MATH,
  volume =       "16",
  pages =        "145--156",
  year =         "1970",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@TechReport{Brent:1970:AMM,
  author =       "R. P. Brent",
  title =        "Algorithms for Matrix Multiplication",
  type =         "Technical Report",
  number =       "CS 157",
  institution =  inst-CS-U-STANFORD,
  address =      inst-U-STANFORD:adr,
  pages =        "ii + 52",
  month =        mar,
  year =         "1970",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Brent:1973:PAV,
  author =       "Richard P. Brent",
  title =        "On the Precision Attainable with Various
                 Floating-Point Number Systems",
  journal =      j-IEEE-C,
  volume =       "C-22",
  number =       "6",
  pages =        "601--607",
  year =         "1973",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Brent:19xx:FMP,
  author =       "Richard P. Brent",
  title =        "A {Fortran} Multiple-Precision Arithmetic Package",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "57--70",
  year =         "{\noopsort{a}}1978",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Brent:19xx:AMF,
  author =       "Richard P. Brent",
  title =        "{ALGORITHM 524} {MP}, {A} {Fortran} Multiple-Precision
                 Arithmetic Package",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "71--81",
  year =         "{\noopsort{b}}1978",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@InCollection{Brezinski:1996:ALC,
  author =       "Claude Brezinski",
  booktitle =    "{A} Numerical Analysis Conference in Honour of {Jean
                 Meinguet}",
  title =        "{Andr\'e Louis Cholesky}",
  pages =        "45--50",
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Published as a supplement to the Bulletin of the
                 Belgian Mathematical Society. Also available as
                 Publication ANO-347, Laboratoire d'Analyse Num\'erique
                 et d'Optimisation, Universit\'e des Sciences et
                 Technologies de Lille, Nov. 1995,
                 \path|http://ano.univ-lille1.fr|",
}

@Book{Briggs:1995:DOM,
  author =       "William L. Briggs and Van Emden Henson",
  title =        "The {DFT}: {An} Owner's Manual for the Discrete
                 {Fourier} Transform",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xv + 434",
  year =         "1995",
  ISBN =         "0-89871-342-0",
  ISBN-13 =      "978-0-89871-342-8",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Britton:1992:CWM,
  editor =       "J. L. Britton",
  title =        "Collected Works of {A. M. Turing}: {Pure}
                 Mathematics",
  publisher =    pub-NH,
  address =      pub-NH:adr,
  pages =        "xxii + 287",
  year =         "1992",
  ISBN =         "0-444-88059-3",
  ISBN-13 =      "978-0-444-88059-8",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bleher:1987:SFE,
  author =       "J. H. Bleher and S. M. Rump and U. Kulisch and M.
                 Metzger and Ch. Ullrich and W. Walter",
  title =        "A Study of a {FORTRAN} Extension for
                 Engineering/Scientific Computation with Access to
                 {ACRITH}",
  journal =      j-COMPUTING,
  volume =       "39",
  pages =        "93--110",
  year =         "1987",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Brown:1981:SRM,
  author =       "W. S. Brown",
  title =        "A Simple but Realistic Model of Floating-Point
                 Arithmetic",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "445--480",
  year =         "1981",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@InProceedings{Bleher:1985:AHA,
  author =       "J. H. Bleher and A. E. Roeder and S. M. Rump",
  editor =       "Kai Hwang",
  booktitle =    "Proceedings of the 7th Symposium on Computer
                 Arithmetic",
  title =        "{ACRITH}: {High}-Accuracy Arithmetic. {An} Advanced
                 Tool for Numerical Computation",
  publisher =    "IEEE Computer Society Press, Silver Spring, MD, USA",
  pages =        "318--321",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@PhdThesis{Brunet:1989:CFL,
  author =       "Marie-Christine Brunet",
  title =        "Contribution {\`a} la Fiabilit{\'e} de Logiciels
                 Num{\'e}riques et {\`a} {L}'analyse de Leur
                 Comportement: Une Approche Statistique",
  school =       "Universit\'e de Paris IX Dauphine, U.E.R.
                 Math\'ematiques de la D\'ecision",
  pages =        "viii + 214",
  month =        jan,
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bailey:1989:FPA,
  author =       "David H. Bailey and Horst D. Simon and John T. Barton
                 and Martin J. Fouts",
  title =        "Floating Point Arithmetic in Future Supercomputers",
  journal =      j-IJSA,
  volume =       "3",
  number =       "3",
  pages =        "86--90",
  year =         "1989",
  CODEN =        "IJSAE9",
  ISSN =         "0890-2720",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "International Journal of Supercomputer Applications",
  journal-URL =  "http://hpc.sagepub.com/content/by/year",
}

@Article{Bauer:1961:AMN,
  author =       "F. L. Bauer and J. Stoer and C. Witzgall",
  title =        "Absolute and Monotonic Norms",
  journal =      j-NUM-MATH,
  volume =       "3",
  pages =        "257--264",
  year =         "1961",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Buchholz:1959:FFC,
  author =       "W. Buchholz",
  title =        "Fingers or Fists? ({The} Choice of Decimal or Binary
                 Representation)",
  journal =      j-CACM,
  volume =       "2",
  number =       "12",
  pages =        "3--11",
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Buchholz:1981:OWE,
  author =       "W. Buchholz",
  title =        "Origin of the Word {\emph{Byte}}",
  journal =      j-AHC,
  volume =       "3",
  number =       "1",
  pages =        "72",
  year =         "1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bukhberger:1973:MIT,
  author =       "B. Bukhberger and G. A. Emel'yanenko",
  title =        "Methods of Inverting Tridiagonal Matrices",
  journal =      j-USSR-COMP-MATH-MATH-PHYS,
  volume =       "13",
  pages =        "10--20",
  year =         "1973",
  CODEN =        "CMMPA9",
  ISSN =         "0041-5553, 0502-9902",
  ISSN-L =       "0041-5553",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "U.S.S.R. Computational Mathematics and Mathematical Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00415553",
}

@Article{Businger:1965:LLS,
  author =       "P. Businger and G. H. Golub",
  title =        "Linear Least Squares Solutions by {Householder}
                 Transformations",
  journal =      j-NUM-MATH,
  volume =       "7",
  pages =        "269--276",
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Also in \cite[pp.~111--118]{Wilkinson:1971:LA},
                 Contribution I/8",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Bunch:1977:SSM,
  author =       "James R. Bunch and Linda Kaufman",
  title =        "Some Stable Methods for Calculating Inertia and
                 Solving Symmetric Linear Systems",
  journal =      j-MATH-COMP,
  volume =       "31",
  number =       "137",
  pages =        "163--179",
  year =         "1977",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bunch:1971:ESM,
  author =       "James R. Bunch",
  title =        "Equilibration of Symmetric Matrices in the Max-Norm",
  journal =      j-ACM,
  volume =       "18",
  number =       "4",
  pages =        "566--572",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bunch:1971:ADP,
  author =       "James R. Bunch",
  title =        "Analysis of the Diagonal Pivoting Method",
  journal =      j-SINUM,
  volume =       "8",
  number =       "4",
  pages =        "656--680",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bunch:1974:PPS,
  author =       "James R. Bunch",
  title =        "Partial Pivoting Strategies for Symmetric Matrices",
  journal =      j-SINUM,
  volume =       "11",
  number =       "3",
  pages =        "521--528",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bunch:1982:NSD,
  author =       "James R. Bunch",
  title =        "A Note on the Stable Decomposition of Skew-Symmetric
                 Matrices",
  journal =      j-MATH-COMP,
  volume =       "38",
  number =       "158",
  pages =        "475--479",
  year =         "1982",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bunch:1987:WSS,
  author =       "James R. Bunch",
  title =        "The Weak and Strong Stability of Algorithms in
                 Numerical Linear Algebra",
  journal =      j-LAA,
  volume =       "88/89",
  pages =        "49--66",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Bunch:1971:DMS,
  author =       "James R. Bunch and Beresford N. Parlett",
  title =        "Direct Methods for Solving Symmetric Indefinite
                 Systems of Linear Equations",
  journal =      j-SINUM,
  volume =       "8",
  number =       "4",
  pages =        "639--655",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Burdakov:1997:GAO,
  author =       "Oleg Burdakov",
  title =        "A Greedy Algorithm for the Optimal Basis Problem",
  journal =      j-BIT,
  volume =       "37",
  number =       "3",
  pages =        "591--599",
  year =         "1997",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Businger:1968:MWC,
  author =       "P. A. Businger",
  title =        "Matrices Which Can Be Optimally Scaled",
  journal =      j-NUM-MATH,
  volume =       "12",
  pages =        "346--348",
  year =         "1968",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Businger:1971:MNS,
  author =       "P. A. Businger",
  title =        "Monitoring the numerical stability of {Gaussian}
                 elimination",
  journal =      j-NUM-MATH,
  volume =       "16",
  pages =        "360--361",
  year =         "1971",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Book{Butcher:1987:NAO,
  author =       "J. C. Butcher",
  title =        "The Numerical Analysis of Ordinary Differential
                 Equations: {Runge--Kutta} and General Linear Methods",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr-C,
  pages =        "xv + 512",
  year =         "1987",
  ISBN =         "0-471-91046-5",
  ISBN-13 =      "978-0-471-91046-6",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Buchanan:1992:NMA,
  author =       "James L. Buchanan and Peter R. Turner",
  title =        "Numerical Methods and Analysis",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  pages =        "xv + 751",
  year =         "1992",
  ISBN =         "0-07-008717-2, 0-07-112922-7 (international \pbk\
                 edition)",
  ISBN-13 =      "978-0-07-008717-0, 978-0-07-112922-0 (international
                 \pbk\ edition)",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Byers:1984:LSC,
  author =       "Ralph Byers",
  title =        "A {LINPACK}-Style Condition Estimator for the Equation
                 {$AX-XB^T=C$}",
  journal =      j-IEEE-AC,
  volume =       "AC-29",
  number =       "10",
  pages =        "926--928",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Byers:1985:NCA,
  author =       "Ralph Byers",
  editor =       "B. N. Datta",
  booktitle =    "Linear Algebra and Its Role in Systems Theory",
  title =        "Numerical Condition of the Algebraic {Riccati}
                 Equation",
  volume =       "47",
  publisher =    pub-AMS # ", " # pub-AMS:adr,
  pages =        "35--49",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Contemporary Math.",
}

@Article{Byers:1987:SAR,
  author =       "Ralph Byers",
  title =        "Solving the Algebraic {Riccati} Equation with the
                 Matrix Sign Function",
  journal =      j-LAA,
  volume =       "85",
  pages =        "267--279",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Byers:1988:BMM,
  author =       "Ralph Byers",
  title =        "A Bisection Method for Measuring the Distance of a
                 Stable Matrix to the Unstable Matrices",
  journal =      j-SISSC,
  volume =       "9",
  number =       "5",
  pages =        "875--881",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Byers:1987:SVL,
  author =       "Ralph Byers and Stephen Nash",
  title =        "On the Singular ``Vectors'' of the {Lyapunov}
                 Operator",
  journal =      j-SIAD,
  volume =       "8",
  number =       "1",
  pages =        "59--66",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Carpenter:1986:MTA,
  editor =       "B. E. Carpenter and R. W. Doran",
  title =        "{A. M. Turing's} {ACE} Report of 1946 and Other
                 Papers",
  volume =       "10",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  pages =        "vii + 141",
  year =         "1986",
  ISBN =         "0-262-03114-0",
  ISBN-13 =      "978-0-262-03114-1",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Charles Babbage Institute Reprint Series for the
                 History of Computing",
}

@Article{Caffney:1963:ATM,
  author =       "John Caffney",
  title =        "Another Test Matrix for Determinants and Inverses",
  journal =      j-CACM,
  volume =       "6",
  number =       "6",
  pages =        "310",
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Book{Campbell:1979:GIL,
  author =       "S. L. Campbell and C. D. {Meyer, Jr.}",
  title =        "Generalized Inverses of Linear Transformations",
  publisher =    "Pitman",
  address =      "London",
  pages =        "xi + 272",
  year =         "1979",
  ISBN =         "0-486-66693-X",
  ISBN-13 =      "978-0-486-66693-8",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted by Dover, New York, 1991",
}

@Article{Campbell-Kelly:1981:PPA,
  author =       "Martin Campbell-Kelly",
  title =        "Programming the {Pilot ACE}: {Early} Programming
                 Activity at the {National Physical Laboratory}",
  journal =      j-AHC,
  volume =       "3",
  number =       "2",
  pages =        "133--162",
  year =         "1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Campbell-Kelly:1984:RAT,
  author =       "Martin Campbell-Kelly",
  title =        "Review of {``Alan Turing: The Enigma'', by Andrew
                 Hodges}",
  journal =      j-AHC,
  volume =       "6",
  number =       "2",
  pages =        "176--178",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Caprani:1971:ILR,
  author =       "Ole Caprani",
  title =        "Implementation of a Low Round-Off Summation Method",
  journal =      j-BIT,
  volume =       "11",
  pages =        "271--275",
  year =         "1971",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Calvetti:1992:CVS,
  author =       "D. Calvetti and L. Reichel",
  title =        "A {Chebychev-Vandermonde} Solver",
  journal =      j-LAA,
  volume =       "172",
  pages =        "219--229",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Calvetti:1993:FIV,
  author =       "D. Calvetti and L. Reichel",
  title =        "Fast Inversion of {Vandermonde}-Like Matrices
                 Involving Orthogonal Polynomials",
  journal =      j-BIT,
  volume =       "33",
  pages =        "473--484",
  year =         "1993",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Carr:1959:EAF,
  author =       "John W. {Carr III}",
  title =        "Error Analysis in Floating Point Arithmetic",
  journal =      j-CACM,
  volume =       "2",
  number =       "5",
  pages =        "10--15",
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Carter:1991:MFP,
  author =       "Russell Carter",
  title =        "{Y-MP} Floating Point and {Cholesky} Factorization",
  journal =      j-INT-J-HIGH-SPEED-COMPUTING,
  volume =       "3",
  number =       "3/4",
  pages =        "215--222",
  year =         "1991",
  CODEN =        "IHSCEZ",
  ISSN =         "0129-0533",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "International Journal of High Speed Computing",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ijhsc",
}

@Article{Cao:1986:NIH,
  author =       "Wei-Lu Cao and William J. Stewart",
  title =        "A Note on Inverses of {Hessenberg}-Like Matrices",
  journal =      j-LAA,
  volume =       "76",
  pages =        "233--240",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Cauchy:1841:EAP,
  author =       "A. Cauchy",
  title =        "Exercices d'Analyse et de Phys. Math.",
  volume =       "2",
  address =      "Paris",
  year =         "1841",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Cited in \cite{Savage:1954:TIF}",
}

@Article{Cody:1984:PRW,
  author =       "W. J. Cody and J. T. Coonen and D. M. Gay and K.
                 Hanson and D. Hough and W. Kahan and R. Karpinski and
                 J. Palmer and F. N. Ris and D. Stevenson",
  title =        "A Proposed Radix- and Word-Length-Independent Standard
                 for Floating-Point Arithmetic",
  journal =      j-IEEE-MICRO,
  volume =       "4",
  number =       "4",
  pages =        "86--100",
  year =         "1984",
  CODEN =        "IEMIDZ",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@InProceedings{Cline:1982:GLC,
  author =       "Alan K. Cline and Andrew R. Conn and Charles F. {Van
                 Loan}",
  editor =       "J. P. Hennart",
  booktitle =    "Numerical Analysis, Mexico 1981",
  title =        "Generalizing the {LINPACK} Condition Estimator",
  volume =       "909",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "73--83",
  year =         "1982",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Mathematics",
}

@Article{Chan:1983:ACS,
  author =       "Tony F. Chan and Gene H. Golub and Randall J.
                 LeVeque",
  title =        "Algorithms for Computing the Sample Variance:
                 {Analysis} and Recommendations",
  journal =      j-AMER-STAT,
  volume =       "37",
  number =       "3",
  pages =        "242--247",
  year =         "1983",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Concus:1985:BPC,
  author =       "P. Concus and G. H. Golub and G. Meurant",
  title =        "Block Preconditioning for the Conjugate Gradient
                 Method",
  journal =      j-SISSC,
  volume =       "6",
  number =       "1",
  pages =        "220--252",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Conn:1992:LFP,
  author =       "Andrew R. Conn and Nicholas I. M. Gould and Philippe
                 L. Toint",
  title =        "{LANCELOT}: {A Fortran} Package for Large-Scale
                 Nonlinear Optimization (Release {A})",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "xviii + 330",
  year =         "1992",
  ISBN =         "0-387-55470-X",
  ISBN-13 =      "978-0-387-55470-9",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Chatelin:1993:EM,
  author =       "Fran{\c{c}}oise Chatelin",
  title =        "Eigenvalues of Matrices",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xviii + 382",
  year =         "1993",
  ISBN =         "0-471-93538-7",
  ISBN-13 =      "978-0-471-93538-4",
  LCCN =         "QA188 .C44 1993",
  MRclass =      "65-01 (15A18 65F15 65F50)",
  MRnumber =     "1232655 (94d:65002)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "With exercises by Mario Ahu{\'e}s and the author,
                 Translated from the French and with additional material
                 by Walter Ledermann",
  series =       "Pure and applied mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0707/93003430-d.html;
                 http://www.loc.gov/catdir/toc/onix04/93003430.html",
  acknowledgement = ack-nhfb # " and " # ack-rah,
  subject =      "Matrices; Eigenvalues",
  tableofcontents = "Preface / xi \\
                 Preface to the English Edition / xv \\
                 Notation / xvii \\
                 1: Supplements from Linear Algebra / 1 \\
                 1.1 Notation and definitions / 1 \\
                 1.2 The canonical angles between two subspaces / 5 \\
                 1.3 Projections / 8 \\
                 1.4 The gap between two subspaces / 10 \\
                 1.5 Convergence of a sequence of subspaces / 14 \\
                 1.6 Reduction of Square matrices / 18 \\
                 1.7 Spectral decomposition / 27 \\
                 1.8 Rank and linear independence / 31 \\
                 1.9 Hermitian and normal matrices / 32 \\
                 1.10 Non-negative matrices / 33 \\
                 1.11 Sections and Rayleigh quotients / 34 \\
                 1.12 Sylvester's equation / 35 \\
                 1.13 Regular pencils of matrices / 42 \\
                 1.14 Bibliographical comments / 43 \\
                 Exercises / 43 \\
                 2: Elements of Spectral Theory / 61 \\
                 2.1 Revision of some properties of functions of a
                 complex variable / 61 \\
                 2.2 Singularities of the resolvent / 63 \\
                 2.3 The reduced resolvent and the partial inverse / 73
                 \\
                 2.4 The block-reduced resolvent / 76 \\
                 2.5 Linear perturbations of the matrix A / 79 \\
                 2.6 Analyticity of the resolvent / 82 \\
                 2.7 Analyticity of the spectral projection / 84 \\
                 2.8 The Rellich--Kato expansions / 85 \\
                 2.9 The Rayleigh--Schr{\"o}dinger expansions / 86 \\
                 2.10 Non-linear equation and Newton's method / 89 \\
                 2.11 Modified methods / 92 \\
                 2.12 The local approximate inverse and the method of
                 residual correction / 95 \\
                 2.13 Bibliographical comments / 98 \\
                 Exercises / 98 \\
                 3: Why Compute Eigenvalues? / 111 \\
                 3.1 Differential equations and difference equations /
                 111 \\
                 3.2 Markov chains / 114 \\
                 3.3 Theory of economics / 117 \\
                 3.4 Factorial analysis of data / 119 \\
                 3.5 The dynamics of structures / 120 \\
                 3.6 Chemistry / 122 \\
                 3.7 Fredholm's integral equation / 124 \\
                 3.8 Bibliographical comments / 126 \\
                 Exercises / 126 \\
                 4: Error Analysis / 149 \\
                 4.1 Revision of the conditioning of a System / 149 \\
                 4.2 Stability of a spectral problem / 150 \\
                 4.3 A priori analysis of errors / 165 \\
                 4.4 A posteriori analysis of errors / 170 \\
                 4.5 A is almost diagonal / 177 \\
                 4.6 A is Hermitian / 180 \\
                 4.7 Bibliographical comments / 190 \\
                 Exercises / 191 \\
                 5: Foundations of Methods for Computing Eigenvalues /
                 205 \\
                 5.1 Convergence of a Krylov sequence of subspaces / 205
                 \\
                 5.2 The method of subspace iteration / 208 \\
                 5.3 The power method / 213 \\
                 5.4 The method of inverse iteration / 217 \\
                 5.5 The $Q R$ algorithm / 221 \\
                 5.6 Hermitian matrices / 226 \\
                 5.7 The $Q Z$ algorithm / 226 \\
                 5.8 Newton's method and the Rayleigh quotient iteration
                 / 227 \\
                 5.9 Modified Newton's method and simultaneous inverse
                 iterations / 228 \\
                 5.10 Bibliographical comments / 235 \\
                 Exercises / 235 \\
                 6: Numerical Methods for Large Matrices / 251 \\
                 6.1 The principle of the methods / 251 \\
                 6.2 The method of subspace iteration revisited / 253
                 \\
                 6.3 The Lanczos method / 257 \\
                 6.4 The block Lanczos method / 266 \\
                 6.5 The generalized problem $K x = I M x$ / 270 \\
                 6.6 Arnoldi's method / 272 \\
                 6.7 Oblique projections / 279 \\
                 6.8 Bibliographical comments / 280 \\
                 Exercises / 281 \\
                 7: Chebyshev's Iterative Methods / 293 \\
                 7.1 Elements of the theory of uniform approximation for
                 a compact set in C / 293 \\
                 7.2 Chebyshev polynomials of a real variable / 299 \\
                 7.3 Chebyshev polynomials of a complex variable / 300
                 \\
                 7.4 The Chebyshev acceleration for the power method /
                 304 \\
                 7.5 The Chebyshev iteration method / 305 \\
                 7.6 Simultaneous Chebyshev iterations (with projection)
                 / 308 \\
                 7.7 Determination of the optimal parameters / 311 \\
                 7.8 Least Squares polynomials on a polygon / 312 \\
                 7.9 The hybrid methods of Saad / 314 \\
                 7.10 Bibliographical comments / 316 \\
                 Exercises / 316 \\
                 Appendices / 323 \\
                 A Solution to Exercises / 323 \\
                 B References for Exercises / 367 \\
                 C References / 371 \\
                 Index / 378",
}

@InProceedings{Brunet:1986:CTS,
  author =       "Marie-Christine Brunet and Fran{\c{c}}oise Chatelin",
  editor =       "R. Vichnevetsky and J. Vignes",
  booktitle =    "Numerical Mathematics and Applications",
  title =        "{CESTAC}, a Tool for a Stochastic Round-off Error
                 Analysis in Scientific Computing",
  publisher =    "Elsevier Science Publishers B.V. (North-Holland)",
  address =      pub-NH:adr,
  pages =        "11--20",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Chatelin:1990:PRE,
  author =       "Fran{\c{c}}oise Chatelin and Marie-Christine Brunet",
  editor =       "M. G. Cox and S. J. Hammarling",
  booktitle =    "Reliable Numerical Computation",
  title =        "A Probabilistic Round-off Error Propagation Model.
                 {Application} to the Eigenvalue Problem",
  publisher =    pub-OUP,
  pages =        "139--160",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@PhdThesis{Cheng:1998:SIM,
  author =       "Sheung Hun Cheng",
  title =        "Symmetric Indefinite Matrices: Linear System Solvers
                 and Modified Inertia Problems",
  school =       inst-U-Manchester,
  address =      inst-U-Manchester:adr,
  pages =        "150",
  month =        jan,
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Chan:1988:EWC,
  author =       "Tony F. Chan and David E. Foulser",
  title =        "Effectively Well-Conditioned Linear Systems",
  journal =      j-SISSC,
  volume =       "9",
  number =       "6",
  pages =        "963--969",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Chatelin:1992:ECT,
  author =       "Fran{\c{c}}oise Chatelin and Val{\'e}rie Frayss{\'e}",
  editor =       "R. Beauwens and P. de Groen",
  booktitle =    "Iterative Methods in Linear Algebra",
  title =        "Elements of a Condition Theory for the Computational
                 Analysis of Algorithms",
  publisher =    "Elsevier Science Publishers B.V. (North-Holland)",
  address =      pub-NH:adr,
  pages =        "15--25",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Chaitin-Chatelin:1996:LFP,
  author =       "Fran{\c{c}}oise Chaitin-Chatelin and Val{\'e}rie
                 Frayss{\'e}",
  title =        "Lectures on Finite Precision Computations",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xv + 235",
  year =         "1996",
  ISBN =         "0-89871-358-7",
  ISBN-13 =      "978-0-89871-358-9",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Chartres:1967:CEB,
  author =       "Bruce A. Chartres and James C. Geuder",
  title =        "Computable Error Bounds for Direct Solution of Linear
                 Equations",
  journal =      j-ACM,
  volume =       "14",
  number =       "1",
  pages =        "63--71",
  year =         "1967",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Chu:1985:NEE,
  author =       "Eleanor Chu and Alan George",
  title =        "A Note on Estimating the Error in {Gaussian}
                 Elimination Without Pivoting",
  journal =      j-SIGNUM,
  volume =       "20",
  number =       "2",
  pages =        "2--7",
  year =         "1985",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J690",
}

@Article{Cohen:1983:CCP,
  author =       "Marty S. Cohen and T. E. Hull and V. Carl Hamacher",
  title =        "{CADAC}: {A} Controlled-Precision Decimal Arithmetic
                 Unit",
  journal =      j-IEEE-C,
  volume =       "C-32",
  number =       "4",
  pages =        "370--377",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Chan:1992:SAR,
  author =       "T. F. Chan and P. C. Hansen",
  title =        "Some Applications of the Rank Revealing {QR}
                 Factorization",
  journal =      j-SISSC,
  volume =       "13",
  number =       "3",
  pages =        "727--741",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Christiansen:1994:ECN,
  author =       "S{\o}ren Christiansen and Per Christian Hansen",
  title =        "The Effective Condition Number Applied to Error
                 Analysis of Certain Boundary Collocation Methods",
  journal =      j-JCAM,
  volume =       "54",
  pages =        "15--36",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Cheng:2001:PIB,
  author =       "Sheung Hun Cheng and Nicholas J. Higham",
  editor =       "Rizos Sakellariou and John Keane and John Gurd and Len
                 Freeman",
  booktitle =    "Euro-Par \textup{2001}, Parallel Processing",
  title =        "Parallel Implementation of a Block Algorithm for
                 Matrix 1-Norm Estimation",
  volume =       "2150",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "568--577",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Computer Science",
}

@TechReport{Cheng:2001:ILB,
  author =       "Sheung Hun Cheng and Nicholas J. Higham",
  title =        "Implementation for {LAPACK} of a Block Algorithm for
                 Matrix 1-Norm Estimation",
  type =         t-NAREP,
  number =       "No. 393",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "19",
  month =        aug,
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "LAPACK Working Note 152",
}

@Article{Cheng:1998:MCA,
  author =       "Sheung Hun Cheng and Nicholas J. Higham",
  title =        "A Modified {Cholesky} Algorithm Based on a Symmetric
                 Indefinite Factorization",
  journal =      j-SIMAX,
  volume =       "19",
  number =       "4",
  pages =        "1097--1110",
  month =        oct,
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Chandrasekaran:1994:BEE,
  author =       "Shivkumar Chandrasekaran and Ilse C. F. Ipsen",
  title =        "Backward Errors for Eigenvalue and Singular Value
                 Decompositions",
  journal =      j-NUM-MATH,
  volume =       "68",
  pages =        "215--223",
  year =         "1994",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Chandrasekaran:1995:SSC,
  author =       "Shivkumar Chandrasekaran and Ilse C. F. Ipsen",
  title =        "On the Sensitivity of Solution Components in Linear
                 Systems of Equations",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "1",
  pages =        "93--112",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Cheng:2001:ALM,
  author =       "Sheung Hun Cheng and Nicholas J. Higham and Charles S.
                 Kenney and Alan J. Laub",
  title =        "Approximating the Logarithm of a Matrix to Specified
                 Accuracy",
  journal =      j-SIMAX,
  volume =       "22",
  number =       "4",
  pages =        "1112--1125",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Chan:1979:CSD,
  author =       "Tony F. Chan and John Gregg Lewis",
  title =        "Computing Standard Deivations: {Accuracy}",
  journal =      j-CACM,
  volume =       "22",
  number =       "9",
  pages =        "526--531",
  year =         "1979",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Chan:1983:DEE,
  author =       "N. N. Chan and Kim-Hung Li",
  title =        "Diagonal Elements and Eigenvalues of a Real Symmetric
                 Matrix",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "91",
  pages =        "562--566",
  year =         "1983",
  CODEN =        "JMANAK",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
}

@Article{Chan:1983:AFS,
  author =       "N. N. Chan and Kim-Hung Li",
  title =        "{Algorithm 115}: {A} {FORTRAN} Subroutine for Finding
                 a Real Symmetric Matrix with Prescribed Diagonal
                 Elements and Eigenvalues",
  journal =      j-COMP-J,
  volume =       "26",
  number =       "2",
  pages =        "184--186",
  year =         "1983",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Chan:1996:CGM,
  author =       "Raymond H. Chan and Michael K. Ng",
  title =        "Conjugate Gradient Methods for {Toeplitz} Systems",
  journal =      j-SIREV,
  volume =       "38",
  number =       "3",
  pages =        "427--482",
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Cho:1968:TDC,
  author =       "Choong Yun Cho",
  title =        "On the Triangular Decomposition of {Cauchy} Matrices",
  journal =      j-MATH-COMP,
  volume =       "2",
  number =       "104",
  pages =        "819--825",
  year =         "1968",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Choi:1983:TTH,
  author =       "Man-Duen Choi",
  title =        "Tricks or Treats with the {Hilbert} Matrix",
  journal =      j-AMM,
  volume =       "90",
  pages =        "301--312",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Chang:2001:CPA,
  author =       "{Xiao-Wen} Chang and Christopher C. Paige",
  title =        "Componentwise Perturbation Analyses for the {QR}
                 Factorization",
  journal =      j-NUM-MATH,
  volume =       "88",
  pages =        "319--345",
  year =         "2001",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Chang:1998:SLF,
  author =       "{Xiao-Wen} Chang and Christopher C. Paige",
  title =        "On the Sensitivity of the {LU} Factorization",
  journal =      j-BIT,
  volume =       "38",
  number =       "3",
  pages =        "486--501",
  year =         "1998",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Chu:2000:FRA,
  author =       "Moody T. Chu",
  title =        "A Fast Recursive Algorithm for Constructing Matrices
                 with Prescribed Eigenvalues and Singular Values",
  journal =      j-SINUM,
  volume =       "37",
  number =       "3",
  pages =        "1004--1020",
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Chu:1987:SME,
  author =       "{King-wah} Eric Chu",
  title =        "The Solution of the Matrix Equations {$AXB - CXD = E$}
                 and {$(YA - DZ, YC - BZ) = (E,F)$}",
  journal =      j-LAA,
  volume =       "93",
  pages =        "93--105",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Chu:1999:CMP,
  author =       "Moody T. Chu",
  title =        "On Constructing Matrices with Prescribed Singular
                 Values and Diagonal Elements",
  journal =      j-LAA,
  volume =       "288",
  pages =        "11--22",
  year =         "1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{OCinneide:1993:EPT,
  author =       "Colm Art O'Cinneide",
  title =        "Entrywise Perturbation Theory and Error Analysis for
                 {Markov} Chains",
  journal =      j-NUM-MATH,
  volume =       "65",
  pages =        "109--120",
  year =         "1993",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Coomes:1995:RCS,
  author =       "Brian A. Coomes and H{\"u}seyin Ko{\c{c}}ak and
                 Kenneth J. Palmer",
  title =        "Rigorous Computational Shadowing of Orbits of Ordinary
                 Differential Equations",
  journal =      j-NUM-MATH,
  volume =       "69",
  number =       "4",
  pages =        "401--421",
  year =         "1995",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Clenshaw:1955:NSC,
  author =       "C. W. Clenshaw",
  title =        "A Note on the Summation of {Chebyshev} Series",
  journal =      j-MTAC,
  volume =       "9",
  number =       "51",
  pages =        "118--120",
  year =         "1955",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Cline:1973:EMS,
  author =       "A. K. Cline",
  title =        "An Elimination Method for the Solution of Linear Least
                 Squares Problems",
  journal =      j-SINUM,
  volume =       "10",
  number =       "2",
  pages =        "283--289",
  year =         "1973",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Clinger:1990:HRF,
  author =       "William D. Clinger",
  title =        "How to Read Floating Point Numbers Accurately",
  journal =      j-SIGPLAN,
  volume =       "25",
  number =       "6",
  pages =        "92--101",
  year =         "1990",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Article{Clenshaw:1984:BFP,
  author =       "C. W. Clenshaw and F. W. J. Olver",
  title =        "Beyond Floating Point",
  journal =      j-ACM,
  volume =       "31",
  number =       "2",
  pages =        "319--328",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Codenotti:2001:RAF,
  author =       "B. Codenotti and M. Leoncini and F. P. Preparata",
  title =        "The Role of Arithmetic in Fast Parallel Matrix
                 Inversion",
  journal =      j-ALGORITHMICA,
  volume =       "30",
  number =       "4",
  pages =        "685--707",
  year =         "2001",
  CODEN =        "ALGOEJ",
  ISSN =         "0178-4617 (print), 1432-0541 (electronic)",
  ISSN-L =       "0178-4617",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Algorithmica",
  journal-URL =  "http://link.springer.com/journal/453",
}

@Article{Cline:1976:SUL,
  author =       "R. E. Cline and R. J. Plemmons",
  title =        "{$l_2$}-Solutions to Underdetermined Linear Systems",
  journal =      j-SIREV,
  volume =       "18",
  number =       "1",
  pages =        "92--106",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Cline:1983:SCE,
  author =       "A. K. Cline and R. K. Rew",
  title =        "A Set of Counter-Examples to Three Condition Number
                 Estimators",
  journal =      j-SISSC,
  volume =       "4",
  number =       "4",
  pages =        "602--611",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Cline:1979:ECN,
  author =       "A. K. Cline and C. B. Moler and G. W. Stewart and J.
                 H. Wilkinson",
  title =        "An Estimate for the Condition Number of a Matrix",
  journal =      j-SINUM,
  volume =       "16",
  number =       "2",
  pages =        "368--375",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Cody:1993:AFS,
  author =       "W. J. Cody and Jerome T. Coonen",
  title =        "{ALGORITHM 722}: {Functions} to Support the {IEEE}
                 Standard for Binary Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "443--451",
  year =         "1993",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Book{Conte:1980:ENA,
  author =       "Samuel D. Conte and Carl de Boor",
  title =        "Elementary Numerical Analysis: {An} Algorithmic
                 Approach",
  publisher =    pub-MH,
  address =      "Tokyo",
  edition =      "Third",
  pages =        "xii + 432",
  year =         "1980",
  ISBN =         "0-07-066228-2",
  ISBN-13 =      "978-0-07-066228-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Cody:1973:SDN,
  author =       "William J. {Cody, Jr.}",
  title =        "Static and Dynamic Numerical Characteristics of
                 Floating-Point Arithmetic",
  journal =      j-IEEE-C,
  volume =       "C-22",
  number =       "6",
  pages =        "598--601",
  year =         "1973",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Cody:1982:ITF,
  author =       "W. J. Cody",
  editor =       "Paul C. Messina and Almerico Murli",
  booktitle =    "Problems and Methodologies in Mathematical Software
                 Production",
  title =        "Implementation and Testing of Function Software",
  volume =       "142",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "24--47",
  year =         "1982",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Computer Science",
}

@Article{Cody:1988:AMS,
  author =       "W. J. Cody",
  title =        "{ALGORITHM 665 MACHAR}: {A} Subroutine to Dynamically
                 Determine Machine Parameters",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "303--311",
  year =         "1988",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@InProceedings{Cody:1988:FPS,
  author =       "W. J. Cody",
  editor =       "Ramon E. Moore",
  booktitle =    "Reliability in Computing: {The} Role of Interval
                 Methods in Scientific Computing",
  title =        "Floating-Point Standards---{Theory} and Practice",
  publisher =    pub-AP # ", " # pub-AP:adr-B,
  pages =        "99--107",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Cody:1993:ACP,
  author =       "W. J. Cody",
  title =        "Algorithm 714. {CELEFUNT}: {A} Portable Test Package
                 for Complex Elementary Functions",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "121",
  year =         "1993",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Cohen:1974:NPS,
  author =       "A. M. Cohen",
  title =        "A Note on Pivot Size in {Gaussian} Elimination",
  journal =      j-LAA,
  volume =       "8",
  pages =        "361--368",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Cohen:1975:IPM,
  author =       "A. M. Cohen",
  title =        "The Inverse of a {Pascal} Matrix",
  journal =      j-MATH-GAZ,
  volume =       "59",
  number =       "408",
  pages =        "111--112",
  year =         "1975",
  CODEN =        "MAGAAS",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}

@InProceedings{Cox:1998:SHQ,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  editor =       "D. F. Griffiths and D. J. Higham and G. A. Watson",
  booktitle =    "Numerical Analysis \textup{1997}, Proceedings of the
                 \textup{17}th Dundee Biennial Conference",
  title =        "Stability of {Householder QR} Factorization for
                 Weighted Least Squares Problems",
  volume =       "380",
  publisher =    pub-AWLongman # ", " # pub-AWLongman:adr,
  pages =        "57--73",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Pitman Research Notes in Mathematics",
}

@Article{Cox:1999:ASN,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  title =        "Accuracy and Stability of the Null Space Method for
                 Solving the Equality Constrained Least Squares
                 Problem",
  journal =      j-BIT,
  volume =       "39",
  number =       "1",
  pages =        "34--50",
  year =         "1999",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Cox:1999:BEB,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  title =        "Backward Error Bounds for Constrained Least Squares
                 Problems",
  journal =      j-BIT,
  volume =       "39",
  number =       "2",
  pages =        "210--227",
  year =         "1999",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Cox:1999:RWB,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  title =        "Row-Wise Backward Stable Elimination Methods for the
                 Equality Constrained Least Squares Problem",
  journal =      j-SIMAX,
  volume =       "21",
  number =       "1",
  pages =        "313--326",
  year =         "1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Cornea-Hasegan:1999:IFP,
  author =       "Marius Cornea-Hasegan and Bob Norin",
  title =        "{IA-64} Floating-Point Operations and the {IEEE}
                 Standard for Binary Floating-Point Arithmetic",
  journal =      j-INTEL-TECH-J,
  volume =       "Q4",
  year =         "1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "\path|http://developer.intel.com/technology/itj/|",
}

@InProceedings{cool90,
  author =       "James W. Cooley",
  editor =       "Stephen G. Nash",
  booktitle =    "A History of Scientific Computing",
  title =        "How the {FFT} Gained Acceptance",
  publisher =    pub-AW # ", " # pub-AW:adr,
  pages =        "133--140",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Cooley:1994:LFD,
  author =       "James W. Cooley",
  editor =       "J. David Brown and Moody T. Chu and Donald C. Ellison
                 and Robert J. Plemmons",
  booktitle =    "Proceedings of the {Cornelius Lanczos} International
                 Centenary Conference",
  title =        "{Lanczos} and the {FFT}: {A} Discovery Before Its
                 Time",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "3--9",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Coonen:1981:UDN,
  author =       "Jerome T. Coonen",
  title =        "Underflow and the Denormalized Numbers",
  journal =      j-COMPUTER,
  volume =       "14",
  pages =        "75--87",
  year =         "1981",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computer",
  journal-URL =  "http://www.computer.org/portal/web/csdl/magazines/computer",
}

@Article{Cope:1979:BSL,
  author =       "J. E. Cope and B. W. Rust",
  title =        "Bounds on Solutions of Linear Systems with Inaccurate
                 Data",
  journal =      j-SINUM,
  volume =       "16",
  number =       "6",
  pages =        "950--963",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Clenshaw:1989:LIA,
  author =       "C. W. Clenshaw and F. W. J. Olver and P. R. Turner",
  editor =       "Peter R. Turner",
  booktitle =    "Numerical Analysis and Parallel Processing, Lancaster
                 1987",
  title =        "Level-Index Arithmetic: {An} Introductory Survey",
  volume =       "1397",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "95--168",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Mathematics",
}

@Article{Cottle:1974:MSC,
  author =       "Richard W. Cottle",
  title =        "Manifestations of the {Schur} Complement",
  journal =      j-LAA,
  volume =       "8",
  pages =        "189--211",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Cooley:1965:AMC,
  author =       "James W. Cooley and John W. Tukey",
  title =        "An Algorithm for the Machine Calculation of Complex
                 {Fourier} Series",
  journal =      j-MATH-COMP,
  volume =       "19",
  number =       "90",
  pages =        "297--301",
  year =         "1965",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Cooley:1993:OPF,
  author =       "James W. Cooley and John W. Tukey",
  title =        "On the Origin and Publication of the {FFT} Paper",
  journal =      "Current Contents",
  number =       "51--52",
  pages =        "8--9",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Cody:1980:SME,
  author =       "William J. {Cody, Jr.} and William Waite",
  title =        "Software Manual for the Elementary Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "x + 269",
  year =         "1980",
  ISBN =         "0-13-822064-6",
  ISBN-13 =      "978-0-13-822064-8",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Coppersmith:1987:MMA,
  author =       "Don Coppersmith and Shmuel Winograd",
  booktitle =    "Proceedings of the Nineteenth Annual ACM Symposium on
                 Theory of Computing",
  title =        "Matrix Multiplication via Arithmetic Progressions",
  publisher =    "ACM Press, New York",
  pages =        "1--6",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Chang:1996:NPA,
  author =       "{Xiao-Wen} Chang and Christopher C. Paige and G. W.
                 Stewart",
  title =        "New Perturbation Analyses for the {Cholesky}
                 Factorization",
  journal =      j-IMAJNA,
  volume =       "16",
  number =       "4",
  pages =        "457--484",
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Chang:1997:PAQ,
  author =       "{Xiao-Wen} Chang and Christopher C. Paige and G. W.
                 Stewart",
  title =        "Perturbation Analyses for the {QR} Factorization",
  journal =      j-SIMAX,
  volume =       "18",
  number =       "3",
  pages =        "775--791",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Crary:1979:VPN,
  author =       "Fred D. Crary",
  title =        "A Versatile Precompiler for Nonstandard Arithmetics",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "204--217",
  year =         "1979",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Book{Inc:1989:UMS,
  author =       "Cray Research Inc.",
  key =          "Cray",
  title =        "{UNICOS} Math and Scientific Library Reference
                 Manual",
  publisher =    "Number SR-2081, Version 5.0",
  address =      "Eagan, MN, USA",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Crout:1941:SME,
  author =       "Prescott D. Crout",
  title =        "A Short Method for Evaluating Determinants and Solving
                 Systems of Linear Equations with Real or Complex
                 Coefficients",
  journal =      j-TRANS-AMER-INST-ELEC-ENG,
  volume =       "60",
  pages =        "1235--1241",
  year =         "1941",
  CODEN =        "TAEEA5",
  ISSN =         "0096-3860",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Transactions of the American Institute of Electrical Engineers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
}

@Article{Cryer:1968:PSG,
  author =       "Colin W. Cryer",
  title =        "Pivot Size in {Gaussian} Elimination",
  journal =      j-NUM-MATH,
  volume =       "12",
  pages =        "335--345",
  year =         "1968",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Cryer:1973:FTP,
  author =       "Colin W. Cryer",
  title =        "The {$LU$}-Factorization of Totally Positive
                 Matrices",
  journal =      j-LAA,
  volume =       "7",
  pages =        "83--92",
  year =         "1973",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Cryer:1976:SPT,
  author =       "Colin W. Cryer",
  title =        "Some Properties of Totally Positive Matrices",
  journal =      j-LAA,
  volume =       "15",
  pages =        "1--25",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Csanky:1976:FPM,
  author =       "L. Csanky",
  title =        "Fast Parallel Matrix Inversion Algorithms",
  journal =      j-SICOMP,
  volume =       "5",
  number =       "4",
  pages =        "618--623",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Curtis:1972:ASM,
  author =       "A. R. Curtis and J. K. Reid",
  title =        "On the Automatic Scaling of Matrices for {Gaussian}
                 Elimination",
  journal =      j-JIMA,
  volume =       "10",
  pages =        "118--124",
  year =         "1972",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Cybenko:1986:CME,
  author =       "George Cybenko and Charles F. {Van Loan}",
  title =        "Computing the Minimum Eigenvalue of a Symmetric
                 Positive Definite {Toeplitz} matrix",
  journal =      j-SISSC,
  volume =       "7",
  number =       "1",
  pages =        "123--131",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Dahlquist:1974:NM,
  author =       "Germund Dahlquist and {\AA}ke Bj{\"o}rck and Ned
                 Anderson",
  title =        "Numerical Methods",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xviii + 573",
  year =         "1974",
  ISBN =         "0-13-627315-7",
  ISBN-13 =      "978-0-13-627315-8",
  LCCN =         "QA297 .D131 1969",
  bibdate =      "Tue Dec 14 22:44:59 1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "Translated by Ned Anderson.",
  series =       "Prentice-Hall Series in Automatic Computation",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "1: Some General Principles of Numerical
                 Calculation / 1 \\
                 2: How to Obtain and Estimate Accuracy in Numerical
                 Calculations / 21 \\
                 3: Numerical Uses of Series / 60 \\
                 4: Approximation of Functions / 81 \\
                 5: Numerical Linear Algebra / 137 \\
                 6: Nonlinear Equations / 218 \\
                 7: Finite Differences with Applications to Numerical
                 Integration, Differentiation, and Interpolation / 255
                 \\
                 8: Differential Equations / 330 \\
                 9: Fourier Methods / 405 \\
                 10: Optimization / 422 \\
                 11: The Monte Carlo Method and Simulation / 448 \\
                 12: Solutions to Problems / 465 \\
                 13: Bibliography and Published Algorithms / 536 \\
                 Index by Subject to Algorithms, 1960--1970 / 548 \\
                 Appendix Tables / 563 \\
                 Index / 565",
  tableofcontents = "Preface / xvii \\
                 Conventions / xix \\
                 1: Some General Principles of Numerical Calculation / 1
                 \\
                 1.1. Introduction / 1 \\
                 1.2. Some Common Ideas and Concepts in Numerical
                 Methods / 2 \\
                 1.3. Numerical Problems and Algorithms / 13 \\
                 1.3.1. Definitions / 13 \\
                 1.3.2. Recursive Formulas; Homer's Rule / 14 \\
                 1.3.3. An Example of Numerical Instability / 16 \\
                 2: How to Obtain and Estimate Accuracy in Numerical
                 Calculations / 21 \\
                 2.1. Basic Concepts in Error Estimation / 21 \\
                 2.1.1. Introduction / 21 \\
                 2.1.2. Sources of Error / 22 \\
                 2.1.3. Absolute and Relative Errors / 23 \\
                 2.1.4. Rounding and Chopping / 24 \\
                 2.2 Propagation of Errors / 26 \\
                 2.2.1. Simple Examples of Error Analysis / 26 \\
                 2.2.2. The General Formula for Error Propagation;
                 Maximum Error and Standard Error / 29 \\
                 2.2.3. On the Practical Application of Error Estimation
                 / 34 \\
                 2.2.4. The Use of Experimental Perturbations / 36 \\
                 2.2.5. Automatic Control of Accuracy / 37 \\
                 2.3. Number Systems; Floating and Fixed Representation
                 / 42 \\
                 2.3.1. The Position System / 42 \\
                 2.3.2. Floating and Fixed Representation / 43 \\
                 2.3.3. Floating Decimal Point / 44 \\
                 2.3.4. Fixed Decimal Point / 46 \\
                 2.3.5. Round-off Errors in Computation with Floating
                 Arithmetic Operations / 46 \\
                 2.4. Backward Error Analysis; Condition Numbers / 51
                 \\
                 2.4.1. Backward Error Analysis / 51 \\
                 2.4.2. Condition Numbers for Problems and Algorithms /
                 53 \\
                 2.4.3. Geometrical Illustration of Error Analysis / 56
                 \\
                 3: Numerical Uses of Series / 60 \\
                 3.1. Elementary Uses of Series / 60 \\
                 3.1.1. Simple Examples / 60 \\
                 3.1.2. Estimating the Remainder / 62 \\
                 3.1.3. Power Series / 65 \\
                 3.2. Acceleration of Convergence / 71 \\
                 3.2.1. Slowly Converging Alternating Series / 71 \\
                 3.2.2. Slowly Converging Series with Positive Terms /
                 73 \\
                 3.2.3. Other Simple Ways to Accelerate Convergence / 74
                 \\
                 3.2.4. Ill-Conditioned Series / 75 \\
                 3.2.5. Numerical Use of Divergent Series / 77 \\
                 4: Approximation of Functions / 81 \\
                 4.1. Basic Concepts in Approximation / 81 \\
                 4.1.1. Introduction / 81 \\
                 4.1.2. The Idea of a Function Space / 84 \\
                 4.1.3. Norms and Seminorms / 85 \\
                 4.1.4. Approximation of Functions as a Geometric
                 Problem in Function Space / 87 \\
                 4.2. The Approximation of Functions by the Method of
                 Least Squares / 88 \\
                 4.2.t. Statement of the Problems / 88 \\
                 4.2.2. Orthogonal Systems / 89 \\
                 4.2.3. Solution of the Approximation Problem / 92 \\
                 4.3. Polynomials / 97 \\
                 4.3.1. Basic Terminology; the Weierstrass Approximation
                 Theorem / 97 \\
                 4.3.2. Triangle Families of Polynomials / 98 \\
                 4.3.3. A Triangle Family and Its Application to
                 Interpolation / 99 \\
                 4.3.4. Equidistant Interpolation and the Runge
                 Phenomenon / 101 \\
                 4.4. Orthogonal Polynomials and Applications / 104 \\
                 4.4.1. Tchebycheff Polynomials / 104 \\
                 4.4.2. Tchebycheff Interpolation and Smoothing / 106
                 \\
                 4.4.3. General Theory of Orthogonal Polynomials / 108
                 \\
                 4.4.4. Legendre Polynomials and Gram Polynomials / 113
                 \\
                 4.5. Complementary Observations on Polynomial
                 Approximation / 117 \\
                 4.5.1. Summary of the Use of Polynomials / 117 \\
                 4.5.2. Some Inequalities for $E_n(f)$ with Applications
                 to the Computation of Linear Functionals / 120 \\
                 4.5.3. Approximation in the Maximum Norm / 124 \\
                 4.5.4. Economization of Power Series; Standard
                 Functions / 125 \\
                 4.5.5. Some Statistical Aspects of the Method of Least
                 Squares / 126 \\
                 4.6. Spline Functions / 131 \\
                 5: Numerical Linear Algebra / 137 \\
                 5,1. Introduction / 137 \\
                 5.2. Basic Concepts of Linear Algebra / 138 \\
                 5.2.1. Fundamental Definitions / 138 \\
                 5.2.2. Partitioned Matrices / 140 \\
                 5.2.3. Linear Vector Spaces / 141 \\
                 5.2.4. Eigenvalues and Similarity Transformations / 142
                 \\
                 5.2.5. Singular-Value Decomposition and Pseudo-Inverse
                 / 143 \\
                 5.3. Direct Methods for Solving Systems of Linear
                 Equations / 146 \\
                 5.3.1. Triangular Systems / 146 \\
                 5.3.2. Gaussian Elimination / 147 \\
                 5.3.3. Pivoting Strategies / 150 \\
                 5.3.4. $L U$-Decomposition / 152 \\
                 5.3.5. Compact Schemes for Gaussian Elimination / 157
                 \\
                 5.3.6. Inverse Matrices / 159 \\
                 5.4. Special Matrices / 162 \\
                 5.4.1. Symmetric Positive-Definite Matrices / 162 \\
                 5.4.2. Band Matrices / 165 \\
                 5.4.3. Large-Scale Linear Systems / 168 \\
                 5.4.4. Other Sparse Matrices / 169 \\
                 5.5. Error Analysis for Linear Systems / 174 \\
                 5.5.1. An Ill-Conditioned Example / 174 \\
                 5.5.2. Vector and Matrix Norms / 175 \\
                 5.5.3. Perturbation Analysis / 176 \\
                 5.5.4. Rounding Errors in Gaussian Elimination / 177
                 \\
                 5.5.5. Scaling of Linear Systems / 181 \\
                 5.5.6. Iterative Improvement of a Solution / 183 \\
                 5.6. Iterative Methods / 188 \\
                 5.7. Overdetermined Linear Systems / 196 \\
                 5.7.1. The Normal Equations / 197 \\
                 5.7.2. Orthogonalization Methods / 201 \\
                 5.7.3. Improvement of Least-Squares Solutions / 204 \\
                 5.7.4. Least-Squares Problems with Linear Constraints /
                 205 \\
                 5.8. Computation of Eigenvalues and Eigenvectors / 208
                 \\
                 5.8.1. The Power Method / 209 \\
                 5.8.2. Methods Based on Similarity Transformations /
                 211 \\
                 5.8.3. Eigenvalues by Equation Solving / 215 \\
                 5.8.4. The $Q R$-Algorithm / 216 \\
                 6: Nonlinear Equations / 218 \\
                 6.1. Introduction / 218 \\
                 6.2. Initial Approximations; Starting Methods / 219 \\
                 6.2.1. Introduction / 219 \\
                 6.2.2. The Bisection Method / 220 \\
                 6.3. Newton--Raphson's Method / 222 \\
                 6.4. The Secant Method / 227 \\
                 6.4.1. Description of the Method / 227 \\
                 6.4.2. Error Analysis for the Secant Method / 228 \\
                 6.4.3. Regula Falsi / 230 \\
                 6.4.4. Other Related Methods / 230 \\
                 6.5. General Theory of Iteration Methods / 233 \\
                 6.6. Error Estimation and Attainable Accuracy in
                 Iteration Methods / 238 \\
                 6.6.1. Error Estimation / 238 \\
                 6.6.2. Attainable Accuracy; Termination Criteria / 240
                 \\
                 6.7. Multiple Roots / 242 \\
                 6.8. Algebraic Equations / 243 \\
                 6.8.1. Introduction / 243 \\
                 6.8.2. Deflation / 245 \\
                 6.8.3. Ill-Conditioned Algebraic Equations / 246 \\
                 6.9. Systems of Nonlinear Equations / 248 \\
                 6.9.1. Iteration / 249 \\
                 6.9.2. Newton--Raphson's Method and Some Modifications
                 / 249 \\
                 6.9.3. Other Methods / 251 \\
                 7: Finite Differences with Applications to Numerical
                 Integration, Differentiation, and Interpolation / 255
                 \\
                 7.1. Difference Operators and Their Simplest Properties
                 / 255 \\
                 7.2. Simple Methods for Deriving Approximation Formulas
                 and Error Estimates / 263 \\
                 7.2.1. Statement of the Problems and Some Typical
                 Examples / 263 \\
                 7.2.2, Repeated Richardson Extrapolation / 269 \\
                 7.3. Interpolation / 275 \\
                 7.3.1. Introduction / 275 \\
                 7.3.2. When is Linear Interpolation Sufficient? / 276
                 \\
                 7.3.3. Newton's General Interpolation Formula / 277 \\
                 7.3.4. Formulas for Equidistant Interpolation / 279 \\
                 7.3.5. Complementary Remarks on Interpolation / 282 \\
                 7.3.6. Lagrange's Interpolation Formula / 284 \\
                 7.3.7. Hermite Interpolation / 285 \\
                 7.3.8. Inverse Interpolation / 286 \\
                 7.4. Numerical Integration / 290 \\
                 7.4.1. The Rectangle Rule, Trapezoidal Rule, and
                 Romberg's Method / 291 \\
                 7.4.2. The Truncation Error of the Trapezoidal Rule /
                 293 \\
                 7.4.3. Some Difficulties and Possibilities in Numerical
                 Integration / 294 \\
                 7.4.4. The Euler--Maclaurin Summation Formula / 297 \\
                 7.4.5. Uses of the Euler--Maclaurin Formula / 300 \\
                 7.4.6. Other Methods for Numerical Integration / 302
                 \\
                 7.5. Numerical Differentiation / 307 \\
                 7.6. The Calculus of Operators / 311 \\
                 7.6.1. Operator Algebra / 311 \\
                 7.6.2. Operator Series with Applications / 312 \\
                 7.7. Functions of Several Variables / 318 \\
                 7.7.1. Working with One Variable at a Time / 319 \\
                 7.7.2. Rectangular Grids / 319 \\
                 7.7.3. Irregular Triangular Grids / 322 \\
                 8: Differential Equations / 330 \\
                 8.1. Theoretical Background / 330 \\
                 8.1.1. Initial-Value Problems for Ordinary Differential
                 Equations / 330 \\
                 8.1.2. Error Propagation / 333 \\
                 8.1.3. Other Differential Equation Problems / 337 \\
                 8.2. Euler's Method, with Repeated Richardson
                 Extrapolation / 338 \\
                 8.3. Other Methods for Initial-Value Problems in
                 Ordinary Differential Equations / 342 \\
                 8.3.1. The Modified Midpoint Method / 342 \\
                 8.3.2. The Power-Series Method / 345 \\
                 8.3.3. Runge--Kutta Methods / 346 \\
                 8.3.4. Implicit Methods / 347 \\
                 8.3.5. Stiff Problems / 349 \\
                 8.3.6. Control of Step Size / 350 \\
                 8.3.7. A Finite-Difference Method for a Second-Order
                 Equation / 352 \\
                 8.4. Orientation on Boundary and Eigenvalue Problems
                 for Ordinary Differential Equations / 359 \\
                 8.4.1. Introduction / 359 \\
                 8.4.2. The Shooting Method / 359 \\
                 8.4.3. The Band Matrix Method / 361 \\
                 8.4.4. Numerical Example of an Eigenvalue Problem / 363
                 \\
                 8.5. Difference Equations / 367 \\
                 8.5.1. Homogeneous Linear Difference Equations with
                 Constant Coefficients / 368 \\
                 8.5.2. General Linear Difference Equations / 370 \\
                 8.5.3. Analysis of a Numerical Method with the Help of
                 a Test Problem / 372 \\
                 8.5.4. Linear Multistep Methods / 375 \\
                 8.6. Partial Differential Equations / 383 \\
                 8.6.1. Introduction / 383 \\
                 8.6.2. An Example of an Initial-Value Problem / 384 \\
                 8.6.3. An Example of a Boundary-Value Problem / 389 \\
                 8.6.4. Methods of Undetermined Coefficients and
                 Variational Methods / 392 \\
                 8.6.5. Finite-Element Methods / 395 \\
                 8.6.6. Integral Equations / 397 \\
                 9: Fourier Methods / 405 \\
                 9.1. Introduction / 405 \\
                 9.2. Basic Formulas and Theorems in Fourier Analysis /
                 406 \\
                 9.2.1. Functions of One Variable / 406 \\
                 9.2.2. Functions of Several Variables / 411 \\
                 9.3. Fast Fourier Analysis / 413 \\
                 9.3.1. An Important Special Case / 413 \\
                 9.3.2. Fast Fourier Analysis, General Case / 414 \\
                 9.4. Periodic Continuation of a Nonperiodic Function /
                 417 \\
                 9.5. The Fourier Integral Theorem / 419 \\
                 10: Optimization / 422 \\
                 10.1. Statement of the Problem, Definitions, and Normal
                 Form / 422 \\
                 10.2. The Simplex Method / 426 \\
                 10.3. Duality / 435 \\
                 10.4. The Transportation Problem and Some Other
                 Optimization Problems / 436 \\
                 10.5. Nonlinear Optimization Problems / 438 \\
                 10.5.1. Basic Concepts and Introductory Examples / 438
                 \\
                 10.5.2. Line Search / 440 \\
                 10.5.3. Algorithms for Unconstrained Optimization / 441
                 \\
                 10.5.4. Overdetermined Nonlinear Systems / 443 \\
                 10.5.5. Constrained Optimization / 444 \\
                 11: The Monte Carlo Method and Simulation / 448 \\
                 11.1. Introduction / 448 \\
                 11.2. Random Digits and Random Numbers / 449 \\
                 11.3. Applications; Reduction of Variance / 455 \\
                 11.4. Pseudorandom Numbers / 463 \\
                 12: Solutions to Problems / 465 \\
                 13: Bibliography and Published Algorithms / 536 \\
                 13.1. Introduction / 536 \\
                 13.2. General Literature in Numerical Analysis / 536
                 \\
                 13.3. Tables, Collections of Formulas, and Problems /
                 539 \\
                 13.4. Error Analysis and Approximation of Functions /
                 540 \\
                 13.5. Linear Algebra and Nonlinear Systems of Equations
                 / 541 \\
                 13.6. Interpolation, Numerical Integration, and
                 Numerical Treatment of Differential Equations / 543 \\
                 13.7. Optimization; Simulation / 545 \\
                 13.8. Reviews, Abstracts and Other Periodicals / 547
                 \\
                 13.9. Survey of Published Algorithms / 548 \\
                 Index by Subject to Algorithms, 1960--1970 / 548 \\
                 Appendix Tables / 563 \\
                 Index / 565",
}

@Article{Davies:2000:NSG,
  author =       "Philip I. Davies and Nicholas J. Higham",
  title =        "Numerically Stable Generation of Correlation Matrices
                 and their Factors",
  journal =      j-BIT,
  volume =       "40",
  number =       "4",
  pages =        "640--651",
  year =         "2000",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Dahlquist:1983:MMM,
  author =       "G. Dahlquist",
  title =        "On matrix majorants and minorants, with applications
                 to differential equations",
  journal =      j-LAA,
  volume =       "52/53",
  pages =        "199--216",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Dax:1977:PTS,
  author =       "Achiya Dax and S. Kaniel",
  title =        "Pivoting Techniques for Symmetric {Gaussian}
                 Elimination",
  journal =      j-NUM-MATH,
  volume =       "28",
  pages =        "221--241",
  year =         "1977",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Danloy:1976:CSH,
  author =       "B. Danloy",
  title =        "On the Choice of Signs for {Householder's} Matrices",
  journal =      j-JCAM,
  volume =       "2",
  number =       "1",
  pages =        "67--69",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Day:1988:GGE,
  author =       "Jane M. Day and Brian Peterson",
  title =        "Growth in {Gaussian} Elimination",
  journal =      j-AMM,
  volume =       "95",
  number =       "6",
  pages =        "489--513",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Davis:1984:MNI,
  author =       "Philip J. Davis and Philip Rabinowitz",
  title =        "Methods of Numerical Integration",
  publisher =    pub-AP,
  address =      pub-AP:adr-L,
  edition =      "Second",
  pages =        "xiv + 612",
  year =         "1984",
  ISBN =         "0-12-206360-0",
  ISBN-13 =      "978-0-12-206360-2",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Datta:1988:MEA,
  author =       "Karabi Datta",
  title =        "The Matrix Equation {$XA-BX=R$} and Its Applications",
  journal =      j-LAA,
  volume =       "109",
  pages =        "91--105",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Davis:1979:CM,
  author =       "Philip J. Davis",
  title =        "Circulant Matrices",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  pages =        "xv + 250",
  year =         "1979",
  ISBN =         "0-471-05771-1",
  ISBN-13 =      "978-0-471-05771-0",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Dax:1982:PPS,
  author =       "Achiya Dax",
  title =        "Partial Pivoting Strategies for Symmetric {Gaussian}
                 Elimination",
  journal =      j-MATH-PROG,
  volume =       "22",
  pages =        "288--303",
  year =         "1982",
  CODEN =        "MHPGA4",
  ISSN =         "0025-5610",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Mathematical Programming",
  journal-URL =  "http://link.springer.com/journal/10107",
}

@Article{Dax:1990:CLS,
  author =       "Achiya Dax",
  title =        "The Convergence of Linear Stationary Iterative
                 Processes for Solving Singular Unstructured Systems of
                 Linear Equations",
  journal =      j-SIREV,
  volume =       "32",
  number =       "4",
  pages =        "611--635",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Dongarra:1979:LUG,
  author =       "J. J. Dongarra and J. R. Bunch and C. B. Moler and G.
                 W. Stewart",
  title =        "{LINPACK} Users' Guide",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1979",
  ISBN =         "0-89871-172-X",
  ISBN-13 =      "978-0-89871-172-1",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Boor:1977:BEA,
  author =       "Carl de Boor and Allan Pinkus",
  title =        "Backward Error Analysis for Totally Positive Linear
                 Systems",
  journal =      j-NUM-MATH,
  volume =       "27",
  pages =        "485--490",
  year =         "1977",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Dongarra:19xx:SLB,
  author =       "J. J. Dongarra and J. J. Du Croz and I. S. Duff and S.
                 J. Hammarling",
  title =        "A Set of {Level 3} Basic Linear Algebra Subprograms",
  journal =      j-TOMS,
  volume =       "16",
  pages =        "1--17",
  year =         "{\noopsort{a}}1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Dongarra:19xx:ASL,
  author =       "J. J. Dongarra and J. J. Du Croz and I. S. Duff and S.
                 J. Hammarling",
  title =        "Algorithm 679. {A} set of {Level 3} Basic Linear
                 Algebra Subprograms: {Model} Implementation and Test
                 Programs",
  journal =      j-TOMS,
  volume =       "16",
  pages =        "18--28",
  year =         "{\noopsort{b}}1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Dongarra:19xx:ESF,
  author =       "Jack J. Dongarra and Jeremy J. Du Croz and Sven J.
                 Hammarling and Richard J. Hanson",
  title =        "An Extended Set of {Fortran} Basic Linear Algebra
                 Subprograms",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "1--17",
  year =         "{\noopsort{a}}1988",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Dongarra:19xx:AES,
  author =       "Jack J. Dongarra and Jeremy J. Du Croz and Sven J.
                 Hammarling and Richard J. Hanson",
  title =        "Algorithm 656. {An} Extended Set of {Fortran} Basic
                 Linear Algebra Subprograms: {Model} Implementation and
                 Test Programs",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "18--32",
  year =         "{\noopsort{b}}1988",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@InProceedings{Demmel:1992:DPH,
  author =       "James W. Demmel and J. J. Dongarra and W. Kahan",
  editor =       "D. F. Griffiths and G. A. Watson",
  booktitle =    "Numerical Analysis \textup{1991}, Proceedings of the
                 \textup{14}th Dundee Conference",
  title =        "On Designing Portable High Performance Numerical
                 Libraries",
  volume =       "260",
  publisher =    pub-Longman-ST # ", " # pub-Longman-ST:adr,
  pages =        "69--84",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Pitman Research Notes in Mathematics",
}

@Article{Demmel:2001:CCE,
  author =       "James W. Demmel and Benjamin Diament and Gregorio
                 Malajovich",
  title =        "On the Complexity of Computing Error Bounds",
  journal =      j-FOCM,
  volume =       "1",
  number =       "1",
  pages =        "101--125",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Demmel:1995:CSB,
  author =       "James W. Demmel and Inderjit Dhillon and Huan Ren",
  title =        "On the Correctness of Some Bisection-Like Parallel
                 Eigenvalue Algorithms in Floating Point Arithmetic",
  journal =      j-ETNA,
  volume =       "3",
  pages =        "116--149",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Dongarra:1998:NLA,
  author =       "Jack J. Dongarra and Iain S. Duff and Danny C.
                 Sorensen and Henk A. van der Vorst",
  title =        "Numerical Linear Algebra for High-Performance
                 Computers",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xviii + 342",
  year =         "1998",
  ISBN =         "0-89871-428-1",
  ISBN-13 =      "978-0-89871-428-9",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Demmel:1992:SBA,
  author =       "James W. Demmel and Nicholas J. Higham",
  title =        "Stability of Block Algorithms with Fast Level-3
                 {BLAS}",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "274--291",
  month =        sep,
  year =         "1992",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Demmel:1993:IEB,
  author =       "James W. Demmel and Nicholas J. Higham",
  title =        "Improved Error Bounds for Underdetermined System
                 Solvers",
  journal =      j-SIMAX,
  volume =       "14",
  number =       "1",
  pages =        "1--14",
  month =        jan,
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Dekker:1989:RGJ,
  author =       "T. J. Dekker and W. Hoffmann",
  title =        "Rehabilitation of the {Gauss--Jordan} Algorithm",
  journal =      j-NUM-MATH,
  volume =       "54",
  pages =        "591--599",
  year =         "1989",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Demmel:1987:CSE,
  author =       "James W. Demmel and Bo K{\aa}gstr{\"o}m",
  title =        "Computing Stable Eigendecompositions of Matrix
                 Pencils",
  journal =      j-LAA,
  volume =       "88/89",
  pages =        "139--186",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Demmel:1988:ASI,
  author =       "James W. Demmel and Bo K{\aa}gstr{\"o}m",
  title =        "Accurate Solutions of Ill-Posed Problems in Control
                 Theory",
  journal =      j-SIMAX,
  volume =       "9",
  number =       "1",
  pages =        "126--145",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Demmel:1990:ASV,
  author =       "James W. Demmel and W. Kahan",
  title =        "Accurate Singular Values of Bidiagonal Matrices",
  journal =      j-SISSC,
  volume =       "11",
  number =       "5",
  pages =        "873--912",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Dekker:1971:FPT,
  author =       "T. J. Dekker",
  title =        "A Floating-Point Technique for Extending the Available
                 Precision",
  journal =      j-NUM-MATH,
  volume =       "18",
  pages =        "224--242",
  year =         "1971",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Demmel:1985:IAS,
  author =       "James W. Demmel and F. Kr{\"u}ckeberg",
  title =        "An Interval Algorithm for Solving Systems of Linear
                 Equations to Prespecified Accuracy",
  journal =      j-COMPUTING,
  volume =       "34",
  pages =        "117--129",
  year =         "1985",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@InProceedings{Dongarra:2000:RAS,
  author =       "Jack Dongarra and Victor Eijkhout and Piotr Luszczek",
  booktitle =    "Proceedings of the 1st SGI Users Conference",
  title =        "Recursive Approach in Sparse Matrix {LU}
                 Factorization",
  organization = "ACC Cyfronet UMM",
  address =      "Cracow, Poland",
  pages =        "409--418",
  month =        oct,
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Demmel:1994:FNA,
  author =       "James W. Demmel and Xiaoye Li",
  title =        "Faster Numerical Algorithms via Exception Handling",
  journal =      j-IEEE-C,
  volume =       "43",
  number =       "8",
  pages =        "983--992",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Demmel:1989:TMG,
  author =       "James W. Demmel and A. McKenney",
  title =        "A Test Matrix Generation Suite",
  type =         "Preprint",
  number =       "MCS-P69-0389",
  institution =  inst-MCS-Argonne,
  address =      inst-MCS-Argonne:adr,
  pages =        "16",
  month =        mar,
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "LAPACK Working Note 9",
}

@Article{Demeure:1989:FFV,
  author =       "C{\'e}dric J. Demeure",
  title =        "Fast {$QR$} Factorization of {Vandermonde} Matrices",
  journal =      j-LAA,
  volume =       "122/3/4",
  pages =        "165--194",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Demeure:1990:FCV,
  author =       "C{\'e}dric J. Demeure",
  title =        "{$QR$} Factorization of Confluent {Vandermonde}
                 Matrices",
  journal =      j-IEEE-ASSP,
  volume =       "38",
  number =       "10",
  pages =        "1799--1802",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Unpublished{Demmel:2001:NAF,
  author =       "James W. Demmel",
  title =        "A Note on Accurate Floating Point Summation",
  pages =        "5",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Manuscript",
}

@Article{Demmel:1983:CNE,
  author =       "James W. Demmel",
  title =        "The Condition Number of Equivalence Transformations
                 that Block Diagonalize Matrix Pencils",
  journal =      j-SINUM,
  volume =       "20",
  number =       "3",
  pages =        "599--610",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Demmel:1984:URN,
  author =       "James W. Demmel",
  title =        "Underflow and the Reliability of Numerical Software",
  journal =      j-SISSC,
  volume =       "5",
  number =       "4",
  pages =        "887--919",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Demmel:1987:CND,
  author =       "James W. Demmel",
  title =        "On Condition Numbers and the Distance to the Nearest
                 Ill-Posed Problem",
  journal =      j-NUM-MATH,
  volume =       "51",
  pages =        "251--289",
  year =         "1987",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@InProceedings{Demmel:1987:EAA,
  author =       "James W. Demmel",
  editor =       "Mary Jane Irwin and Renato Stefanelli",
  booktitle =    "Proceedings of the Eighth Symposium on Computer
                 Arithmetic, Como, Italy",
  title =        "On Error Analysis in Arithmetic With Varying Relative
                 Precision",
  publisher =    "IEEE Computer Society, Washington, D.C.",
  pages =        "148--152",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Demmel:1989:FPE,
  author =       "James W. Demmel",
  title =        "On Floating Point Errors in {Cholesky}",
  type =         "Technical Report",
  number =       "CS-89-87",
  institution =  inst-CS-U-Tenn,
  address =      inst-CS-U-Tenn:adr,
  pages =        "6",
  month =        oct,
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "LAPACK Working Note 14",
}

@Article{Demmel:1991:OIA,
  author =       "James W. Demmel",
  title =        "On the Odor of {IEEE} Arithmetic",
  journal =      j-NA-DIGEST,
  volume =       "Volume 91, Issue 39",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "(Response to a message ``IEEE Arithmetic Stinks'' in
                 Volume 91, Issue 33)",
  fjournal =     "NA Digest",
}

@Article{demm92,
  author =       "James W. Demmel",
  title =        "The Componentwise Distance to the Nearest Singular
                 Matrix",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "10--19",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Demmel:1992:OPN,
  author =       "James W. Demmel",
  title =        "Open Problems in Numerical Linear Algebra",
  type =         "IMA Preprint Series",
  number =       "\#961",
  institution =  inst-IMA,
  address =      inst-IMA:adr,
  pages =        "21",
  month =        apr,
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "LAPACK Working Note 47",
}

@TechReport{Demmel:1992:SFP,
  author =       "James W. Demmel",
  title =        "A Specification for Floating Point Parallel Prefix",
  type =         "Technical Report",
  number =       "CS-92-167",
  institution =  inst-CS-U-Tenn,
  address =      inst-CS-U-Tenn:adr,
  pages =        "8",
  month =        jul,
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "LAPACK Working Note 49",
}

@InProceedings{Demmel:1993:TPN,
  author =       "James W. Demmel",
  editor =       "Marc S. Moonen and Gene H. Golub and Bart L. De Moor",
  booktitle =    "Linear Algebra for Large Scale and Real-Time
                 Applications",
  title =        "Trading Off Parallelism and Numerical Stability",
  volume =       "232",
  publisher =    pub-Kluwer # ", " # pub-Kluwer:adr,
  pages =        "49--68",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "NATO ASI Series E",
}

@Book{Demmel:1997:ANL,
  author =       "James W. Demmel",
  title =        "Applied Numerical Linear Algebra",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xi + 419",
  year =         "1997",
  ISBN =         "0-89871-389-7",
  ISBN-13 =      "978-0-89871-389-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Demmel:1999:ASV,
  author =       "James W. Demmel",
  title =        "Accurate Singular Value Decompositions of Structured
                 Matrices",
  journal =      j-SIMAX,
  volume =       "21",
  number =       "2",
  pages =        "562--580",
  year =         "1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Duff:1986:DMS,
  author =       "I. S. Duff and A. M. Erisman and J. K. Reid",
  title =        "Direct Methods for Sparse Matrices",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xiii + 341",
  year =         "1986",
  ISBN =         "0-19-853408-6 (hardcover), 0-19-853421-3 (paperback)",
  ISBN-13 =      "978-0-19-853408-2 (hardcover), 978-0-19-853421-1
                 (paperback)",
  LCCN =         "QA188 .D841 1986",
  bibdate =      "Tue Dec 14 22:47:43 1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$37.50",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "1: Introduction \\
                 2: Sparse matrices: storage schemes and simple
                 Operations \\
                 3: Gaussian elimination for dense matrices: the
                 algebraic problem \\
                 4: Gaussian elimination for dense matrices: numerical
                 considerations \\
                 5: Gaussian elimination for sparse matrices: an
                 introduction \\
                 6: Reduction to block triangular form \\
                 7: Local pivotal strategies for sparse matrices \\
                 8: Ordering sparse matrices to special forms \\
                 9: Implementing Gaussian elimination: ANALYSE with
                 numerical values \\
                 10: Implementing Gaussian elimination with symbolic
                 ANALYSE \\
                 11: Partitioning, matrix modification, and tearing \\
                 12: Other sparsity-oriented issues \\
                 Appendix A: Matrix and vector norms / 281 \\
                 Appendix B: The LINPACK condition number estimate / 285
                 \\
                 Appendix C: Fortran Conventions / 287 \\
                 Appendix D: Pictures of sparse matrices / 289 \\
                 Solutions to selected exercises / 297 \\
                 References / 313 \\
                 Author index / 327 \\
                 Subject index / 331",
  tableofcontents = "1: Introduction \\
                 1.1 Introduction / 1 \\
                 1.2 Graph theory / 2 \\
                 1.3 Example / 4 \\
                 1.4 Advanced Computer architectures / 9 \\
                 1.5 Problem formulation / 11 \\
                 1.6 A sparse matrix test collection / 14 \\
                 2: Sparse matrices: storage schemes and simple
                 Operations \\
                 2.1 Introduction / 19 \\
                 2.2 Sparse vector storage / 19 \\
                 2.3 Inner product of two packed vectors / 20 \\
                 2.4 Adding packed vectors / 21 \\
                 2.5 Use of full-sized arrays / 22 \\
                 2.6 Coordinate scheme for storing sparse matrices / 23
                 \\
                 2.7 Sparse matrix as a collection of sparse vectors /
                 24 \\
                 2.8 Linked lists / 25 \\
                 2.9 Sparse matrix in row-linked list / 28 \\
                 2.10 Generating collections of sparse vectors / 30 \\
                 2.11 Access by rows and columns / 31 \\
                 2.12 Matrix by vector products / 32 \\
                 2.13 Matrix by matrix products / 33 \\
                 2.14 Permutation matrices / 34 \\
                 2.15 Clique (or finite-element) storage / 36 \\
                 2.16 Comparisons between sparse matrix structures / 37
                 \\
                 3: Gaussian elimination for dense matrices: the
                 algebraic problem \\
                 3.1 Introduction / 41 \\
                 3.2 Solution of triangular Systems / 41 \\
                 3.3 Gaussian elimination / 43 \\
                 3.4 Required row interchanges / 45 \\
                 3.5 Relationship with $L U$ factorization / 46 \\
                 3.6 Equivalent factorization methods, including
                 Doolittle and Crout / 49 \\
                 3.7 Computational sequences / 51 \\
                 3.8 Symmetric matrices / 53 \\
                 3.9 Gauss--Jordan elimination / 55 \\
                 3.10 Multiple right-hand sides and inverses / 56 \\
                 3.11 Computational cost / 57 \\
                 3.12 Block factorization / 59 \\
                 4: Gaussian elimination for dense matrices: numerical
                 considerations \\
                 4.1 Introduction / 65 \\
                 4.2 Computer arithmetic error / 66 \\
                 4.3 Algorithm instability / 67 \\
                 4.4 Controlling algorithm stability / 69 \\
                 4.5 Monitoring the stability / 72 \\
                 4.6 Special stability considerations / 76 \\
                 4.7 Solving indefinite symmetric systems / 77 \\
                 4.8 Ill-conditioning: introduction / 78 \\
                 4.9 Ill-conditioning: theoretical discussion / 79 \\
                 4.10 Ill-conditioning: automatic detection / 81 \\
                 4.11 Iterative refinement / 85 \\
                 4.12 Scaling / 86 \\
                 4.13 Prevention of ill-conditioning / 88 \\
                 4.14 Overall error bound / 89 \\
                 5: Gaussian elimination for sparse matrices: an
                 introduction \\
                 5.1 Introduction / 93 \\
                 5.2 Features of a sparse matrix code / 94 \\
                 5.3 Orderings / 96 \\
                 5.4 Numerical stability in sparse computation / 98 \\
                 5.5 Estimating condition numbers in sparse computation
                 / 100 \\
                 5.6 The ANALYSE phase / 101 \\
                 5.7 The FACTORIZE and SOLVE phases / 102 \\
                 5.8 Writing compared with using sparse matrix Software
                 / 103 \\
                 6: Reduction to block triangular form \\
                 6.1 Introduction / 105 \\
                 6.2 Background for finding a transversal / 107 \\
                 6.3 A depth-first search algorithm for transversal
                 extension / 109 \\
                 6.4 Analysis of the depth-first search transversal
                 algorithm / 111 \\
                 6.5 Implementation of the transversal algorithm / 112
                 \\
                 6.6 Symmetric permutations to block triangular form /
                 113 \\
                 6.7 The algorithm of Sargent and Westerberg / 114 \\
                 6.8 Tarjan's algorithm / 117 \\
                 6.9 Implementation of Tarjan's algorithm / 120 \\
                 6.10 Essential uniqueness of the block triangular form
                 / 121 \\
                 6.11 Experience with block triangular forms / 122 \\
                 6.12 Maximum transversals / 124 \\
                 7: Local pivotal strategies for sparse matrices \\
                 7.1 Introduction / 127 \\
                 7.2 The Markowitz criterion / 128 \\
                 7.3 Minimum degree (Tinney scheme 2) / 129 \\
                 7.4 Simpler strategies / 130 \\
                 7.5 Local minimum fill-in / 133 \\
                 7.6 Other local strategies / 135 \\
                 7.7 The effect of tie-breaking on the minimum degree
                 algorithm / 136 \\
                 7.8 Numerical pivoting / 139 \\
                 7.9 Sparsity in the right-hand side and partial
                 Solution / 140 \\
                 7.10 Variability-type ordering / 143 \\
                 7.11 The Symmetric indefinite case / 145 \\
                 7.12 Solution methods based on orthogonalization / 145
                 \\
                 8: Ordering sparse matrices to special forms \\
                 8.1 Introduction / 149 \\
                 8.2 Desirable forms / 149 \\
                 8.3 Band and variable-band matrices / 151 \\
                 8.4 Ordering for small bandwidth / 153 \\
                 8.5 Refined quotient trees / 157 \\
                 8.6 One-way dissection / 161 \\
                 8.7 Nested dissection / 163 \\
                 8.8 The Boeing version of the Hellerman--Rarick
                 algorithm / 168 \\
                 8.9 The Hellerman--Rarick ordering / 172 \\
                 9: Implementing Gaussian elimination: ANALYSE with
                 numerical values \\
                 9.1 Introduction / 177 \\
                 9.2 Markowitz ANALYSE / 178 \\
                 9.3 FACTORIZE / 183 \\
                 9.4 SOLVE / 186 \\
                 9.5 Switching to full form / 188 \\
                 9.6 Loop-free code / 191 \\
                 9.7 Interpretative code / 192 \\
                 9.8 A posteriori ordering for stability / 193 \\
                 9.9 The use of drop tolerances to preserve sparsity /
                 195 \\
                 10: Implementing Gaussian elimination with symbolic
                 ANALYSE 10.1 Introduction / 199 \\
                 10.2 Band methods / 200 \\
                 10.3 Variable-band (profile) methods / 204 \\
                 10.4 Special methods for banded Systems / 205 \\
                 10.5 Frontal methods for finite-element problems / 210
                 \\
                 10.6 Frontal methods for non-element problems / 216 \\
                 10.7 Multifrontal (substructuring) methods for
                 finite-element problems / 218 \\
                 10.8 Multifrontal methods for non-element problems /
                 222 \\
                 10.9 Minimum degree ordering / 226 \\
                 10.10 Generating static data structures for FACTORIZE /
                 229 \\
                 10.11 Numerical FACTORIZE and SOLVE using static data
                 structures / 232 \\
                 10.12 Accommodating numerical pivoting within static
                 data structures / 233 \\
                 10.13 Nested dissection, refined quotient tree, and
                 one-way dissection / 234 \\
                 10.14 Effects of Computer architecture / 234 \\
                 11: Partitioning, matrix modification, and tearing \\
                 11.1 Introduction / 239 \\
                 11.2 Exploiting the partitioned form / 240 \\
                 11.3 Using partitioning to handle low-rank
                 perturbations / 242 \\
                 11.4 The matrix modification formula / 243 \\
                 11.5 Low-rank modifications / 244 \\
                 11.6 Use of the modification formula to solve equations
                 / 245 \\
                 11.7 Perturbations that are full-rank submatrices / 247
                 \\
                 11.8 The equivalence of modification and partitioning /
                 249 \\
                 11.9 Modifications that change the matrix Order / 250
                 \\
                 11.10 Artificial perturbations / 251 \\
                 11.11 Branch tearing / 252 \\
                 11.12 Node tearing / 254 \\
                 11.13 Implementation of node and branch tearing / 255
                 \\
                 11.14 Manual choice of partitions and tear sets / 255
                 \\
                 11.15 Automatic choice of partitions and tear sets /
                 257 \\
                 11.16 Nonlinear tearing / 259 \\
                 11.17 Conclusions / 260 \\
                 12: Other sparsity-oriented issues \\
                 12.1 Introduction / 265 \\
                 12.2 Sparsity in nonlinear computations / 266 \\
                 12.3 Estimating a sparse Jacobian matrix / 267 \\
                 12.4 Updating a sparse Hessian matrix / 269 \\
                 12.5 Approximating a sparse matrix by a
                 positive-definite one / 270 \\
                 12.6 The inverse of a sparse matrix / 271 \\
                 12.7 Computing entries of the inverse of a sparse
                 matrix / 273 \\
                 12.8 Sparsity constrained backward error analysis / 275
                 \\
                 12.9 Assembling large finite-element matrices to band
                 form / 277 \\
                 12.10 Hypermatrices / 278 \\
                 Appendix A: Matrix and vector norms / 281 \\
                 Appendix B: The LINPACK condition number estimate / 285
                 \\
                 Appendix C: Fortran Conventions / 287 \\
                 Appendix D: Pictures of sparse matrices / 289 \\
                 Solutions to selected exercises / 297 \\
                 References / 313 \\
                 Author index / 327 \\
                 Subject index / 331",
}

@Article{Dembo:1982:INM,
  author =       "Ron S. Dembo and Stanley C. Eisenstat and Trond
                 Steihaug",
  title =        "Inexact {Newton} Methods",
  journal =      j-SINUM,
  volume =       "19",
  number =       "2",
  pages =        "400--408",
  year =         "1982",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Descloux:1963:NRE,
  author =       "J. Descloux",
  title =        "Note on the Round-Off Errors in Iterative Processes",
  journal =      j-MATH-COMP,
  volume =       "17",
  pages =        "18--27",
  year =         "1963",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Dennis:1983:NMU,
  author =       "John E. {Dennis, Jr.} and Robert B. Schnabel",
  title =        "Numerical Methods for Unconstrained Optimization and
                 Nonlinear Equations",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xiii + 378",
  year =         "1983",
  ISBN =         "0-13-627216-9 (original), 0-89871-364-1 (reprint)",
  ISBN-13 =      "978-0-13-627216-8 (original), 978-0-89871-364-0
                 (reprint)",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted by SIAM (1996).",
}

@Article{Dennis:1991:DSM,
  author =       "John E. {Dennis, Jr.} and Virginia Torczon",
  title =        "Direct Search Methods on Parallel Machines",
  journal =      j-SIOPT,
  volume =       "1",
  number =       "4",
  pages =        "448--474",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Dennis:1984:IQN,
  author =       "John E. {Dennis, Jr.} and Homer F. Walker",
  title =        "Inaccuracy in Quasi-{Newton} Methods: {Local}
                 Improvement Theorems",
  journal =      j-MATH-PROG-STUDY,
  volume =       "22",
  pages =        "70--85",
  year =         "1984",
  CODEN =        "MPSTDF",
  ISSN =         "0303-3929",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Mathematical Programming Study",
}

@Article{Dennis:1993:SLC,
  author =       "John E. {Dennis, Jr.} and Henry Wolkowicz",
  title =        "Sizing and Least-Change Secant Methods",
  journal =      j-SINUM,
  volume =       "30",
  number =       "5",
  pages =        "1291--1314",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Demmel:1999:CSV,
  author =       "James W. Demmel and Ming Gu and Stanley Eisenstat and
                 Ivan Slapni\v{c}ar and Kre\v{s}imir Veseli{\'c} and
                 Zlatko Drma\v{c}",
  title =        "Computing the Singular Value Decomposition with High
                 Relative Accuracy",
  journal =      j-LAA,
  volume =       "299",
  pages =        "21--80",
  year =         "1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Dongarra:1984:ILA,
  author =       "J. J. Dongarra and F. G. Gustavson and A. Karp",
  title =        "Implementing Linear Algebra Algorithms for Dense
                 Matrices on a Vector Pipeline Machine",
  journal =      j-SIREV,
  volume =       "26",
  number =       "1",
  pages =        "91--112",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Daniel:1976:RSA,
  author =       "J. W. Daniel and W. B. Gragg and L. Kaufman and G. W.
                 Stewart",
  title =        "Reorthogonalization and Stable Algorithms for Updating
                 the {Gram--Schmidt} {QR} Factorization",
  journal =      j-MATH-COMP,
  volume =       "30",
  number =       "136",
  pages =        "772--795",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Duff:1989:SMT,
  author =       "Iain S. Duff and Roger G. Grimes and John G. Lewis",
  title =        "Sparse Matrix Test Problems",
  journal =      j-TOMS,
  volume =       "15",
  number =       "1",
  pages =        "1--14",
  year =         "1989",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@TechReport{Duff:1992:UGH,
  author =       "Iain S. Duff and Roger G. Grimes and John G. Lewis",
  title =        "Users' Guide for the {Harwell--Boeing} Sparse Matrix
                 Collection (Release 1)",
  type =         "Report",
  number =       "RAL-92-086",
  institution =  inst-RAL,
  address =      inst-RAL:adr,
  pages =        "84",
  month =        dec,
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Duff:1991:FSS,
  author =       "I. S. Duff and N. I. M. Gould and J. K. Reid and J. A.
                 Scott and K. Turner",
  title =        "The Factorization of Sparse Symmetric Indefinite
                 Matrices",
  journal =      j-IMAJNA,
  volume =       "11",
  pages =        "181--204",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Drkosova:1995:NSG,
  author =       "J. Drko{\v{s}}ov{\'a} and A. Greenbaum and M.
                 Rozlo{\v{z}}n{\'\i}k and Z. Strako{\u{s}}",
  title =        "Numerical Stability of {GMRES}",
  journal =      j-BIT,
  volume =       "35",
  pages =        "309--330",
  year =         "1995",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Dhillon:1998:RCC,
  author =       "Inderjit Dhillon",
  title =        "Reliable Computation of the Condition Number of a
                 Tridiagonal Matrix in {$O(n)$} Time",
  journal =      j-SIMAX,
  volume =       "19",
  number =       "3",
  pages =        "776--796",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Demmel:1995:SBF,
  author =       "James W. Demmel and Nicholas J. Higham and Robert S.
                 Schreiber",
  title =        "Stability of Block {$LU$} Factorization",
  journal =      j-NLAA,
  volume =       "2",
  number =       "2",
  pages =        "173--190",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Douglas:1994:GPL,
  author =       "Craig C. Douglas and Michael Heroux and Gordon
                 Slishman and Roger M. Smith",
  title =        "{GEMMW}: {A} Portable Level 3 {BLAS Winograd} Variant
                 of {Strassen's} Matrix--Matrix Multiply Algorithm",
  journal =      j-JCOMP-PHYS,
  volume =       "110",
  pages =        "1--10",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Diamond:1978:SRI,
  author =       "Harold G. Diamond",
  title =        "Stability of Rounded Off Inverses Under Iteration",
  journal =      j-MATH-COMP,
  volume =       "32",
  number =       "141",
  pages =        "227--232",
  year =         "1978",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Dixon:1983:EEE,
  author =       "John D. Dixon",
  title =        "Estimating Extremal Eigenvalues and Condition Numbers
                 of Matrices",
  journal =      j-SINUM,
  volume =       "20",
  number =       "4",
  pages =        "812--814",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Dongarra:1987:DMS,
  author =       "Jack J. Dongarra and Eric Grosse",
  title =        "Distribution of Mathematical Software Via Electronic
                 Mail",
  journal =      j-CACM,
  volume =       "30",
  number =       "5",
  pages =        "403--407",
  year =         "1987",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@TechReport{Dongarra:2001:PVC,
  author =       "Jack J. Dongarra",
  title =        "Performance of Various Computers Using Standard Linear
                 Equations Software",
  type =         "Technical Report",
  number =       "CS-89-85",
  institution =  inst-CS-U-Tenn,
  address =      inst-CS-U-Tenn:adr,
  pages =        "58",
  month =        aug,
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Douglas:1994:VMM,
  author =       "Craig C. Douglas and Gordon Slishman",
  title =        "Variants of Matrix-Matrix Multiplication for
                 {Fortran}-90",
  journal =      j-SIGNUM,
  volume =       "29",
  pages =        "4--6",
  year =         "1994",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J690",
}

@Article{Douglas:1959:REN,
  author =       "Jim {Douglas, Jr.}",
  title =        "Round-Off Error in the Numerical Solution of the Heat
                 Equation",
  journal =      j-ACM,
  volume =       "6",
  pages =        "48--58",
  year =         "1959",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Drmac:1994:PCF,
  author =       "Zlatko Drma\v{c} and Matja\v{z} Omladi\v{c} and
                 Kre\v{s}imir Veseli{\'c}",
  title =        "On the Perturbation of the {Cholesky} Factorization",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "4",
  pages =        "1319--1332",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Doyle:1957:ISC,
  author =       "Thomas C. Doyle",
  title =        "Inversion of Symmetric Coefficient Matrix of
                 Positive-Definite Quadratic Form",
  journal =      j-MTAC,
  volume =       "11",
  pages =        "55--58",
  year =         "1957",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Duff:1979:DSS,
  author =       "Iain S. Duff and John K. Reid and Neils Munskgaard and
                 Hans B. Nielsen",
  title =        "Direct Solution of Sets of Linear Equations Whose
                 Matrix is Sparse, Symmetric and Indefinite",
  journal =      j-JIMA,
  volume =       "23",
  pages =        "235--250",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Dubrulle:1983:CNM,
  author =       "Augustin A. Dubrulle",
  title =        "A Class of Numerical Methods for the Computation of
                 {Pythagorean} Sums",
  journal =      j-IBM-JRD,
  volume =       "27",
  number =       "6",
  pages =        "582--589",
  year =         "1983",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@Article{Dubrulle:1994:MQI,
  author =       "Augustin A. Dubrulle and Gene H. Golub",
  title =        "A Multishift {QR} Iteration Without Computation of the
                 Shifts",
  journal =      j-NUM-ALG,
  volume =       "7",
  pages =        "173--181",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Croz:1992:SMM,
  author =       "Jeremy J. Du Croz and Nicholas J. Higham",
  title =        "Stability of Methods for Matrix Inversion",
  journal =      j-IMAJNA,
  volume =       "12",
  pages =        "1--19",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Dumitrescu:1998:IEA,
  author =       "Bogdan Dumitrescu",
  title =        "Improving and Estimating the Accuracy of {Strassen's}
                 Algorithm",
  journal =      j-NUM-MATH,
  volume =       "79",
  pages =        "485--499",
  year =         "1998",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Book{Dunham:1990:JTG,
  author =       "William Dunham",
  title =        "Journey Through Genius: {The} Great Theorems of
                 Mathematics",
  publisher =    pub-Penguin,
  address =      pub-Penguin:adr-NY,
  pages =        "xiii + 300",
  year =         "1990",
  ISBN =         "0-14-014739-X",
  ISBN-13 =      "978-0-14-014739-1",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Duff:1982:MSF,
  author =       "Iain S. Duff and John K. Reid",
  title =        "{MA27}---{A} Set of {Fortran} Subroutines for Solving
                 Sparse Symmetric Sets of Linear Equations",
  number =       "AERE R10533",
  institution =  inst-HARWELL,
  month =        jul,
  year =         "1982",
  ISBN =         "0-7058-0985-4",
  ISBN-13 =      "978-0-7058-0985-6",
  note =         "Published by " # pub-HMSO # ", " # pub-HMSO:adr,
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{dure95,
  author =       "Iain S. Duff and John K. Reid",
  title =        "{MA47}, a {Fortran} Code for Direct Solution of
                 Indefinite Sparse Symmetric Linear Systems",
  type =         "Report",
  number =       "RAL-95-001",
  institution =  inst-RAL,
  address =      inst-RAL:adr,
  pages =        "63",
  month =        jan,
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Dwyer:1951:LC,
  author =       "Paul S. Dwyer",
  title =        "Linear Computations",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  pages =        "xi + 344",
  year =         "1951",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Eckart:1936:AOM,
  author =       "Carl Eckart and Gale Young",
  title =        "The Approximation of One Matrix by Another of Lower
                 Rank",
  journal =      j-PSYCHO,
  volume =       "1",
  number =       "3",
  pages =        "211--218",
  year =         "1936",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Edelman:1988:ECN,
  author =       "Alan Edelman",
  title =        "Eigenvalues and Condition Numbers of Random Matrices",
  journal =      j-SIMAX,
  volume =       "9",
  number =       "4",
  pages =        "543--560",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Edelman:1991:FAL,
  author =       "Alan Edelman",
  title =        "The First Annual Large Dense Linear System Survey",
  journal =      j-SIGNUM,
  volume =       "26",
  pages =        "6--12",
  month =        oct,
  year =         "1991",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J690",
}

@Article{edel91a,
  key =          "Editor",
  title =        "Editor's Note",
  journal =      j-SIMAX,
  volume =       "12",
  number =       "3",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Edelman:1991:DMS,
  author =       "Alan Edelman",
  title =        "The Distribution and Moments of the Smallest
                 Eigenvalue of a Random Matrix of {Wishart} Type",
  journal =      j-LAA,
  volume =       "159",
  pages =        "55--80",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Edelman:1992:CPC,
  author =       "Alan Edelman",
  title =        "The Complete Pivoting Conjecture for {Gaussian}
                 Elimination is False",
  journal =      j-MATHEMATICA-J,
  volume =       "2",
  pages =        "58--61",
  year =         "1992",
  ISSN =         "1047-5974 (print), 1097-1610 (electronic)",
  ISSN-L =       "1047-5974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Mathematica Journal",
  journal-URL =  "http://www.mathematica-journal.com/",
}

@Article{Edelman:1992:DSC,
  author =       "Alan Edelman",
  title =        "On the Distribution of a Scaled Condition Number",
  journal =      j-MATH-COMP,
  volume =       "58",
  number =       "197",
  pages =        "185--190",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Edelman:1993:ERR,
  author =       "Alan Edelman",
  editor =       "Marc S. Moonen and Gene H. Golub and Bart L. De Moor",
  booktitle =    "Linear Algebra for Large Scale and Real-Time
                 Applications",
  title =        "Eigenvalue Roulette and Random Test Matrices",
  volume =       "232",
  publisher =    pub-Kluwer # ", " # pub-Kluwer:adr,
  pages =        "365--368",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "NATO ASI Series E",
}

@Article{Edelman:1993:LDN,
  author =       "Alan Edelman",
  title =        "Large Dense Numerical Linear Algebra in 1993: {The}
                 Parallel Computing Influence",
  journal =      j-IJSA,
  volume =       "7",
  number =       "2",
  pages =        "113--128",
  year =         "1993",
  CODEN =        "IJSAE9",
  ISSN =         "0890-2720",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "International Journal of Supercomputer Applications",
  journal-URL =  "http://hpc.sagepub.com/content/by/year",
}

@InProceedings{Edelman:1994:SDN,
  author =       "Alan Edelman",
  editor =       "John G. Lewis",
  booktitle =    "Proceedings of the Fifth SIAM Conference on Applied
                 Linear Algebra",
  title =        "Scalable Dense Numerical Linear Algebra in 1994: {The}
                 Multicomputer Influence",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "344--348",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Unpublished{Edelman:1994:W,
  author =       "Alan Edelman",
  title =        "When is {$x*(1/x) \ne 1$}?",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Manuscript",
}

@Article{Edelman:1997:MPD,
  author =       "Alan Edelman",
  title =        "The Mathematics of the {Pentium} Division Bug",
  journal =      j-SIREV,
  volume =       "39",
  number =       "1",
  pages =        "54--67",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Edelman:1995:CPC,
  author =       "Alan Edelman and Walter Mascarenhas",
  title =        "On the Complete Pivoting Conjecture for a {Hadamard}
                 Matrix of Order 12",
  journal =      j-LMA,
  volume =       "38",
  number =       "3",
  pages =        "181--188",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Edelman:1995:PRC,
  author =       "Alan Edelman and H. Murakami",
  title =        "Polynomial Roots from Companion Matrix Eigenvalues",
  journal =      j-MATH-COMP,
  volume =       "64",
  number =       "210",
  pages =        "763--776",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Edelman:1993:SO,
  author =       "Alan Edelman and G. W. Stewart",
  title =        "Scaling for Orthogonality",
  journal =      j-IEEE-SP,
  volume =       "41",
  number =       "4",
  pages =        "1676--1677",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Egecioglu:1990:PMF,
  author =       "{\"O}mer E\v{g}ecio\u{g}lu and E. Gallopoulos and
                 {\c{C}}. K. Ko{\c{c}}",
  title =        "A Parallel Method for Fast and Practical High-Order
                 {Newton} Interpolation",
  journal =      j-BIT,
  volume =       "30",
  pages =        "268--288",
  year =         "1990",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Erisman:1987:EOU,
  author =       "A. M. Erisman and R. G. Grimes and J. G. Lewis and W.
                 G. Poole and H. D. Simon",
  title =        "Evaluation of Orderings for Unsymmetric Sparse
                 Matrices",
  journal =      j-SISSC,
  volume =       "8",
  number =       "4",
  pages =        "600--624",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Eirola:1993:ABE,
  author =       "Timo Eirola",
  title =        "Aspects of Backward Error Analysis of Numerical
                 {ODE}s",
  journal =      j-JCAM,
  volume =       "45",
  number =       "1-2",
  pages =        "65--73",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Edelman:1994:HME,
  author =       "Alan Edelman and Eric Kostlan and Michael Shub",
  title =        "How Many Eigenvalues of a Random Matrix are Real?",
  journal =      j-JAMS,
  volume =       "7",
  number =       "1",
  pages =        "247--267",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Elden:1980:PTL,
  author =       "Lars Eld{\'e}n",
  title =        "Perturbation Theory for the Least Squares Problem with
                 Linear Equality Constraints",
  journal =      j-SINUM,
  volume =       "17",
  number =       "3",
  pages =        "338--350",
  year =         "1980",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Eldersveld:1992:BUL,
  author =       "Samuel K. Eldersveld and Michael A. Saunders",
  title =        "A Block-{$LU$} Update for Large-Scale Linear
                 Programming",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "191--201",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Enright:1989:NEC,
  author =       "W. H. Enright",
  title =        "A New Error-Control for Initial Value Solvers",
  journal =      j-APP-MATH-COMP,
  volume =       "31",
  pages =        "288--301",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Epton:1980:MSA,
  author =       "Michael A. Epton",
  title =        "Methods for the Solution of {$AXD-BXC=E$} and its
                 Application in the Numerical Solution of Implicit
                 Ordinary Differential Equations",
  journal =      j-BIT,
  volume =       "20",
  pages =        "341--345",
  year =         "1980",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Erisman:1974:MST,
  author =       "A. M. Erisman and J. K. Reid",
  title =        "Monitoring the Stability of the Triangular
                 Factorization of a Sparse Matrix",
  journal =      j-NUM-MATH,
  volume =       "22",
  pages =        "183--186",
  year =         "1974",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Espelid:1995:FPS,
  author =       "Terje O. Espelid",
  title =        "On Floating-Point Summation",
  journal =      j-SIREV,
  volume =       "37",
  number =       "4",
  pages =        "603--607",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Ewing:1991:PHC,
  editor =       "John H. Ewing and F. W. Gehring",
  title =        "{Paul Halmos}: {Celebrating} 50 Years of Mathematics",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-NY,
  pages =        "viii + 320",
  year =         "1991",
  ISBN =         "3-540-97509-8",
  ISBN-13 =      "978-3-540-97509-0",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Ewing:1994:CMT,
  editor =       "John Ewing",
  title =        "A Century of Mathematics Through the Eyes of the
                 {Monthly}",
  publisher =    "Mathematical Association of America",
  address =      "Washington, D.C.",
  pages =        "xi + 323",
  year =         "1994",
  ISBN =         "0-88385-459-7",
  ISBN-13 =      "978-0-88385-459-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Faddeeva:1959:CML,
  author =       "V. N. Faddeeva",
  title =        "Computational Methods of Linear Algebra",
  publisher =    pub-Dover,
  address =      pub-Dover:adr,
  pages =        "x + 252",
  year =         "1959",
  ISBN =         "0-486-60424-1",
  ISBN-13 =      "978-0-486-60424-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Fan:1955:SMI,
  author =       "Ky Fan and A. J. Hoffman",
  title =        "Some Metric Inequalities in the Space of Matrices",
  journal =      j-PROC-AMS,
  volume =       "6",
  pages =        "111--116",
  year =         "1955",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Fallat:2001:BFT,
  author =       "Shaun M. Fallat",
  title =        "Bidiagonal Factorizations of Totally Nonnegative
                 Matrices",
  journal =      j-AMM,
  volume =       "108",
  number =       "8",
  pages =        "697--712",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Farebrother:1987:MLM,
  author =       "R. W. Farebrother",
  title =        "A Memoir of the Life of {M. H. Doolittle}",
  journal =      j-IMA-BULL,
  volume =       "23",
  number =       "6/7",
  pages =        "102",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "IMA Bulletin",
}

@Book{Farebrother:1988:LLS,
  author =       "R. W. Farebrother",
  title =        "Linear Least Squares Computations",
  publisher =    "Marcel Dekker",
  address =      "New York",
  pages =        "xiii + 293",
  year =         "1988",
  ISBN =         "0-8247-7661-5",
  ISBN-13 =      "978-0-8247-7661-9",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Farnum:1988:CSF,
  author =       "Charles Farnum",
  title =        "Compiler Support for Floating-Point Computation",
  journal =      j-SPE,
  volume =       "18",
  number =       "7",
  pages =        "701--709",
  year =         "1988",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}

@Article{Fateman:1982:HLL,
  author =       "Richard J. Fateman",
  title =        "High-Level Language Implications of the Proposed
                 {IEEE} Floating-Point Standard",
  journal =      j-TOPLAS,
  volume =       "4",
  number =       "2",
  pages =        "239--257",
  month =        apr,
  year =         "1982",
  CODEN =        "ATPSDT",
  DOI =          "https://doi.org/10.1145/357162.357168",
  ISSN =         "0164-0925 (print), 1558-4593 (electronic)",
  ISSN-L =       "0164-0925",
  bibdate =      "Thu Nov 8 14:50:28 2007",
  bibsource =    "Compiler/bevan.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran2.bib;
                 https://www.math.utah.edu/pub/tex/bib/toplas.bib",
  abstract =     "An IEEE Computer Society working group on
                 floating-point arithmetic has recommended a standard
                 for binary floating-point number formats, operations,
                 and semantics. This paper, which has evolved in part
                 during the deliberations of that committee, describes
                 the significance to languages and, in particular, to
                 FORTRAN and its variants, of various novel features of
                 the recommended standard.",
  acknowledgement = ack-pb,
  checked =      "19940302",
  fjournal =     "ACM Transactions on Programming Languages and
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J783",
  keywords =     "computer arithmetic; control structures; data types
                 and structures; error handling and recovery;
                 floating-point arithmetic; FORTRAN; run-time
                 environments",
  source =       "Dept. Library",
}

@InProceedings{Ferguson:1991:AMA,
  author =       "Warren E. {Ferguson, Jr.} and Tom Brightman",
  editor =       "Peter Kornerup and David W. Matula",
  booktitle =    "Proc. 10th IEEE Symposium on Computer Arithmetic",
  title =        "Accurate and Monotone Approximations of Some
                 Transcendental Functions",
  publisher =    "IEEE Computer Society Press, Los Alamitos, CA, USA",
  pages =        "237--244",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Feldstein:1982:LSF,
  author =       "Alan Feldstein and Richard Goodman",
  title =        "Loss of Significance in Floating Point Subtraction and
                 Addition",
  journal =      j-IEEE-C,
  volume =       "C-31",
  number =       "4",
  pages =        "328--335",
  year =         "1982",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Ferguson:1995:ECS,
  author =       "Warren E. {Ferguson, Jr.}",
  editor =       "Simon Knowles and William H. McAllister",
  booktitle =    "Proc. 12th IEEE Symposium on Computer Arithmetic,
                 Bath, England",
  title =        "Exact Computation of a Sum or Difference with
                 Applications to Argument Reduction",
  publisher =    "IEEE Computer Society Press, Los Alamitos, CA, USA",
  pages =        "216--221",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Feldstein:1986:OUS,
  author =       "Alan Feldstein and Peter Turner",
  title =        "Overflow, Underflow, and Severe Loss of Significance
                 in Floating-Point Addition and Subtraction",
  journal =      j-IMAJNA,
  volume =       "6",
  pages =        "241--251",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Feingold:1962:BDD,
  author =       "David G. Feingold and Richard S. Varga",
  title =        "Block Diagonally Dominant Matrices and Generalizations
                 of the {Gerschgorin} Circle Theorem",
  journal =      j-PAC-J-MATH,
  volume =       "12",
  pages =        "1241--1250",
  year =         "1962",
  CODEN =        "PJMAAI",
  ISSN =         "0030-8730 (print), 1945-5844 (electronic)",
  ISSN-L =       "0030-8730",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Pacific Journal of Mathematics",
  journal-URL =  "http://msp.org/pjm",
}

@Article{Forsgren:1995:CMN,
  author =       "Anders Forsgren and Philip E. Gill and Walter Murray",
  title =        "Computing Modified {Newton} Directions Using a Partial
                 {Cholesky} Factorization",
  journal =      j-SISC,
  volume =       "16",
  number =       "1",
  pages =        "139--150",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ferng:1991:ALM,
  author =       "William R. Ferng and Gene H. Golub and Robert J.
                 Plemmons",
  title =        "Adaptive {Lanczos} Methods for Recursive Condition
                 Estimation",
  journal =      j-NUM-ALG,
  volume =       "1",
  number =       "1",
  pages =        "1--19",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Forsgren:1996:SSI,
  author =       "Anders Forsgren and Philip E. Gill and Joseph R.
                 Shinnerl",
  title =        "Stability of Symmetric Ill-Conditioned Systems Arising
                 in Interior Methods for Constrained Optimization",
  journal =      j-SIMAX,
  volume =       "17",
  number =       "1",
  pages =        "187--211",
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Fox:1978:PMS,
  author =       "P. A. Fox and A. D. Hall and N. L. Schryer",
  title =        "The {PORT} Mathematical Subroutine Library",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "104--126",
  year =         "1978",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Fox:1948:NSA,
  author =       "L. Fox and H. D. Huskey and J. H. Wilkinson",
  title =        "Notes on the Solution of Algebraic Linear Simultaneous
                 Equations",
  journal =      j-QJMAM,
  volume =       "1",
  pages =        "149--173",
  year =         "1948",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Fike:1967:MEP,
  author =       "C. T. Fike",
  title =        "Methods of Evaluating Polynomial Approximations in
                 Function Evaluation Routines",
  journal =      j-CACM,
  volume =       "10",
  number =       "3",
  pages =        "175--178",
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Book{Fike:1968:CEM,
  author =       "C. T. Fike",
  title =        "Computer Evaluation of Mathematical Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 227",
  year =         "1968",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Fischer:1974:FSC,
  author =       "Patrick C. Fischer",
  editor =       "Jacques Loeckx",
  booktitle =    "Automata, Languages and Programming",
  title =        "Further Schemes for Combining Matrix Algorithms",
  volume =       "14",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "428--436",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Computer Science",
}

@Article{Fletcher:1976:FSI,
  author =       "R. Fletcher",
  title =        "Factorizing Symmetric Indefinite Matrices",
  journal =      j-LAA,
  volume =       "14",
  pages =        "257--272",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Fletcher:1985:EC,
  author =       "R. Fletcher",
  title =        "Expected Conditioning",
  journal =      j-IMAJNA,
  volume =       "5",
  pages =        "247--273",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Fletcher:1987:PMO,
  author =       "R. Fletcher",
  title =        "Practical Methods of Optimization",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr-C,
  edition =      "Second",
  pages =        "xiv + 436",
  year =         "1987",
  ISBN =         "0-471-91547-5",
  ISBN-13 =      "978-0-471-91547-8",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Fletcher:1974:MF,
  author =       "R. Fletcher and M. J. D. Powell",
  title =        "On the Modification of {$LDL^T$} Factorizations",
  journal =      j-MATH-COMP,
  volume =       "28",
  number =       "128",
  pages =        "1067--1087",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Forsythe:1977:CMM,
  author =       "George E. (George Elmer) Forsythe and Michael A.
                 Malcolm and Cleve B. Moler",
  title =        "Computer Methods for Mathematical Computations",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xi + 259",
  year =         "1977",
  ISBN =         "0-13-165332-6",
  ISBN-13 =      "978-0-13-165332-0",
  LCCN =         "QA297 .F5681",
  MRclass =      "65-01",
  MRnumber =     "MR0458783 (56 \#16983)",
  MRreviewer =   "Sven-{\AA}ke Gustafson",
  bibdate =      "Tue May 25 09:01:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
                 squares, which is available by anonymous ftp from
                 \path=math.liu.se= in \path=pub/references=",
  price =        "US\$16.95",
  series =       "Prentice-Hall series in automatic computation",
  ZMnumber =     "0361.65002",
  acknowledgement = ack-nhfb,
  classmath =    "*65-01 Textbooks (numerical analysis) 68-01 Textbooks
                 (computer science)",
  keywords =     "Fortran (computer program language); numerical
                 analysis -- data processing",
  remark =       "Subroutines and exercises for the computer solution of
                 problems involving matrices, integrals, differential
                 equations, spline functions, zeros and extrema of
                 functions, least squares, and Monte Carlo techniques.",
  subject =      "Numerical analysis; Data processing; Computer
                 programs; Problems, exercises, etc; FORTRAN (Computer
                 program language)",
  tableofcontents = "Introduction \\
                 Floating-point computation \\
                 Linear systems of equations \\
                 Interpolation \\
                 Numerical integration \\
                 Initial value problems in ordinary differential
                 equations \\
                 Solution of nonlinear equations \\
                 Optimization \\
                 Least squares and the singular value decomposition \\
                 Random number generation and Monte Carlo methods",
}

@Article{Funderlic:1982:DGD,
  author =       "R. E. Funderlic and M. Neumann and R. J. Plemmons",
  title =        "{$LU$} Decompositions of Generalized Diagonally
                 Dominant Matrices",
  journal =      j-NUM-MATH,
  volume =       "40",
  pages =        "57--69",
  year =         "1982",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Book{Forsythe:1967:CSL,
  author =       "George E. Forsythe and Cleve B. Moler",
  title =        "Computer Solution of Linear Algebraic Systems",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xi + 148",
  year =         "1967",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ford:1978:PET,
  author =       "Brian Ford",
  title =        "Parameterization of the Environment for Transportable
                 Numerical Software",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "100--103",
  year =         "1978",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Forsythe:1951:GGR,
  author =       "George E. Forsythe",
  title =        "Gauss to {Gerling} on Relaxation",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "5",
  pages =        "255--258",
  year =         "1951",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Forsythe:1953:SLA,
  author =       "George E. Forsythe",
  title =        "Solving Linear Algebraic Equations Can Be
                 Interesting",
  journal =      j-BAMS,
  volume =       "59",
  number =       "4",
  pages =        "299--329",
  year =         "1953",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Forsythe:1959:RNR,
  author =       "George E. Forsythe",
  title =        "Reprint of a Note on Rounding-Off Errors",
  journal =      j-SIREV,
  volume =       "1",
  number =       "1",
  pages =        "66--67",
  year =         "1959",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Forsythe:1960:ACP,
  author =       "George E. Forsythe",
  title =        "{Algorithm 16}: {Crout} with Pivoting",
  journal =      j-CACM,
  volume =       "3",
  number =       "9",
  pages =        "507--508",
  month =        sep,
  year =         "1960",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/367390.367406",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:28 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@Article{Forsythe:1967:TCM,
  author =       "George E. Forsythe",
  title =        "Today's Computational Methods of Linear Algebra",
  journal =      j-SIREV,
  volume =       "9",
  pages =        "489--515",
  year =         "1967",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  nuber =        "3",
}

@InCollection{Forsythe:1969:WSQ,
  author =       "George E. Forsythe",
  editor =       "Bruno Dejon and Peter Henrici",
  booktitle =    "Constructive Aspects of the Fundamental Theorem of
                 Algebra",
  title =        "What is a Satisfactory Quadratic Equation Solver?",
  publisher =    "Wiley-Interscience",
  address =      "London",
  pages =        "53--61",
  year =         "1969",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InCollection{Forsythe:1969:SQE,
  author =       "George E. Forsythe",
  editor =       "National Research Council's Committee on Support of
                 Research in the Mathematical Sciences",
  booktitle =    "The Mathematical Sciences: {A} Collection of Essays",
  title =        "Solving a Quadratic Equation on a Computer",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  pages =        "138--152",
  year =         "1969",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Forsythe:1970:PCW,
  author =       "George E. Forsythe",
  title =        "Pitfalls in Computation, or Why a Math Book Isn't
                 Enough",
  journal =      j-AMM,
  volume =       "77",
  pages =        "931--956",
  year =         "1970",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Forsythe:1955:BCM,
  author =       "George E. Forsythe and E. G. Straus",
  title =        "On Best Conditioned Matrices",
  journal =      j-PROC-AMS,
  volume =       "6",
  pages =        "340--345",
  year =         "1955",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Foster:1991:MNE,
  author =       "Leslie Foster",
  editor =       "G. H. Golub and P. M. {Van Dooren}",
  booktitle =    "Numerical Linear Algebra, Digital Signal Processing
                 and Parallel Algorithms",
  title =        "Modifications of the Normal Equations Method That Are
                 Numerically Stable",
  volume =       "F70",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "501--512",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "NATO ASI Series",
}

@Article{Foster:1994:GEP,
  author =       "Leslie V. Foster",
  title =        "Gaussian Elimination with Partial Pivoting Can Fail in
                 Practice",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "4",
  pages =        "1354--1362",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Foster:1997:GFE,
  author =       "Leslie V. Foster",
  title =        "The Growth Factor and Efficiency of {Gaussian}
                 Elimination with Rook Pivoting",
  journal =      j-JCAM,
  volume =       "86",
  pages =        "177--194",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Corrigendum in " # j-JCAM # ", 98:177, 1998",
}

@Book{Fox:1964:INL,
  author =       "L. Fox",
  title =        "An Introduction to Numerical Linear Algebra",
  publisher =    pub-OUP,
  pages =        "xi + 328",
  year =         "1964",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Fox:1971:HGM,
  author =       "L. Fox",
  title =        "How to Get Meaningless Answers in Scientific
                 Computation (and What to Do About It)",
  journal =      j-IMA-BULL,
  volume =       "7",
  number =       "10",
  pages =        "296--302",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "IMA Bulletin",
}

@InProceedings{Fox:1978:AAJ,
  author =       "L. Fox",
  booktitle =    "The Contribution of {Dr. J. H. Wilkinson} to Numerical
                 Analysis",
  title =        "All About {Jim Wilkinson}, with a Commemorative
                 Snippet on Backward Error Analysis",
  publisher =    inst-IMA-UK # ", " # inst-IMA-UK:adr,
  pages =        "1--20",
  year =         "1978",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Symposium Proceedings Series No. 19",
}

@Article{Fox:1987:JHW,
  author =       "L. Fox",
  title =        "{James Hardy Wilkinson}, 1919--1986",
  journal =      j-BIOGRAPH-MEMOIRS-FELLOWS-ROY-SOC,
  volume =       "33",
  pages =        "671--708",
  year =         "1987",
  CODEN =        "BMFRA3",
  DOI =          "https://doi.org/10.1098/rsbm.1987.0024",
  ISSN =         "0080-4606 (print), 1748-8494 (electronic)",
  ISSN-L =       "0080-4606",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Biographical Memoirs of Fellows of the Royal Society",
  journal-URL =  "http://www.jstor.org/journals/00804606.html;
                 https://royalsocietypublishing.org/loi/rsbm",
}

@TechReport{fpv86,
  key =          "NAG",
  title =        "{FPV}: {A} Floating-Point Validation Package. {Release
                 I}. {User's} Guide",
  type =         "Technical Report",
  number =       "NP 1201",
  institution =  "NAG Ltd.",
  address =      "Oxford",
  month =        may,
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Frank:1958:CEC,
  author =       "Werner L. Frank",
  title =        "Computing Eigenvalues of Complex Matrices by
                 Determinant Evaluation and by Methods of {Danilewski}
                 and {Wielandt}",
  journal =      j-SIAM,
  volume =       "6",
  number =       "4",
  pages =        "378--392",
  year =         "1958",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@PhdThesis{Fraysse:1992:RCS,
  author =       "V. Frayss{\'e}",
  title =        "Reliability of Computer Solutions",
  school =       "L'Institut National Polytechnique de Toulouse",
  address =      "Toulouse, France",
  month =        jul,
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "CERFACS Report TH/PA/92/11",
}

@Article{Friedland:1991:RMS,
  author =       "Shmuel Friedland",
  title =        "Revisiting Matrix Squaring",
  journal =      j-LAA,
  volume =       "154--156",
  pages =        "59--63",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Frigo:1998:FAS,
  author =       "Matteo Frigo and Steven G. Johnson",
  booktitle =    "Proceedings of International Conference on Acoustics,
                 Speech and Signal Processing, Volume 3",
  title =        "{FFTW}: {An} Adaptive Software Architecture for the
                 {FFT}",
  pages =        "1381 +",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Francois:1991:SPM,
  author =       "Philippe Fran{\c{c}}ois and Jean-Michel Muller",
  booktitle =    "Proceedings of IMACS '91, 13th World Congress on
                 Computation and Applied Mathematics, Dublin, Volume 1",
  title =        "The {SCALP} Perturbation Method",
  pages =        "59--60",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InCollection{Frommer:2001:PCU,
  author =       "Andreas Frommer",
  editor =       "A. Facius and U. Kulisch and R. Lohner",
  booktitle =    "Perspectives on Enclosure Methods",
  title =        "Proving Conjectures by Use of Interval Arithmetic",
  publisher =    pub-Springer # ", " # pub-Springer:adr-NY,
  pages =        "1--13",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Friedland:1980:GPN,
  author =       "Shmuel Friedland and Hans Schneider",
  title =        "The Growth of Powers of a Nonnegative Matrix",
  journal =      j-SIAD,
  volume =       "1",
  number =       "2",
  pages =        "185--200",
  year =         "1980",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gal:1991:AEM,
  author =       "Shmuel Gal and Boris Bachelis",
  title =        "An Accurate Elementary Mathematical Library for the
                 {IEEE} Floating Point Standard",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "26--45",
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Book{Godunov:1993:GAN,
  author =       "S. K. Godunov and A. G. Antonov and O. P. Kiriljuk and
                 V. I. Kostin",
  title =        "Guaranteed Accuracy in Numerical Linear Algebra",
  publisher =    pub-Kluwer,
  address =      pub-Kluwer:adr,
  pages =        "xi + 535",
  year =         "1993",
  ISBN =         "0-7923-2352-1",
  ISBN-13 =      "978-0-7923-2352-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gardiner:1991:PAA,
  author =       "Judith D. Gardiner and Alan J. Laub",
  title =        "Parallel Algorithms for Algebraic {Riccati}
                 Equations",
  journal =      j-IJC,
  volume =       "54",
  number =       "6",
  pages =        "1317--1333",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Gantmacher:1959:TMa,
  author =       "F. R. Gantmacher",
  title =        "The Theory of Matrices",
  volume =       "one",
  publisher =    "Chelsea",
  address =      "New York",
  pages =        "x + 374",
  year =         "1959",
  ISBN =         "0-8284-0131-4",
  ISBN-13 =      "978-0-8284-0131-9",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Gantmacher:1959:TMb,
  author =       "F. R. Gantmacher",
  title =        "The Theory of Matrices",
  volume =       "two",
  publisher =    "Chelsea",
  address =      "New York",
  pages =        "ix + 276",
  year =         "1959",
  ISBN =         "0-8284-0133-0",
  ISBN-13 =      "978-0-8284-0133-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gasca:1992:TPN,
  author =       "M. Gasca and J. M. Pe{\~n}a",
  title =        "Total Positivity and {Neville} Elimination",
  journal =      j-LAA,
  volume =       "165",
  pages =        "25--44",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Gardner:1961:MMP,
  author =       "Martin Gardner",
  title =        "More Mathematical Puzzles and Diversions",
  publisher =    pub-Penguin,
  address =      pub-Penguin:adr-NY,
  pages =        "187",
  year =         "1961",
  ISBN =         "0-14-020748-1",
  ISBN-13 =      "978-0-14-020748-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Garner:1976:SSR,
  author =       "Harvey L. Garner",
  title =        "A Survey of Some Recent Contributions to Computer
                 Arithmetic",
  journal =      j-IEEE-C,
  volume =       "C-25",
  number =       "12",
  pages =        "1277--1282",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Gastinel:1983:LNA,
  author =       "Noel Gastinel",
  title =        "Linear Numerical Analysis",
  publisher =    "Kershaw Publishing",
  address =      "London",
  pages =        "ix + 341",
  year =         "1983",
  ISBN =         "0-901665-16-9",
  ISBN-13 =      "978-0-901665-16-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "First published in English by Academic Press, London,
                 1970",
}

@Article{Gautschi:1953:ABP,
  author =       "Walter Gautschi",
  title =        "The Asymptotic Behaviour of Powers of Matrices",
  journal =      j-DUKE-MATH-J,
  volume =       "20",
  pages =        "127--140",
  year =         "1953",
  CODEN =        "DUMJAO",
  ISSN =         "0012-7094 (print), 1547-7398 (electronic)",
  ISSN-L =       "0012-7094",
  bibdate =      "Thu Jan 19 07:49:45 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Duke Mathematical Journal",
  journal-URL =  "http://projecteuclid.org/info/euclid.dmj",
}

@Article{Gautschi:1962:IVC,
  author =       "Walter Gautschi",
  title =        "On Inverses of {Vandermonde} and Confluent
                 {Vandermonde} Matrices",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "117--123",
  year =         "1962",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Gautschi:1975:NEI,
  author =       "Walter Gautschi",
  title =        "Norm Estimates for Inverses of {Vandermonde}
                 Matrices",
  journal =      j-NUM-MATH,
  volume =       "23",
  pages =        "337--347",
  year =         "1975",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Gautschi:1978:IVC,
  author =       "Walter Gautschi",
  title =        "On Inverses of {Vandermonde} and Confluent
                 {Vandermonde} Matrices {III}",
  journal =      j-NUM-MATH,
  volume =       "29",
  pages =        "445--450",
  year =         "1978",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Gautschi:1983:CVL,
  author =       "Walter Gautschi",
  title =        "The Condition of {Vandermonde}-Like Matrices Involving
                 Orthogonal Polynomials",
  journal =      j-LAA,
  volume =       "52/53",
  pages =        "293--300",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Gautschi:1990:HSV,
  author =       "Walter Gautschi",
  editor =       "R. Wong",
  booktitle =    "Asymptotic and Computational Analysis",
  title =        "How (Un)stable are {Vandermonde} Systems?",
  volume =       "124",
  publisher =    pub-DEKKER,
  address =      pub-DEKKER:adr,
  pages =        "193--210",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Pure and Applied Mathematics",
  mynote =       "crossref Wong:1990:ACA",
}

@TechReport{Gay:1990:CRB,
  author =       "David M. Gay",
  title =        "Correctly Rounded Binary-Decimal and Decimal-Binary
                 Conversions",
  type =         "Numerical Analysis Manuscript",
  number =       "90-10",
  institution =  inst-ATT,
  address =      inst-ATT:adr,
  pages =        "16",
  month =        nov,
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{gaze24,
  key =          "Mathematical Gazette",
  title =        "Gleanings Far and Near",
  journal =      j-MATH-GAZ,
  volume =       "22",
  number =       "170",
  pages =        "95",
  year =         "1924",
  CODEN =        "MAGAAS",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}

@Book{Garbow:1977:MER,
  author =       "B. S. Garbow and J. M. Boyle and J. J. Dongarra and C.
                 B. Moler",
  title =        "Matrix Eigensystem Routines---{EISPACK} Guide
                 Extension",
  volume =       "51",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "viii + 343",
  year =         "1977",
  ISBN =         "3-540-08254-9",
  ISBN-13 =      "978-3-540-08254-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Computer Science",
}

@TechReport{Gu:1994:ECS,
  author =       "Ming Gu and James W. Demmel and Inderjit Dhillon",
  title =        "Efficient Computation of the Singular Value
                 Decomposition with Applications to Least Squares
                 Problems",
  type =         "Technical Report",
  number =       "CS-94-257",
  institution =  inst-CS-U-Tenn,
  address =      inst-CS-U-Tenn:adr,
  pages =        "19",
  month =        oct,
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "LAPACK Working Note 88",
}

@Article{Guggenheimer:1995:SEC,
  author =       "Heinrich W. Guggenheimer and Alan S. Edelman and
                 Charles R. Johnson",
  title =        "A Simple Estimate of the Condition Number of a Linear
                 System",
  journal =      j-CMJ,
  volume =       "26",
  number =       "1",
  pages =        "2--5",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{George:1981:CSL,
  author =       "Alan George and Joseph W-H Liu",
  title =        "Computer Solution of Large Sparse Positive Definite
                 Systems",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 324",
  year =         "1981",
  ISBN =         "0-13-165274-5",
  ISBN-13 =      "978-0-13-165274-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gentleman:1974:MAR,
  author =       "W. Morven Gentleman and Scott B. Marovich",
  title =        "More on Algorithms that Reveal Properties of Floating
                 Point Arithmetic Units",
  journal =      j-CACM,
  volume =       "17",
  number =       "5",
  pages =        "276--277",
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Geman:1986:SRL,
  author =       "Stuart Geman",
  title =        "The Spectral Radius of Large Random Matrices",
  journal =      j-ANN-PROBAB,
  volume =       "14",
  number =       "4",
  pages =        "1318--1328",
  month =        oct,
  year =         "1986",
  CODEN =        "APBYAE",
  ISSN =         "0091-1798 (print), 2168-894X (electronic)",
  ISSN-L =       "0091-1798",
  bibdate =      "Sun Apr 20 10:44:17 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/annprobab1980.bib",
  URL =          "http://projecteuclid.org/euclid.aop/1176992372",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Probability",
  journal-URL =  "http://projecteuclid.org/all/euclid.aop",
}

@Article{Gentleman:1969:EAG,
  author =       "W. M. Gentleman",
  title =        "An Error Analysis of {Goertzel's (Watt's)} Method for
                 Computing {Fourier} Coefficients",
  journal =      j-COMP-J,
  volume =       "12",
  pages =        "160--165",
  year =         "1969",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Gentleman:1973:LSC,
  author =       "W. Morven Gentleman",
  title =        "Least Squares Computations by {Givens} Transformations
                 Without Square Roots",
  journal =      j-JIMA,
  volume =       "12",
  pages =        "329--336",
  year =         "1973",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gentleman:1975:EAD,
  author =       "W. Morven Gentleman",
  title =        "Error Analysis of {$QR$} Decompositions by {Givens}
                 Transformations",
  journal =      j-LAA,
  volume =       "10",
  pages =        "189--197",
  year =         "1975",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Gentleman:1966:FFT,
  author =       "W. M. Gentleman and G. Sande",
  booktitle =    "Fall Joint Computer Conference",
  title =        "Fast {Fourier} Transforms---For Fun and Profit",
  volume =       "29",
  publisher =    "Spartan Books, Washington, D.C.",
  pages =        "563--578",
  year =         "1966",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "AFIPS Conference Proceedings",
}

@Article{Geurts:1982:CTC,
  author =       "A. J. Geurts",
  title =        "A Contribution to the Theory of Condition",
  journal =      j-NUM-MATH,
  volume =       "39",
  pages =        "85--96",
  year =         "1982",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Goodman:1985:REF,
  author =       "R. H. Goodman and A. Feldstein and J. Bustoz",
  title =        "Relative Error in Floating-Point Multiplication",
  journal =      j-COMPUTING,
  volume =       "35",
  pages =        "127--139",
  year =         "1985",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Ghavimi:1995:BES,
  author =       "Ali R. Ghavimi and Alan J. Laub",
  title =        "Backward Error, Sensitivity, and Refinement of
                 Computed Solutions of Algebraic {Riccati} Equations",
  journal =      j-NUM-LIN-ALG-APPL,
  volume =       "2",
  number =       "1",
  pages =        "29--49",
  year =         "1995",
  CODEN =        "NLAAEM",
  ISSN =         "1070-5325 (print), 1099-1506 (electronic)",
  ISSN-L =       "1070-5325",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerical Linear Algebra with Applications",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
}

@Article{Ghavimi:1995:RBD,
  author =       "Ali R. Ghavimi and Alan J. Laub",
  title =        "Residual Bounds for Discrete-Time {Lyapunov}
                 Equations",
  journal =      j-IEEE-AC,
  volume =       "40",
  number =       "7",
  pages =        "1244--1249",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{George:2002:GFG,
  author =       "Alan George and Khakim D. Ikramov and Andrey B.
                 Kucherov",
  title =        "On the Growth Factor in {Gaussian} Elimination for
                 Generalized {Higham} Matrices",
  journal =      j-NLAA,
  volume =       "9",
  pages =        "107--114",
  year =         "2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gill:1951:PSS,
  author =       "S. Gill",
  title =        "A Process for the Step-By-Step Integration of
                 Differential Equations in an Automatic Digital
                 Computing Machine",
  journal =      j-PROC-CAMBRIDGE-PHIL-SOC,
  volume =       "47",
  pages =        "96--108",
  year =         "1951",
  CODEN =        "PCPSA4",
  ISSN =         "0008-1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Proceedings of the Cambridge Philosophical Society. Mathematical and physical sciences",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PSP",
}

@InCollection{Gillespie:1991:NVT,
  author =       "T. A. Gillespie",
  editor =       "John H. Ewing and F. W. Gehring",
  booktitle =    "{Paul Halmos}: {Celebrating} 50 Years of Mathematics",
  title =        "Noncommutative Variations on Theorems of {Marcel
                 Riesz} and Others",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "221--236",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gill:1973:NSF,
  author =       "P. E. Gill and W. Murray",
  title =        "A Numerically Stable Form of the Simplex Algorithm",
  journal =      j-LAA,
  volume =       "7",
  pages =        "99--138",
  year =         "1973",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Givens:1954:NCC,
  author =       "Wallace J. Givens",
  title =        "Numerical Computation of the Characteristic Values of
                 a Real Symmetric Matrix",
  number =       "ORNL-1574",
  institution =  inst-ORNL,
  address =      inst-ORNL:adr,
  pages =        "107",
  year =         "1954",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gudmundsson:1995:SSS,
  author =       "Thorkell Gudmundsson and Charles S. Kenney and Alan J.
                 Laub",
  title =        "Small-Sample Statistical Estimates for Matrix Norms",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "3",
  pages =        "776--792",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Graham:1994:CM,
  author =       "Ronald L. Graham and Donald E. Knuth and Oren
                 Patashnik",
  title =        "Concrete Mathematics",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xiii + 657",
  year =         "1994",
  ISBN =         "0-201-55802-5",
  ISBN-13 =      "978-0-201-55802-9",
  LCCN =         "QA39.2 .G733 1994",
  MRclass =      "68-01 (00-01 00A05 05-01 68Rxx)",
  MRnumber =     "97d:68003",
  bibdate =      "Wed Jul 6 14:39:36 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
  acknowledgement = ack-nhfb,
  keywords =     "computer science -- mathematics; mathematics",
  shorttableofcontents = "1: Recurrent Problems / 1 \\
                 2: Sums / 21 \\
                 3: Integer Functions / 67 \\
                 4: Number Theory / 102 \\
                 5: Binomial Coefficients / 153 \\
                 6: Special Numbers / 257 \\
                 7: Generating Functions / 320 \\
                 8: Discrete Probability / 381 \\
                 9: Asymptotics / 439 \\
                 A: Answers to Exercises / 497 \\
                 B: Bibliography / 604 \\
                 C: Credits for Exercises / 632 \\
                 Index / 637 \\
                 List of Tables / 657",
  tableofcontents = "1: Recurrent Problems / 1 \\
                 1.1 The Tower of Hanoi / 1 \\
                 1.2 Lines in the Plane / 4 \\
                 1.3 The Josephus Problem / 8 \\
                 Exercises / 17 \\
                 2: Sums / 21 \\
                 2.1 Notation / 21 \\
                 2.2 Sums and Recurrences / 25 \\
                 2.3 Manipulation of Sums / 30 \\
                 2.4 Multiple Sums / 34 \\
                 2.5 General Methods / 41 \\
                 2.6 Finite and Infinite Calculus / 47 \\
                 2.7 Infinite Sums / 56 \\
                 Exercises / 62 \\
                 3: Integer Functions / 67 \\
                 3.1 Floors and Ceilings / 67 \\
                 3.2 Floor/Ceiling Applications / 70 \\
                 3.3 Floor/Ceiling Recurrences / 78 \\
                 3.4 `mod': The Binary Operation / 81 \\
                 3.5 Floor/Ceiling Sums / 86 \\
                 Exercises / 95 \\
                 4: Number Theory / 102 \\
                 4.1 Divisibility / 102 \\
                 4.2 Primes / 105 \\
                 4.3 Prime Examples / 107 \\
                 4.4 Factorial Factors / 111 \\
                 4.5 Relative Primality / 115 \\
                 4.6 `mod': The Congruence Relation / 123 \\
                 4.7 Independent Residues / 126 \\
                 4.8 Additional Applications / 129 \\
                 4.9 Phi and Mu / 133 \\
                 Exercises / 144 \\
                 5: Binomial Coefficients / 153 \\
                 5.1 Basic Identities / 153 \\
                 5.2 Basic Practice / 172 \\
                 5.3 Tricks of the Trade / 186 \\
                 5.4 Generating Functions / 196 \\
                 5.5 Hypergeometric Functions / 204 \\
                 5.6 Hypergeometric Transformations / 216 \\
                 5.7 Partial Hypergeometric Sums / 223 \\
                 5.8 Mechanical Summation / 229 \\
                 Exercises / 242 \\
                 6: Special Numbers / 257 \\
                 6.1 Stirling Numbers / 257 \\
                 6.2 Eulerian Numbers / 267 \\
                 6.3 Harmonic Numbers / 272 \\
                 6.4 Harmonic Summation / 279 \\
                 6.5 Bernoulli Numbers / 283 \\
                 6.6 Fibonacci Numbers / 290 \\
                 6.7 Continuants / 301 \\
                 Exercises / 309 \\
                 7: Generating Functions / 320 \\
                 7.1 Domino Theory and Change / 320 \\
                 7.2 Basic Maneuvers / 331 \\
                 7.3 Solving Recurrences / 337 \\
                 7.4 Special Generating Functions / 350 \\
                 7.5 Convolutions / 353 \\
                 7.6 Exponential Generating Functions / 364 \\
                 7.7 Dirichlet Generating Functions / 370 \\
                 Exercises / 371 \\
                 8: Discrete Probability / 381 \\
                 8.1 Definitions / 381 \\
                 8.2 Mean and Variance / 387 \\
                 8.3 Probability Generating Functions / 394 \\
                 8.4 Flipping Coins / 401 \\
                 8.5 Hashing / 411 \\
                 Exercises / 427 \\
                 9: Asymptotics / 439 \\
                 9.1 A Hierarchy / 440 \\
                 9.2 O Notation / 443 \\
                 9.3 O Manipulation / 450 \\
                 9.4 Two Asymptotic Tricks / 463 \\
                 9.5 Euler's Summation Formula / 469 \\
                 9.6 Final Summations / 476 \\
                 Exercises / 489 \\
                 A: Answers to Exercises / 497 \\
                 B: Bibliography / 604 \\
                 C: Credits for Exercises / 632 \\
                 Index / 637 \\
                 List of Tables / 657",
}

@Article{Gardiner:1992:SSM,
  author =       "Judith D. Gardiner and Alan J. Laub and James J. Amato
                 and Cleve B. Moler",
  title =        "Solution of the {Sylvester} Matrix Equation
                 {$AXB^T+CXD^T=E$}",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "223--231",
  year =         "1992",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Gardiner:1992:AFS,
  author =       "Judith D. Gardiner and Matthew R. Wette and Alan J.
                 Laub and James J. Amato and Cleve B. Moler",
  title =        "Algorithm 705: {A} {FORTRAN}-77 Software Package for
                 Solving the {Sylvester} Matrix Equation
                 {$AXB^T+CXD^T=E$}",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "232--238",
  year =         "1992",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Glanz:1995:MLF,
  author =       "James Glanz",
  title =        "Mathematical Logic Flushes Out the Bugs in Chip
                 Designs",
  journal =      j-SCIENCE,
  volume =       "267",
  pages =        "332--333",
  year =         "1995",
  ISSN =         "0036-8075 (print), 1095-9203 (electronic)",
  ISSN-L =       "0036-8075",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "20 " # jan,
  CODEN =        "SCIEAS",
  fjournal =     "Science",
  journal-URL =  "http://www.sciencemag.org/archive/",
}

@Article{Gahinet:1990:SSD,
  author =       "Pascal M. Gahinet and Alan J. Laub and Charles S.
                 Kenney and Gary A. Hewer",
  title =        "Sensitivity of the Stable Discrete-Time {Lyapunov}
                 Equation",
  journal =      j-IEEE-AC,
  volume =       "AC-35",
  number =       "11",
  pages =        "1209--1217",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gluchowska:1990:SLL,
  author =       "J. Gluchowska and A. Smoktunowicz",
  title =        "Solving the Linear Least Squares Problem with Very
                 High Relative Accuracy",
  journal =      j-COMPUTING,
  volume =       "45",
  pages =        "345--354",
  year =         "1990",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Gill:1992:PIS,
  author =       "Philip E. Gill and Walter Murray and Dulce B.
                 Poncele{\'o}n and Michael A. Saunders",
  title =        "Preconditioners For Indefinite Systems Arising in
                 Optimization",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "292--311",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Gill:1986:UGN,
  author =       "Philip E. Gill and Walter Murray and Michael A.
                 Saunders and Margaret H. Wright",
  title =        "User's Guide for {NPSOL} (Version 4.0): {A} {Fortran}
                 Package for Nonlinear Programming",
  type =         "Technical Report",
  number =       "SOL 86-2",
  institution =  inst-OR-U-STANFORD,
  address =      inst-U-STANFORD:adr,
  pages =        "53",
  month =        jan,
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gill:1991:ICM,
  author =       "Philip E. Gill and Walter Murray and Michael A.
                 Saunders and Margaret H. Wright",
  title =        "Inertia-Controlling Methods for General Quadratic
                 Programming",
  journal =      j-SIREV,
  volume =       "33",
  number =       "1",
  pages =        "1--36",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Gill:1981:PO,
  author =       "Philip E. Gill and Walter Murray and Margaret H.
                 Wright",
  title =        "Practical Optimization",
  publisher =    pub-AP,
  address =      pub-AP:adr-L,
  pages =        "xvi + 401",
  year =         "1981",
  ISBN =         "0-12-283952-8",
  ISBN-13 =      "978-0-12-283952-8",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Golub:1979:HSM,
  author =       "G. H. Golub and S. Nash and C. F. {Van Loan}",
  title =        "A {Hessenberg--Schur} Method for the Problem
                 {$AX+XB=C$}",
  journal =      j-IEEE-AC,
  volume =       "AC-24",
  number =       "6",
  pages =        "909--913",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Goodman:1975:REP,
  author =       "R. Goodman and A. Feldstein",
  title =        "Round-Off Error in Products",
  journal =      j-COMPUTING,
  volume =       "15",
  pages =        "263--273",
  year =         "1975",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Gohberg:1993:MCS,
  author =       "I. Gohberg and I. Koltracht",
  title =        "Mixed, Componentwise, and Structured Condition
                 Numbers",
  journal =      j-SIMAX,
  volume =       "14",
  number =       "3",
  pages =        "688--704",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Goldberg:1967:BED,
  author =       "I. Bennett Goldberg",
  title =        "$ 27 $ Bits Are Not Enough For $8$-Digit Accuracy",
  journal =      j-CACM,
  volume =       "10",
  number =       "2",
  pages =        "105--106",
  month =        feb,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363067.363112",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:11 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "From the inequality $ 10^8 < 2^{27} $, we are likely
                 to conclude that we can represent 8-digit decimal
                 floating-point numbers accurately by 27-bit [binary]
                 floating-point numbers. However, we need 28 significant
                 bits to represent some 8-digit numbers accurately. In
                 general, we can show that if $ 10^p < 2^{q - 1} $, then
                 $q$ significant bits are always enough for $p$-digit
                 decimal accuracy. Finally, we can define a compact
                 27-bit floating-point representation that will give 28
                 significant bits, for numbers of practical
                 importance.",
  acknowledgement = ack-nj # " and " # ack-mfc # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "decimal floating-point arithmetic",
  received =     "August 1966 (revised October 1966)",
}

@Book{Goldstine:1972:CPN,
  author =       "Herman H. Goldstine",
  title =        "The Computer: {From Pascal} to {von Neumann}",
  publisher =    pub-PUP,
  address =      pub-PUP:adr,
  pages =        "xii + 378",
  year =         "1972",
  ISBN =         "0-691-02367-0",
  ISBN-13 =      "978-0-691-02367-0",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "1993 printing with new preface",
}

@Book{Goldstine:1977:HNA,
  author =       "Herman H. Goldstine",
  title =        "A History of Numerical Analysis from the 16th through
                 the 19th Century",
  publisher =    "Springer-Verlag",
  address =      "New York",
  pages =        "xiv + 348",
  year =         "1977",
  ISBN =         "0-387-90277-5",
  ISBN-13 =      "978-0-387-90277-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Goldberg:1991:WEC,
  author =       "David Goldberg",
  title =        "What Every Computer Scientist Should Know About
                 Floating-Point Arithmetic",
  journal =      j-COMP-SURV,
  volume =       "23",
  number =       "1",
  pages =        "5--48",
  year =         "1991",
  CODEN =        "CMSVAN",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}

@Article{Golub:1962:BRE,
  author =       "Gene H. Golub",
  title =        "Bounds for the Round-Off Errors in the {Richardson}
                 Second Order Method",
  journal =      j-BIT,
  volume =       "2",
  pages =        "212--223",
  year =         "1962",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Golub:1965:NMS,
  author =       "G. H. Golub",
  title =        "Numerical Methods for Solving Linear Least Squares
                 Problems",
  journal =      j-NUM-MATH,
  volume =       "7",
  pages =        "206--216",
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Goodnight:1979:TSO,
  author =       "James H. Goodnight",
  title =        "A Tutorial on the {SWEEP} Operator",
  journal =      j-AMER-STAT,
  volume =       "33",
  number =       "3",
  pages =        "149--158",
  year =         "1979",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Gohberg:1994:FIC,
  author =       "I. Gohberg and V. Olshevsky",
  title =        "Fast Inversion of {Chebyshev--Vandermonde} Matrices",
  journal =      j-NUM-MATH,
  volume =       "67",
  number =       "1",
  pages =        "71--92",
  year =         "1994",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Govaerts:1990:BEO,
  author =       "W. Govaerts and J. D. Pryce",
  title =        "Block elimination with one iterative refinement solves
                 bordered linear systems accurately",
  journal =      j-BIT,
  volume =       "30",
  pages =        "490--507",
  year =         "1990",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Goldberg:1983:MNM,
  author =       "Moshe Goldberg and E. G. Straus",
  title =        "Multiplicativity of {$l_p$} Norms for Matrices",
  journal =      j-LAA,
  volume =       "52/53",
  pages =        "351--360",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gould:1991:GGE,
  author =       "N. I. M. Gould",
  title =        "On Growth in {Gaussian} Elimination with Complete
                 Pivoting",
  journal =      j-SIMAX,
  volume =       "12",
  number =       "2",
  pages =        "354--361",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Govaerts:2000:NMB,
  author =       "Willy J. F. Govaerts",
  title =        "Numerical Methods for Bifurcations of Dynamical
                 Equilibria",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xxii + 362",
  year =         "2000",
  ISBN =         "0-89871-442-7",
  ISBN-13 =      "978-0-89871-442-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Golub:1974:CBS,
  author =       "G. H. Golub and J. M. Varah",
  title =        "On a Characterization of the Best {$\ell_2$}-Scaling
                 of a Matrix",
  journal =      j-SINUM,
  volume =       "11",
  number =       "3",
  pages =        "472--479",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Golub:1979:UPD,
  author =       "Gene H. Golub and Charles F. {Van Loan}",
  title =        "Unsymmetric Positive Definite Linear Systems",
  journal =      j-LAA,
  volume =       "28",
  pages =        "85--97",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Golub:1996:MC,
  author =       "Gene H. Golub and Charles F. {Van Loan}",
  title =        "Matrix Computations",
  publisher =    pub-JOHNS-HOPKINS,
  address =      pub-JOHNS-HOPKINS:adr,
  edition =      "Third",
  pages =        "xxvii + 694",
  year =         "1996",
  ISBN =         "0-8018-5413-X (hardcover), 0-8018-5414-8 (paperback)",
  ISBN-13 =      "978-0-8018-5413-2 (hardcover), 978-0-8018-5414-9
                 (paperback)",
  LCCN =         "QA188 .G65 1996",
  MRclass =      "65-02 (65Fxx)",
  MRnumber =     "1417720 (97g:65006)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
  series =       "Johns Hopkins Studies in the Mathematical Sciences",
  URL =          "http://www.loc.gov/catdir/bios/jhu052/96014291.html;
                 http://www.loc.gov/catdir/description/jhu051/96014291.html",
  acknowledgement = ack-njh # " and " # ack-nhfb # " and " # ack-rah,
  author-dates = "Gene H. Golub (1932--2007)",
  tableofcontents = "Preface to the Third Edition / xi \\
                 Software / xiii \\
                 Selected References / xv \\
                 1: Matrix Multiplication Problems \\
                 1.1 Basic Algorithms and Notation / 2 \\
                 1.2 Exploiting Structure / 16 \\
                 1.3 Block Matrices and Algorithms / 24 \\
                 1.4 Vectorization and Re-Use Issues / 34 \\
                 2: Matrix Analysis 48 V 2.1 Basic Ideas from Linear
                 Algebra / 48 \\
                 2.2 Vector Norms / 52 \\
                 2.3 Matrix Norms / 54 \\
                 2.4 Finite Precision Matrix Computations / 59 \\
                 2.5 Orthogonality and the SVD / 69 \\
                 2.6 Projections and the $CS$ Decomposition / 75 \\
                 2.7 The Sensitivity of Square Linear Systems / 80 \\
                 3: General Linear Systems / 87 \\
                 3.1 Triangular Systems / 88 \\
                 3.2 The $L U$ Factorization / 94 \\
                 3.3 Roundoff Analysis of Gaussian Elimination / 104 \\
                 3.4 Pivoting / 109 \\
                 3.5 Improving and Estimating Accuracy / 123 \\
                 4: Special Linear Systems / 133 \\
                 4.1 The $L D M^T$ and $L D L^T$ Factorizations / 135
                 \\
                 4.2 Positive Definite Systems / 140 \\
                 4.3 Banded Systems / 152 \\
                 4.4 Symmetric Indefinite Systems / 161 \\
                 4.5 Block Systems / 174 \\
                 4.6 Vandermonde Systems and the FFT / 183 \\
                 4.7 Toeplitz and Related Systems / 193 \\
                 5: Orthogonalization and Least Squares / 206 \\
                 5.1 Householder and Givens Matrices / 208 \\
                 5.2 The $Q R$ Factorization / 223 \\
                 5.3 The Full Rank LS Problem / 236 \\
                 5.4 Other Orthogonal Factorizations / 248 \\
                 5.5 The Rank Deficient LS Problem / 256 \\
                 5.6 Weighting and Iterative Improvement / 264 \\
                 5.7 Square and Underdetermined Systems / 270 \\
                 6: Parallel Matrix Computations / 275 \\
                 6.1 Basic Concepts / 276 \\
                 6.2 Matrix Multiplication / 292 \\
                 6.3 Factorizations / 300 \\
                 7: The Unsymmetric Eigenvalue Problem / 308 \\
                 7.1 Properties and Decompositions / 310 \\
                 7.2 Perturbation Theory / 320 \\
                 7.3 Power Iterations / 330 \\
                 7.4 The Hessenberg and Real Schur Forms / 341 \\
                 7.5 The Practical $Q R$ Algorithm / 352 \\
                 7.6 Invariant Subspace Computations / 362 \\
                 7.7 The $Q Z$ Method for $A x = \lambda B x$ / 375 \\
                 8: The Symmetric Eigenvalue Problem / 391 \\
                 8.1 Properties and Decompositions / 393 \\
                 8.2 Power Iterations / 405 \\
                 8.3 The Symmetric $Q R$ Algorithm / 414 \\
                 8.4 Jacobi Methods / 426 \\
                 8.5 Tridiagonal Methods / 439 \\
                 8.6 Computing the SVD / 448 \\
                 8.7 Some Generalized Eigenvalue Problems / 461 \\
                 9: Lanczos Methods / 470 \\
                 9.1 Derivation and Convergence Properties / 471 \\
                 9.2 Practical Lanczos Procedures / 479 \\
                 9.3 Applications to $A x = b$ and Least Squares / 490
                 \\
                 9.4 Arnoldi and Unsymmetric Lanczos / 499 \\
                 10: Iterative Methods for Linear Systems / 508 \\
                 10.1 The Standard Iterations / 509 \\
                 10.2 The Conjugate Gradient Method / 520 \\
                 10.3 Preconditioned Conjugate Gradients / 532 \\
                 10.4 Other Krylov Subspace Methods / 544 \\
                 11: Functions of Matrices / 555 \\
                 11.1 Eigenvalue Methods / 556 \\
                 11.2 Approximation Methods / 562 \\
                 11.3 The Matrix Exponential / 572 \\
                 12: Special Topics / 579 \\
                 12.1 Constrained Least Squares / 580 \\
                 12.2 Subset Selection Using the SVD / 590 \\
                 12.3 Total Least Squares / 595 \\
                 12.4 Computing Subspaces with the SVD / 601 \\
                 12.5 Updating Matrix Factorizations / 606 \\
                 12.6 Modified/Structured Eigenproblems / 621 \\
                 Bibliography / 637 \\
                 Index / 687",
}

@Article{Goldstine:1951:NIM,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Numerical Inverting of Matrices of High Order {II}",
  journal =      j-PROC-AMS,
  volume =       "2",
  pages =        "188--202",
  year =         "1951",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted in \cite[pp.~558--572]{Taub:1963:JNC}",
}

@Article{Golub:1966:NIR,
  author =       "G. H. Golub and J. H. Wilkinson",
  title =        "Note on the iterative refinement of least squares
                 solution",
  journal =      j-NUM-MATH,
  volume =       "9",
  pages =        "139--148",
  year =         "1966",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Golub:1976:ICE,
  author =       "G. H. Golub and J. H. Wilkinson",
  title =        "Ill-Conditioned Eigensystems and the Computation of
                 the {Jordan} Canonical Form",
  journal =      j-SIREV,
  volume =       "18",
  number =       "4",
  pages =        "578--619",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gallivan:1990:PAD,
  author =       "K. A. Gallivan and R. J. Plemmons and A. H. Sameh",
  title =        "Parallel Algorithms for Dense Linear Algebra
                 Computations",
  journal =      j-SIREV,
  volume =       "32",
  number =       "1",
  pages =        "54--135",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Granville:1992:ZBB,
  author =       "Andrew Granville",
  title =        "{Zaphod Beeblebrox's} Brain and the Fifty-Ninth Row of
                 {Pascal's} Triangle",
  journal =      j-AMM,
  volume =       "99",
  pages =        "318--331",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Greenbaum:1989:BSP,
  author =       "Anne Greenbaum",
  title =        "Behavior of Slightly Perturbed {Lanczos} and
                 Conjugate-Gradient Recurrences",
  journal =      j-LAA,
  volume =       "113",
  pages =        "7--63",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Greenbaum:1994:LCG,
  author =       "Anne Greenbaum",
  editor =       "J. David Brown and Moody T. Chu and Donald C. Ellison
                 and Robert J. Plemmons",
  booktitle =    "Proceedings of the {Cornelius Lanczos} International
                 Centenary Conference",
  title =        "The {Lanczos} and Conjugate Gradient Algorithms in
                 Finite Precision Arithmetic",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "49--60",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Greenbaum:1997:IMS,
  author =       "Anne Greenbaum",
  title =        "Iterative Methods for Solving Linear Systems",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xiii + 220",
  year =         "1997",
  ISBN =         "0-89871-396-X",
  ISBN-13 =      "978-0-89871-396-1",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Greenbaum:1997:EAA,
  author =       "Anne Greenbaum",
  title =        "Estimating the Attainable Accuracy of Recursively
                 Computed Residual Methods",
  journal =      j-SIMAX,
  volume =       "18",
  number =       "3",
  pages =        "535--551",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Griewank:1985:SNE,
  author =       "Andreas Griewank",
  title =        "On Solving Nonlinear Equations with Simple
                 Singularities or Nearly Singular Solutions",
  journal =      j-SIREV,
  volume =       "27",
  number =       "4",
  pages =        "537--563",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Gregory:1969:CMT,
  author =       "Robert T. Gregory and David L. Karney",
  title =        "A Collection of Matrices for Testing Computational
                 Algorithms",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  pages =        "ix + 154",
  year =         "1969",
  ISBN =         "0-88275-649-4",
  ISBN-13 =      "978-0-88275-649-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted with corrections by Robert E. Krieger,
                 Huntington, New York, 1978",
}

@Article{Grimes:1981:CNE,
  author =       "Roger G. Grimes and John G. Lewis",
  title =        "Condition Number Estimation for Sparse Matrices",
  journal =      j-SISSC,
  volume =       "2",
  number =       "4",
  pages =        "384--388",
  year =         "1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gragg:1976:SVS,
  author =       "W. B. Gragg and G. W. Stewart",
  title =        "A Stable Variant of the Secant Method for Solving
                 Nonlinear Equations",
  journal =      j-SINUM,
  volume =       "13",
  number =       "6",
  pages =        "889--903",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Greenbaum:1992:PBF,
  author =       "Anne Greenbaum and Zden{\u{e}}k Strako{\u{s}}",
  title =        "Predicting the Behavior of Finite Precision {Lanczos}
                 and Conjugate Gradient Computations",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "121--137",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gill:1996:SCF,
  author =       "Philip E. Gill and Michael A. Saunders and Joseph R.
                 Shinnerl",
  title =        "On the Stability of {Cholesky} Factorization for
                 Symmetric Quasidefinite Systems",
  journal =      j-SIMAX,
  volume =       "17",
  number =       "1",
  pages =        "35--46",
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gu:1998:BPB,
  author =       "Ming Gu",
  title =        "Backward Perturbation Bounds for Linear Least Squares
                 Problems",
  journal =      j-SIMAX,
  volume =       "20",
  number =       "2",
  pages =        "363--372",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gustafson:1996:MPS,
  author =       "John L. Gustafson and Srinivas Aluru",
  title =        "Massively Parallel Searching for Better Algorithms or,
                 How to Do a Cross Product with Five Multiplications",
  journal =      j-SCI-PROG,
  volume =       "",
  pages =        "203--213",
  year =         "1996",
  CODEN =        "SCIPEV",
  ISSN =         "1058-9244 (print), 1875-919X (electronic)",
  ISSN-L =       "1058-9244",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Scientific Programming",
  journal-URL =  "http://iospress.metapress.com/content/1058-9244",
}

@Article{Gulliksson:1994:IRC,
  author =       "M{\aa}rten Gulliksson",
  title =        "Iterative Refinement for Constrained and Weighted
                 Linear Least Squares",
  journal =      j-BIT,
  volume =       "34",
  pages =        "239--253",
  year =         "1994",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Gulliksson:1995:BEA,
  author =       "M{\aa}rten Gulliksson",
  title =        "Backward Error Analysis for the Constrained and
                 Weighted Linear Least Squares Problem When Using the
                 Weighted {$QR$} Factorization",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "2",
  pages =        "675--687",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Gustavson:1997:RLA,
  author =       "F. G. Gustavson",
  title =        "Recursion Leads to Automatic Variable Blocking for
                 Dense Linear-Algebra Algorithms",
  journal =      j-IBM-JRD,
  volume =       "41",
  number =       "6",
  pages =        "737--755",
  month =        nov,
  year =         "1997",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@Article{Gulliksson:1992:MQD,
  author =       "M{\aa}rten Gulliksson and Per-{\AA}ke Wedin",
  title =        "Modifying the {QR}-Decomposition to Constrained and
                 Weighted Linear Least Squares",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "4",
  pages =        "1298--1313",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Hull:1985:NT,
  author =       "T. E. Hull and A. Abraham and M. S. Cohen and A. F. X.
                 Curley and C. B. Hall and D. A. Penny and J. T. M.
                 Sawchuk",
  title =        "Numerical {TURING}",
  journal =      j-SIGNUM,
  volume =       "20",
  number =       "3",
  pages =        "26--34",
  year =         "1985",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J690",
}

@Article{Hager:1984:CE,
  author =       "William W. Hager",
  title =        "Condition Estimates",
  journal =      j-SISSC,
  volume =       "5",
  number =       "2",
  pages =        "311--316",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Hall:1967:CT,
  author =       "Marshall {Hall, Jr.}",
  title =        "Combinatorial Theory",
  publisher =    pub-Blaisdell,
  address =      pub-Blaisdell:adr-MA,
  pages =        "x + 310",
  year =         "1967",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Hamada:1987:NRN,
  author =       "Hozumi Hamada",
  editor =       "Mary Jane Irwin and Renato Stefanelli",
  booktitle =    "Proceedings of the Eighth Symposium on Computer
                 Arithmetic, Como, Italy",
  title =        "A New Real Number Representation and its Operation",
  publisher =    "IEEE Computer Society, Washington, D.C.",
  pages =        "153--157",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Hamming:1973:NMS,
  author =       "R. W. Hamming",
  title =        "Numerical Methods for Scientists and Engineers",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  edition =      "Second",
  pages =        "ix + 721",
  year =         "1973",
  ISBN =         "0-07-025887-2",
  ISBN-13 =      "978-0-07-025887-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Hammarling:1974:NMG,
  author =       "Sven Hammarling",
  title =        "A Note on Modifications to the {Givens} Plane
                 Rotation",
  journal =      j-JIMA,
  volume =       "13",
  pages =        "215--218",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Hammarling:1982:NSS,
  author =       "S. J. Hammarling",
  title =        "Numerical Solution of the Stable, Non-Negative
                 Definite {Lyapunov} Equation",
  journal =      j-IMAJNA,
  volume =       "2",
  pages =        "303--323",
  year =         "1982",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Hammarling:1987:NSG,
  author =       "Sven J. Hammarling",
  editor =       "T. S. Durrani and J. B. Abbiss and J. E. Hudson",
  booktitle =    "Mathematics in Signal Processing",
  title =        "The Numerical Solution of the General {Gauss--Markov}
                 Linear Model",
  publisher =    pub-OUP,
  pages =        "451--456",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Unpublished{Hanson:1997:AML,
  author =       "Richard J. Hanson",
  title =        "{Aasen's} Method for Linear Systems with Self-Adjoint
                 Matrices",
  month =        jul,
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Visual Numerics, Inc.,
                 \path|http://www.vni.com/books/whitepapers/Aasen.html|",
}

@Book{Hardy:1967:CPM,
  author =       "G. H. Hardy",
  title =        "A Course of Pure Mathematics",
  publisher =    pub-CUP,
  edition =      "Tenth",
  pages =        "xii + 509",
  year =         "1967",
  ISBN =         "0-521-09227-2",
  ISBN-13 =      "978-0-521-09227-2",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Harter:1972:OWF,
  author =       "Richard Harter",
  title =        "The Optimality of {Winograd's} Formula",
  journal =      j-CACM,
  volume =       "15",
  number =       "5",
  pages =        "352",
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Hartfiel:1980:CSS,
  author =       "D. J. Hartfiel",
  title =        "Concerning the Solution Set of {$Ax = b$} where {$P
                 \le A \le Q$} and {$p \le b \le q$}",
  journal =      j-NUM-MATH,
  volume =       "35",
  pages =        "355--359",
  year =         "1980",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Hauser:1996:HFP,
  author =       "John R. Hauser",
  title =        "Handling Floating-Point Exceptions in Numeric
                 Programs",
  journal =      j-TPLS,
  volume =       "18",
  number =       "2",
  pages =        "139--174",
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Hairer:1991:SOD,
  author =       "E. Hairer and G. Wanner",
  title =        "Solving Ordinary Differential Equations {II}",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "xv + 601",
  year =         "1991",
  ISBN =         "3-540-53775-9",
  ISBN-13 =      "978-3-540-53775-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Hammarling:1976:PBL,
  author =       "S. J. Hammarling and J. H. Wilkinson",
  title =        "The Practical Behaviour of Linear Iterative Methods
                 with Particular Reference to {S.O.R.}",
  type =         "Report",
  number =       "NAC 69",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  pages =        "19",
  month =        sep,
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Hearon:1977:NS,
  author =       "John Z. Hearon",
  title =        "Nonsingular Solutions of {$TA-BT=C$}",
  journal =      j-LAA,
  volume =       "16",
  pages =        "57--63",
  year =         "1977",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Heath:1984:NML,
  author =       "Michael T. Heath",
  title =        "Numerical Methods for Large Sparse Linear Least
                 Squares Problems",
  journal =      j-SISSC,
  volume =       "5",
  number =       "3",
  pages =        "497--513",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Hein:1992:G,
  author =       "Piet Hein",
  title =        "Grooks",
  number =       "85",
  publisher =    "Borgens Forlag",
  address =      "Copenhagen, Denmark",
  edition =      "Second",
  pages =        "53",
  year =         "1992",
  ISBN =         "87-418-1079-1",
  ISBN-13 =      "978-87-418-1079-9",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Borgens Pocketbooks",
}

@Article{Hewer:1988:SSL,
  author =       "Gary Hewer and Charles Kenney",
  title =        "The Sensitivity of the Stable {Lyapunov} Equation",
  journal =      j-SICOPT,
  volume =       "26",
  number =       "2",
  pages =        "321--344",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Henrici:1962:BII,
  author =       "Peter Henrici",
  title =        "Bounds for Iterates, Inverses, Spectral Variation and
                 Fields of Values of Non-Normal Matrices",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "24--40",
  year =         "1962",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Book{Henrici:1962:DVM,
  author =       "Peter Henrici",
  title =        "Discrete Variable Methods in Ordinary Differential
                 Equations",
  publisher =    "John Wiley",
  address =      "New York",
  pages =        "xi + 407",
  year =         "1962",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Henrici:1963:EPD,
  author =       "Peter Henrici",
  title =        "Error Propagation for Difference Methods",
  publisher =    "John Wiley",
  address =      "New York",
  pages =        "vi + 73",
  year =         "1963",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Henrici:1964:ENA,
  author =       "Peter Henrici",
  title =        "Elements of Numerical Analysis",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  pages =        "xv + 328",
  year =         "1964",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Henrici:1966:TPM,
  author =       "Peter Henrici",
  title =        "Test of Probabilistic Models for the Propagation of
                 Roundoff Errors",
  journal =      j-CACM,
  volume =       "9",
  number =       "6",
  pages =        "409--410",
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@InProceedings{Henrici:1980:MPR,
  author =       "Peter Henrici",
  editor =       "Karl L. E. Nickel",
  booktitle =    "Interval Mathematics 1980",
  title =        "A Model for the Propagation of Rounding Error in
                 Floating Arithmetic",
  publisher =    pub-AP # ", " # pub-AP:adr-NY,
  pages =        "49--73",
  year =         "1980",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Hennessy:1996:CAQ,
  author =       "John L. Hennessy and David A. Patterson",
  title =        "Computer Architecture: {A} Quantitative Approach",
  publisher =    "Morgan Kaufmann",
  address =      "San Francisco, CA, USA",
  edition =      "Second",
  pages =        "xxiii + 760 + appendices",
  year =         "1996",
  ISBN =         "1-55860-329-8",
  ISBN-13 =      "978-1-55860-329-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Henderson:1981:DIS,
  author =       "H. V. Henderson and S. R. Searle",
  title =        "On Deriving the Inverse of a Sum of Matrices",
  journal =      j-SIREV,
  volume =       "23",
  number =       "1",
  pages =        "53--60",
  year =         "1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Henderson:1981:VPM,
  author =       "Harold V. Henderson and S. R. Searle",
  title =        "The Vec-Permutation Matrix, the Vec Operator and
                 {Kronecker} Products: {A} Review",
  journal =      j-LMA,
  volume =       "9",
  pages =        "271--288",
  year =         "1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Hull:1994:ICE,
  author =       "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter
                 Tang",
  title =        "Implementing Complex Elementary Functions Using
                 Exception Handling",
  journal =      j-TOMS,
  volume =       "20",
  number =       "2",
  pages =        "215--244",
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@TechReport{Heath:1990:EEI,
  author =       "M. T. Heath and G. A. Geist and J. B. Drake",
  title =        "Early Experience with the {Intel iPSC/860} at {Oak
                 Ridge National Laboratory}",
  type =         "Report",
  number =       "ORNL/TM-11655",
  institution =  inst-ORNL,
  address =      inst-ORNL:adr,
  pages =        "26",
  month =        sep,
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Hammer:1993:NTV,
  author =       "Rolf Hammer and Matthias Hocks and Ulrich Kulisch and
                 Dietmar Ratz",
  title =        "Numerical Toolbox for Verified Computing {I}. {Basic}
                 Numerical Problems: Theory, Algorithms, and
                 {Pascal-XSC} Programs",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "xiii + 337",
  year =         "1993",
  ISBN =         "3-540-57118-3",
  ISBN-13 =      "978-3-540-57118-6",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:2000:QFC,
  author =       "Nicholas J. Higham",
  title =        "{QR} Factorization with Complete Pivoting and Accurate
                 Computation of the {SVD}",
  journal =      j-LAA,
  volume =       "309",
  pages =        "153--174",
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:2001:EPA,
  author =       "Nicholas J. Higham",
  title =        "Evaluating {Pad\'e} Approximants of the Matrix
                 Logarithm",
  journal =      j-SIMAX,
  volume =       "22",
  number =       "4",
  pages =        "1126--1135",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1986:CPD,
  author =       "Nicholas J. Higham",
  title =        "Computing the Polar Decomposition---with
                 Applications",
  journal =      j-SISSC,
  volume =       "7",
  number =       "4",
  pages =        "1160--1174",
  month =        oct,
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1986:EAC,
  author =       "Nicholas J. Higham",
  title =        "Efficient Algorithms for Computing the Condition
                 Number of a Tridiagonal Matrix",
  journal =      j-SISSC,
  volume =       "7",
  number =       "1",
  pages =        "150--165",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1987:CRS,
  author =       "Nicholas J. Higham",
  title =        "Computing Real Square Roots of a Real Matrix",
  journal =      j-LAA,
  volume =       "88/89",
  pages =        "405--430",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1987:SCN,
  author =       "Nicholas J. Higham",
  title =        "A Survey of Condition Number Estimation for Triangular
                 Matrices",
  journal =      j-SIREV,
  volume =       "29",
  number =       "4",
  pages =        "575--596",
  month =        dec,
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1987:EAB,
  author =       "Nicholas J. Higham",
  title =        "Error Analysis of the {Bj\"orck--Pereyra} Algorithms
                 for Solving {Vandermonde} Systems",
  journal =      j-NUM-MATH,
  volume =       "50",
  number =       "5",
  pages =        "613--632",
  year =         "1987",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Higham:1988:CNS,
  author =       "Nicholas J. Higham",
  title =        "Computing a Nearest Symmetric Positive Semidefinite
                 Matrix",
  journal =      j-LAA,
  volume =       "103",
  pages =        "103--118",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1988:FCE,
  author =       "Nicholas J. Higham",
  title =        "{FORTRAN} Codes for Estimating the One-norm of a Real
                 or Complex Matrix, with Applications to Condition
                 Estimation ({Algorithm} 674)",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "381--396",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Higham:1988:FSV,
  author =       "Nicholas J. Higham",
  title =        "Fast Solution of {Vandermonde}-like Systems Involving
                 Orthogonal Polynomials",
  journal =      j-IMAJNA,
  volume =       "8",
  pages =        "473--486",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Higham:1989:MNP,
  author =       "Nicholas J. Higham",
  editor =       "M. J. C. Gover and S. Barnett",
  booktitle =    "Applications of Matrix Theory",
  title =        "Matrix Nearness Problems and Applications",
  publisher =    pub-OUP,
  pages =        "1--27",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1989:AST,
  author =       "Nicholas J. Higham",
  title =        "The Accuracy of Solutions to Triangular Systems",
  journal =      j-SINUM,
  volume =       "26",
  number =       "5",
  pages =        "1252--1265",
  month =        oct,
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Higham:1990:ACD,
  author =       "Nicholas J. Higham",
  editor =       "M. G. Cox and S. J. Hammarling",
  booktitle =    "Reliable Numerical Computation",
  title =        "Analysis of the {Cholesky} Decomposition of a
                 Semi-definite Matrix",
  publisher =    pub-OUP,
  pages =        "161--185",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1990:EMN,
  author =       "Nicholas J. Higham",
  title =        "Experience with a Matrix Norm Estimator",
  journal =      j-SISSC,
  volume =       "11",
  number =       "4",
  pages =        "804--809",
  month =        jul,
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Higham:1990:HAG,
  author =       "Nicholas J. Higham",
  editor =       "D. F. Griffiths and G. A. Watson",
  booktitle =    "Numerical Analysis \textup{1989}, Proceedings of the
                 \textup{13}th Dundee Conference",
  title =        "How Accurate is {Gaussian} Elimination?",
  volume =       "228",
  publisher =    pub-Longman-ST # ", " # pub-Longman-ST:adr,
  pages =        "137--154",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Pitman Research Notes in Mathematics",
}

@TechReport{Higham:1990:IRE,
  author =       "Nicholas J. Higham",
  title =        "Iterative Refinement Enhances the Stability of {$QR$}
                 Factorization Methods for Solving Linear Equations",
  type =         t-NAREP,
  number =       "No. 182",
  institution =  inst-U-MANCHESTER,
  address =      inst-U-MANCHESTER:adr,
  month =        apr,
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Higham:1990:CEB,
  author =       "Nicholas J. Higham",
  editor =       "Philip J. Brown and Wayne A. Fuller",
  booktitle =    "Statistical Analysis of Measurement Error Models and
                 Applications, Contemporary Mathematics 112",
  title =        "Computing Error Bounds for Regression Problems",
  publisher =    pub-AMS # ", " # pub-AMS:adr,
  pages =        "195--208",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1990:EFM,
  author =       "Nicholas J. Higham",
  title =        "Exploiting Fast Matrix Multiplication within the Level
                 3 {BLAS}",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "352--368",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Higham:1990:BEG,
  author =       "Nicholas J. Higham",
  title =        "Bounding the Error in {Gaussian} Elimination for
                 Tridiagonal Systems",
  journal =      j-SIMAX,
  volume =       "11",
  number =       "4",
  pages =        "521--530",
  month =        oct,
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1990:SAA,
  author =       "Nicholas J. Higham",
  title =        "Stability Analysis of Algorithms for Solving Confluent
                 {Vandermonde}-like Systems",
  journal =      j-SIMAX,
  volume =       "11",
  number =       "1",
  pages =        "23--41",
  month =        jan,
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1991:TMP,
  author =       "Nicholas J. Higham",
  title =        "Three Measures of Precision in Floating Point
                 Arithmetic",
  journal =      j-NA-DIGEST,
  volume =       "Volume 91, Issue 16",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Electronic mail magazine:
                 \path|na.help@na-net.ornl.gov|",
  fjournal =     "NA Digest",
}

@Article{Higham:1991:IRE,
  author =       "Nicholas J. Higham",
  title =        "Iterative Refinement Enhances the Stability of {$QR$}
                 Factorization Methods for Solving Linear Equations",
  journal =      j-BIT,
  volume =       "31",
  pages =        "447--468",
  year =         "1991",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Higham:1992:EMN,
  author =       "Nicholas J. Higham",
  title =        "Estimating the Matrix {$p$}-norm",
  journal =      j-NUM-MATH,
  volume =       "62",
  pages =        "539--555",
  year =         "1992",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Higham:1992:SMM,
  author =       "Nicholas J. Higham",
  title =        "Stability of a Method for Multiplying Complex Matrices
                 with Three Real Matrix Multiplications",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "3",
  pages =        "681--687",
  month =        jul,
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1993:ODS,
  author =       "Nicholas J. Higham",
  title =        "Optimization by Direct Search in Matrix Computations",
  journal =      j-SIMAX,
  volume =       "14",
  number =       "2",
  pages =        "317--333",
  month =        apr,
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1993:AFP,
  author =       "Nicholas J. Higham",
  title =        "The Accuracy of Floating Point Summation",
  journal =      j-SISC,
  volume =       "14",
  number =       "4",
  pages =        "783--799",
  month =        jul,
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1993:PTB,
  author =       "Nicholas J. Higham",
  title =        "Perturbation Theory and Backward Error for
                 {$AX-XB=C$}",
  journal =      j-BIT,
  volume =       "33",
  pages =        "124--136",
  year =         "1993",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@InProceedings{Higham:1994:SCP,
  author =       "Nicholas J. Higham",
  editor =       "Walter Gautschi",
  booktitle =    "{Mathematics of Computation} \textup{1943--1993}: {A}
                 Half Century of Computational Mathematics",
  title =        "A Survey of Componentwise Perturbation Theory in
                 Numerical Linear Algebra",
  volume =       "48",
  publisher =    pub-AMS # ", " # pub-AMS:adr,
  pages =        "49--77",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Proceedings of Symposia in Applied Mathematics",
}

@Article{Higham:1994:MSD,
  author =       "Nicholas J. Higham",
  title =        "The Matrix Sign Decomposition and Its Relation to the
                 Polar Decomposition",
  journal =      j-LAA,
  volume =       "212/213",
  pages =        "3--20",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1995:CNT,
  author =       "Desmond J. Higham",
  title =        "Condition Numbers and Their Condition Numbers",
  journal =      j-LAA,
  volume =       "214",
  pages =        "193--213",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Higham:1995:TMT,
  author =       "Nicholas J. Higham",
  title =        "The {Test Matrix Toolbox} for {MATLAB} (Version 3.0)",
  type =         t-NAREP,
  number =       "No. 276",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "70",
  month =        sep,
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1995:SPT,
  author =       "Nicholas J. Higham",
  title =        "Stability of Parallel Triangular System Solvers",
  journal =      j-SISC,
  volume =       "16",
  number =       "2",
  pages =        "400--413",
  month =        mar,
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1997:SDP,
  author =       "Nicholas J. Higham",
  title =        "Stability of the Diagonal Pivoting Method with Partial
                 Pivoting",
  journal =      j-SIMAX,
  volume =       "18",
  number =       "1",
  pages =        "52--65",
  month =        jan,
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1997:IRL,
  author =       "Nicholas J. Higham",
  title =        "Iterative Refinement for Linear Systems and {LAPACK}",
  journal =      j-IMAJNA,
  volume =       "17",
  number =       "4",
  pages =        "495--509",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1997:SIM,
  author =       "Nicholas J. Higham",
  title =        "Stable Iterations for the Matrix Square Root",
  journal =      j-NUM-ALG,
  volume =       "15",
  number =       "2",
  pages =        "227--242",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1998:FCS,
  author =       "Nicholas J. Higham",
  title =        "Factorizing Complex Symmetric Matrices with Positive
                 Definite Real and Imaginary Parts",
  journal =      j-MATH-COMP,
  volume =       "67",
  number =       "224",
  pages =        "1591--1599",
  month =        oct,
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1999:SBF,
  author =       "Nicholas J. Higham",
  title =        "Stability of Block $\mathrm{LDL^T}$ Factorization of a
                 Symmetric Tridiagonal Matrix",
  journal =      j-LAA,
  volume =       "287",
  pages =        "181--189",
  year =         "1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Higham:1999:NAS,
  author =       "Nicholas J. Higham",
  editor =       "Mark Ainsworth and Jeremy Levesley and Marco
                 Marletta",
  booktitle =    "The Graduate Student's Guide to Numerical Analysis
                 '\textup{98}",
  title =        "Notes on Accuracy and Stability of Algorithms in
                 Numerical Linear Algebra",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "48--82",
  year =         "1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Higham:1998:HWM,
  author =       "Nicholas J. Higham",
  title =        "Handbook of Writing for the Mathematical Sciences",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  edition =      "Second",
  pages =        "xvi + 302",
  year =         "1998",
  ISBN =         "0-89871-420-6",
  ISBN-13 =      "978-0-89871-420-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Higham:2002:ASN,
  author =       "Nicholas J. Higham",
  title =        "Accuracy and Stability of Numerical Algorithms",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  edition =      "Second",
  pages =        "xxx + 680",
  year =         "2002",
  ISBN =         "0-89871-521-0",
  ISBN-13 =      "978-0-89871-521-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1989:LGF,
  author =       "Nicholas J. Higham and Desmond J. Higham",
  title =        "Large Growth Factors in {Gaussian} Elimination with
                 Pivoting",
  journal =      j-SIMAX,
  volume =       "10",
  number =       "2",
  pages =        "155--164",
  month =        apr,
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1992:BEC,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "Backward Error and Condition of Structured Linear
                 Systems",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "162--175",
  month =        jan,
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1992:CPT,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "Componentwise Perturbation Theory for Linear Systems
                 with Multiple Right-Hand Sides",
  journal =      j-LAA,
  volume =       "174",
  pages =        "111--129",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Higham:2000:MG,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "{MATLAB} Guide",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xxii + 283",
  year =         "2000",
  ISBN =         "0-89871-516-4",
  ISBN-13 =      "978-0-89871-516-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:2000:NAQ,
  author =       "Nicholas J. Higham and Hyun-Min Kim",
  title =        "Numerical Analysis of a Quadratic Matrix Equation",
  journal =      j-IMAJNA,
  volume =       "20",
  number =       "4",
  pages =        "499--519",
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Higham:1993:CEA,
  author =       "Nicholas J. Higham and Philip A. Knight",
  editor =       "Carl D. Meyer and Robert J. Plemmons",
  booktitle =    "Linear Algebra, Markov Chains, and Queueing Models",
  title =        "Componentwise Error Analysis for Stationary Iterative
                 Methods",
  volume =       "48",
  publisher =    pub-Springer # ", " # pub-Springer:adr-NY,
  pages =        "29--46",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "IMA Volumes in Mathematics and Its Applications",
}

@Article{Higham:1993:FPB,
  author =       "Nicholas J. Higham and Philip A. Knight",
  title =        "Finite Precision Behavior of Stationary Iteration for
                 Solving Singular Systems",
  journal =      j-LAA,
  volume =       "192",
  pages =        "165--186",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1995:MPF,
  author =       "Nicholas J. Higham and Philip A. Knight",
  title =        "Matrix Powers in Finite Precision Arithmetic",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "2",
  pages =        "343--358",
  month =        apr,
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Hilbert:1894:BTL,
  author =       "David Hilbert",
  title =        "{Ein Beitrag zur Theorie des Legendre'schen
                 Polynoms}",
  journal =      j-ACTA-MATH,
  volume =       "18",
  pages =        "155--159",
  year =         "1894",
  CODEN =        "ACMAA8",
  ISSN =         "0001-5962 (print), 1871-2509 (electronic)",
  ISSN-L =       "0001-5962",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Acta Mathematica",
  journal-URL =  "http://link.springer.com/journal/11511",
}

@Book{Hildebrand:1974:INA,
  author =       "F. B. Hildebrand",
  title =        "Introduction to Numerical Analysis",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  edition =      "Second",
  pages =        "xiii + 669",
  year =         "1974",
  ISBN =         "0-486-65363-3",
  ISBN-13 =      "978-0-486-65363-1",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted by Dover, New York, 1987",
}

@Article{Higham:1994:PAC,
  author =       "Nicholas J. Higham and Pythagoras Papadimitriou",
  title =        "A Parallel Algorithm for Computing the Polar
                 Decomposition",
  journal =      j-PAR-COMP,
  volume =       "20",
  number =       "8",
  pages =        "1161--1173",
  month =        aug,
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1994:SPI,
  author =       "Nicholas J. Higham and Alex Pothen",
  title =        "Stability of the Partitioned Inverse Method for
                 Parallel Solution of Sparse Triangular Systems",
  journal =      j-SISC,
  volume =       "15",
  number =       "1",
  pages =        "139--148",
  month =        jan,
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Higham:1987:NLA,
  author =       "Nicholas J. Higham and G. W. Stewart",
  editor =       "A. Iserles and M. J. D. Powell",
  booktitle =    "The State of the Art in Numerical Analysis",
  title =        "Numerical Linear Algebra in Statistical Computing",
  publisher =    pub-OUP,
  pages =        "41--57",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:2000:BAM,
  author =       "Nicholas J. Higham and Fran\c{c}oise Tisseur",
  title =        "A Block Algorithm for Matrix 1-Norm Estimation, with
                 an Application to 1-Norm Pseudospectra",
  journal =      j-SIMAX,
  volume =       "21",
  number =       "4",
  pages =        "1185--1201",
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Higham:2001:BEM,
  author =       "Nicholas J. Higham and Fran\c{c}oise Tisseur",
  title =        "Bounds for Eigenvalues of Matrix Polynomials",
  type =         t-NAREP,
  number =       "371",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "16",
  month =        jan,
  year =         "2001",
  note =         "To appear in " # j-LAA,
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Higham:1993:SO,
  author =       "Desmond J. Higham and Lloyd N. Trefethen",
  title =        "Stiffness of {ODE}s",
  journal =      j-BIT,
  volume =       "33",
  pages =        "285--303",
  year =         "1993",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@InProceedings{Hida:2001:AQD,
  author =       "Yozo Hida and Xiaoye S. Li and David H. Bailey",
  editor =       "",
  booktitle =    "Proc. 15th IEEE Symposium on Computer Arithmetic",
  title =        "Algorithms for Quad-Double Precision Floating Point
                 Arithmetic",
  publisher =    "IEEE Computer Society Press, Los Alamitos, CA, USA",
  pages =        "155--162",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Hardy:1952:I,
  author =       "G. H. Hardy and J. E. Littlewood and G. P{\'o}lya",
  title =        "Inequalities",
  publisher =    pub-CUP,
  edition =      "Second",
  pages =        "xii + 324",
  year =         "1952",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Holt:1988:TPL,
  author =       "R. C. Holt and J. R. Cordy",
  title =        "The {Turing} Programming Language",
  journal =      j-CACM,
  volume =       "31",
  number =       "12",
  pages =        "1410--1423",
  year =         "1988",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@InProceedings{Hodel:1992:RAL,
  author =       "A. Scottedward Hodel",
  editor =       "R. Beauwens and P. de Groen",
  booktitle =    "Iterative Methods in Linear Algebra",
  title =        "Recent Applications of the {Lyapunov} Equation in
                 Control Theory",
  publisher =    "Elsevier Science Publishers B.V. (North-Holland)",
  address =      pub-NH:adr,
  pages =        "217--227",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Hodges:1983:ATE,
  author =       "Andrew Hodges",
  title =        "{Alan Turing}: {The} Enigma",
  publisher =    "Burnett Books",
  address =      "London",
  pages =        "xix + 586",
  year =         "1983",
  ISBN =         "0-09-911641-3",
  ISBN-13 =      "978-0-09-911641-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "1992 edition with preface, Vintage, London",
}

@Article{Hoffmann:1987:SLS,
  author =       "W. Hoffmann",
  title =        "Solving Linear Systems on a Vector Computer",
  journal =      j-JCAM,
  volume =       "18",
  pages =        "353--367",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Hoffmann:1989:IAG,
  author =       "W. Hoffmann",
  title =        "Iterative Algorithms for {Gram--Schmidt}
                 Orthogonalization",
  journal =      j-COMPUTING,
  volume =       "41",
  pages =        "335--348",
  year =         "1989",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Hoffmann:1989:PAR,
  author =       "Christoph M. Hoffmann",
  title =        "The Problems of Accuracy and Robustness in Geometric
                 Computation",
  journal =      j-COMPUTER,
  volume =       "March",
  pages =        "31--41",
  year =         "1989",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computer",
  journal-URL =  "http://www.computer.org/portal/web/csdl/magazines/computer",
}

@Book{Hockney:1988:PCA,
  author =       "Roger W. Hockney and Chris R. Jesshope",
  title =        "Parallel Computers: Architecture, Programming, and
                 Algorithms",
  publisher =    pub-ADAM-HILGER,
  address =      pub-ADAM-HILGER:adr,
  edition =      "Second",
  pages =        "xv + 625",
  year =         "1988",
  ISBN =         "0-85274-811-6 (hardcover), 0-85274-812-4 (paperback)",
  ISBN-13 =      "978-0-85274-811-4 (hardcover), 978-0-85274-812-1
                 (paperback)",
  LCCN =         "QA76.5 .H57 1988",
  MRclass =      "68-02, 65-04, 65Y05, 68N25",
  bibdate =      "Sun Jul 10 01:08:36 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  ZMnumber =     "0641.68001",
  abstract =     "Parallel Computers 2 follows the development of large
                 fast supercomputers and provides a thorough guide to
                 all aspects of the subject; technology, computer
                 architecture, languages and algorithms using successful
                 commercially available products as examples. Of
                 interest to computer scientists, electronics engineers
                 and physicists in academia and industry, students on
                 MSc courses and final year undergraduates in computer
                 science, parallel computers, supercomputers, parallel
                 architectures, etc.",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
}

@Book{Horn:1985:MA,
  author =       "Roger A. Horn and Charles R. Johnson",
  title =        "Matrix Analysis",
  publisher =    pub-CUP,
  pages =        "xiii + 561",
  year =         "1985",
  ISBN =         "0-521-30586-1",
  ISBN-13 =      "978-0-521-30586-0",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Horn:1991:TMA,
  author =       "Roger A. Horn and Charles R. Johnson",
  title =        "Topics in Matrix Analysis",
  publisher =    pub-CUP,
  pages =        "viii + 607",
  year =         "1991",
  ISBN =         "0-521-30587-X",
  ISBN-13 =      "978-0-521-30587-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Horning:1979:NPR,
  author =       "Jim Horning",
  title =        "Note on Program Reliability",
  journal =      j-ACM-SIGSOFT,
  volume =       "4",
  number =       "4",
  pages =        "6",
  year =         "1979",
  CODEN =        "SFENDP",
  ISSN =         "0163-5948 (print), 1943-5843 (electronic)",
  ISSN-L =       "0163-5948",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Cited in \cite{Tropp:1984:FA}",
  fjournal =     "ACM Sigsoft",
}

@Article{Hochbruck:1995:PKS,
  author =       "Marlis Hochbruck and Gerhard Starke",
  title =        "Preconditioned {Krylov} Subspace Methods for
                 {Lyapunov} Matrix Equations",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "1",
  pages =        "156--171",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Hotelling:1943:SNM,
  author =       "Harold Hotelling",
  title =        "Some New Methods in Matrix Calculation",
  journal =      j-ANN-MATH-STAT,
  volume =       "14",
  number =       "1",
  pages =        "1--34",
  year =         "1943",
  CODEN =        "AASTAD",
  ISSN =         "0003-4851 (print), 2168-8990 (electronic)",
  ISSN-L =       "0003-4851",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Annals of Mathematical Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoms/",
}

@Article{Hough:1981:API,
  author =       "David Hough",
  title =        "Applications of the Proposed {IEEE 754} Standard for
                 Floating-Point Arithmetic",
  journal =      j-COMPUTER,
  volume =       "14",
  pages =        "70--74",
  year =         "1981",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computer",
  journal-URL =  "http://www.computer.org/portal/web/csdl/magazines/computer",
}

@Article{Hough:1989:RS,
  author =       "David Hough",
  title =        "Random Story",
  journal =      j-NA-DIGEST,
  volume =       "Volume 89, Issue 1",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "NA Digest",
}

@Article{hous58,
  author =       "Alston S. Householder",
  title =        "Unitary Triangularization of a Nonsymmetric Matrix",
  journal =      j-ACM,
  volume =       "5",
  pages =        "339--342",
  year =         "1958",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Householder:1964:TMN,
  author =       "Alston S. Householder",
  title =        "The Theory of Matrices in Numerical Analysis",
  publisher =    pub-Blaisdell,
  address =      pub-Blaisdell:adr-NY,
  pages =        "xi + 257",
  year =         "1964",
  ISBN =         "0-486-61781-5",
  ISBN-13 =      "978-0-486-61781-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted by Dover, New York, 1975",
}

@Article{Hough:1997:COD,
  author =       "Patricia D. Hough and Stephen A. Vavasis",
  title =        "Complete Orthogonal Decomposition for Weighted Least
                 Squares",
  journal =      j-SIMAX,
  volume =       "18",
  number =       "2",
  pages =        "369--392",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{hp82,
  key =          "Hewlett--Packard",
  title =        "{HP-\textup{15}C} Advanced Functions Handbook",
  publisher =    "Hewlett--Packard",
  address =      "Portable Computer Division, Corvallis, OR, USA",
  pages =        "221",
  year =         "1982",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Part number 00015-90011 Rev.~C",
}

@Book{hp93,
  key =          "Hewlett--Packard",
  title =        "{HP \textup{48}G} Series User's Guide",
  publisher =    "Hewlett--Packard",
  address =      "Corvallis Division, Corvallis, OR, USA",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Part number 00048-90126, Edition 3",
}

@Article{Henderson:1983:HKP,
  author =       "Harold V. Henderson and Friedrich Pukelsheim and
                 Shayle R. Searle",
  title =        "On the History of the {Kronecker} Product",
  journal =      j-LMA,
  volume =       "14",
  pages =        "113--120",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Hedayat:1999:OAT,
  author =       "A. S. Hedayat and N. J. A. Sloane and John Stufken",
  title =        "Orthogonal Arrays: {Theory} and Applications",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-NY,
  pages =        "xxiii + 416",
  year =         "1999",
  ISBN =         "0-387-98766-5",
  ISBN-13 =      "978-0-387-98766-8",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Hull:1979:CNS,
  author =       "T. E. Hull",
  editor =       "Lloyd D. Fosdick",
  booktitle =    "Performance Evaluation of Numerical Software",
  title =        "Correctness of Numerical Software",
  publisher =    pub-NH # ", " # pub-NH:adr,
  pages =        "3--15",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Hull:1982:PCE,
  author =       "T. E. Hull",
  editor =       "G. A. Watson",
  booktitle =    "Numerical Analysis Proceedings, Dundee 1981",
  title =        "Precision Control, Exception Handling and {A} Choice
                 of Numerical Algorithms",
  volume =       "912",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "169--178",
  year =         "1982",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Mathematics",
}

@Article{Hunt:1997:ROA,
  author =       "Julian Hunt",
  title =        "Rounding and Other Approximations for Measurements,
                 Records and Targets",
  journal =      j-MATH-TODAY,
  volume =       "33",
  pages =        "73--77",
  year =         "1997",
  ISSN =         "1361-2042",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Mathematics Today",
  journal-URL =  "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
  nuber =        "3",
}

@Article{Hu:1992:KSM,
  author =       "D. Y. Hu and L. Reichel",
  title =        "Krylov Subspace Methods for the {Sylvester} Equation",
  journal =      j-LAA,
  volume =       "172",
  pages =        "283--313",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Hull:1966:TPM,
  author =       "T. E. Hull and J. R. Swenson",
  title =        "Tests of Probabilistic Models for Propagation of
                 Roundoff Errors",
  journal =      j-CACM,
  volume =       "9",
  number =       "2",
  pages =        "108--113",
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Misc{Hyman:1957:EEG,
  author =       "M. A. Hyman",
  title =        "Eigenvalues and Eigenvectors of General Matrices",
  howpublished = "Presented at the 12th National Meeting of the
                 Association for Computing Machinery, Houston, Texas",
  year =         "1957",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Cited in \cite{Wilkinson:1963:REA}",
}

@Book{IBM:1988:ESS,
  author =       "IBM",
  title =        "Engineering and Scientific Subroutine Library, Guide
                 and Reference, Release 3",
  publisher =    "Fourth Edition (Program Number 5668-863)",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Group:1981:PSB,
  author =       "{IEEE Computer Society Microprocessor Standards
                 Committee, Floating-Point Working Group}",
  title =        "A Proposed Standard for Binary Floating-Point
                 Arithmetic, {Draft} 8.0 of {IEEE Task P754} (With
                 Introductory Comments by {David Stevenson})",
  journal =      j-COMPUTER,
  volume =       "14",
  pages =        "51--62",
  year =         "1981",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computer",
  journal-URL =  "http://www.computer.org/portal/web/csdl/magazines/computer",
}

@Book{ieee85,
  key =          "IEEE Computer Society",
  title =        "{IEEE} Standard for Binary Floating-Point Arithmetic,
                 {ANSI/IEEE} Standard 754-1985",
  publisher =    "Institute of Electrical and Electronics Engineers",
  address =      "New York",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted in SIGPLAN Notices, 22(2):9--25, 1987",
}

@Book{ieee87,
  key =          "IEEE Computer Society",
  title =        "A Radix-Independent Standard for Floating-Point
                 Arithmetic, {IEEE} Standard 854-1987",
  publisher =    "IEEE Computer Society",
  address =      "New York",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ikebe:1979:IHM,
  author =       "Yasuhiko Ikebe",
  title =        "On Inverses of {Hessenberg} Matrices",
  journal =      j-LAA,
  volume =       "24",
  pages =        "93--97",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ikramov:2000:BGF,
  author =       "Khakim D. Ikramov and Andrey B. Kucherov",
  title =        "Bounding the Growth Factor in {Gaussian} Elimination
                 for {Buckley's} Class of Complex Symmetric Matrices",
  journal =      j-NLAA,
  volume =       "7",
  number =       "5",
  pages =        "269--274",
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ikramov:1998:RNC,
  author =       "Khakim D. Ikramov",
  title =        "A Remark on ``{A} Note on Constructing a Symmetric
                 Matrix with Specified Diagonal Entries and
                 Eigenvalues''",
  journal =      j-BIT,
  volume =       "38",
  number =       "4",
  pages =        "807",
  year =         "1998",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Misc{Committee:1993:RGL,
  author =       "{ILAS Education Committee}",
  title =        "Report on Graduate Linear Algebra Courses",
  howpublished = "Manuscript from the International Linear Algebra
                 Society",
  pages =        "4",
  month =        nov,
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "\path|http://gauss.technion.ac.il/iic/GRAD-ED.SYLLABI|",
}

@Article{Incertis:1985:FMC,
  author =       "F. Incertis",
  title =        "A Faster Method of Computing Matrix {Pythagorean}
                 Sums",
  journal =      j-IEEE-AC,
  volume =       "AC-30",
  number =       "3",
  pages =        "273--275",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Ince:1992:CWM,
  editor =       "D. C. Ince",
  title =        "Collected Works of {A. M. Turing}: {Mechanical}
                 Intelligence",
  publisher =    pub-NH,
  address =      pub-NH:adr,
  pages =        "xix + 227",
  year =         "1992",
  ISBN =         "0-444-88058-5",
  ISBN-13 =      "978-0-444-88058-1",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ipsen:1994:USM,
  author =       "Ilse C. F. Ipsen and Carl D. Meyer",
  title =        "Uniform Stability of {Markov} Chains",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "4",
  pages =        "1061--1074",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Iri:1991:HAD,
  author =       "Masao Iri",
  editor =       "Andreas Griewank and George F. Corliss",
  booktitle =    "Automatic Differentiation of Algorithms: {Theory},
                 Implementation, and Application",
  title =        "History of Automatic Differentiation and Rounding
                 Error Estimation",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "3--16",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Isaacson:1966:ANM,
  author =       "Eugene Isaacson and Herbert Bishop Keller",
  title =        "Analysis of Numerical Methods",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  pages =        "xv + 541",
  year =         "1966",
  ISBN =         "0-486-68029-0",
  ISBN-13 =      "978-0-486-68029-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted by Dover, New York, 1994",
}

@Article{Jang:1997:CLS,
  author =       "Ho-Jong Jang",
  title =        "A Constrained Least-Squares Approach to the Rapid
                 Reanalysis of Structures",
  journal =      j-LAA,
  volume =       "265",
  pages =        "185--202",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Jalby:1991:SAI,
  author =       "William Jalby and Bernard Philippe",
  title =        "Stability Analysis and Improvement of the Block
                 {Gram--Schmidt} Algorithm",
  journal =      j-SISSC,
  volume =       "12",
  number =       "5",
  pages =        "1058--1073",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Jansen:1986:HAA,
  author =       "Paul Jansen and Peter Weidner",
  title =        "High-Accuracy Arithmetic Software---Some Tests of the
                 {ACRITH} Problem-Solving Routines",
  journal =      j-TOMS,
  volume =       "12",
  number =       "1",
  pages =        "62--70",
  year =         "1986",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Jankowski:1977:IRI,
  author =       "M. Jankowski and H. Wo{\'z}niakowski",
  title =        "Iterative Refinement Implies Numerical Stability",
  journal =      j-BIT,
  volume =       "17",
  pages =        "303--311",
  year =         "1977",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Jankowski:1985:ASC,
  author =       "M. Jankowski and H. Wo{\'z}niakowski",
  title =        "The Accurate Solution of Certain Continuous Problems
                 Using Only Single Precision Arithmetic",
  journal =      j-BIT,
  volume =       "25",
  pages =        "635--651",
  year =         "1985",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Jennings:1982:BSV,
  author =       "A. Jennings",
  title =        "Bounds for the Singular Values of a Matrix",
  journal =      j-IMAJNA,
  volume =       "2",
  pages =        "459--474",
  year =         "1982",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Jennings:1974:DEA,
  author =       "L. S. Jennings and M. R. Osborne",
  title =        "A Direct Error Analysis for Least Squares",
  journal =      j-NUM-MATH,
  volume =       "22",
  pages =        "325--332",
  year =         "1974",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Jong:1977:TFD,
  author =       "Lieuwe Sytse de Jong",
  title =        "Towards a Formal Definition of Numerical Stability",
  journal =      j-NUM-MATH,
  volume =       "28",
  pages =        "211--219",
  year =         "1977",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Jones:1993:BKF,
  author =       "Mark T. Jones and Merrell L. Patrick",
  title =        "{Bunch--Kaufman} Factorization for Real Symmetric
                 Indefinite Banded Matrices",
  journal =      j-SIMAX,
  volume =       "14",
  number =       "2",
  pages =        "553--559",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Jones:1994:FSI,
  author =       "Mark T. Jones and Merrell L. Patrick",
  title =        "Factoring Symmetric Indefinite Matrices on
                 High-Performance Architectures",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "1",
  pages =        "273--283",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Jordan:1968:EEG,
  author =       "T. L. Jordan",
  title =        "Experiments on Error Growth Associated with Some
                 Linear Least-Squares Procedures",
  journal =      j-MATH-COMP,
  volume =       "22",
  pages =        "579--588",
  year =         "1968",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Joseph:1991:CPN,
  author =       "George Gheverghese Joseph",
  title =        "The Crest of the Peacock: {Non-European} Roots of
                 Mathematics",
  publisher =    pub-Penguin,
  address =      pub-Penguin:adr-L,
  pages =        "xv + 371",
  year =         "1991",
  ISBN =         "0-14-012529-9",
  ISBN-13 =      "978-0-14-012529-0",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Jones:1974:NSE,
  author =       "William B. Jones and W. J. Thron",
  title =        "Numerical Stability in Evaluating Continued
                 Fractions",
  journal =      j-MATH-COMP,
  volume =       "28",
  number =       "127",
  pages =        "795--810",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Jankowski:1983:NFP,
  author =       "M. Jankowski and A. Smoktunowicz and H.
                 Wo{\'z}niakowski",
  title =        "A Note on Floating-Point Summation of Very Many
                 Terms",
  journal =      j-J-INFO-PROC-CYBERNETICS-EIK,
  volume =       "19",
  number =       "9",
  pages =        "435--440",
  year =         "1983",
  CODEN =        "JICYE5",
  ISSN =         "0863-0593",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Journal of Information Processing and Cybernetics: EIK",
}

@Article{Kahan:1963:ANIa,
  author =       "W. Kahan and I. Farkas",
  title =        "Algorithm 168: {Newton} Interpolation with Backward
                 Divided Differences",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "165",
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Kahan:1963:ANIb,
  author =       "W. Kahan and I. Farkas",
  title =        "Algorithm 169: {Newton} Interpolation with Forward
                 Divided Differences",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "165",
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Kaagstrom:1994:PAG,
  author =       "Bo K{\aa}gstr{\"o}m",
  title =        "A Perturbation Analysis of the Generalized {Sylvester}
                 Equation {$(AR-LB, DR-LE) = (C,F)$}",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "4",
  pages =        "1045--1060",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Unpublished{Kahan:2001:WVT,
  author =       "W. Kahan",
  title =        "What has the Volume of a Tetrahedron to do with
                 Computer Programming Languages?",
  pages =        "31",
  month =        apr,
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Manuscript",
}

@Article{Kahan:1965:FRR,
  author =       "W. Kahan",
  title =        "Further Remarks on Reducing Truncation Errors",
  journal =      j-CACM,
  volume =       "8",
  number =       "1",
  pages =        "40",
  year =         "1965",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363707.363723",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Kahan:1966:NLA,
  author =       "W. M. Kahan",
  title =        "Numerical Linear Algebra",
  journal =      j-CAN-MATH-BULL,
  volume =       "9",
  number =       "??",
  pages =        "757--801",
  month =        "????",
  year =         "1966",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-1966-083-2",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  bibdate =      "Thu Sep 8 10:03:18 MDT 2011",
  bibsource =    "http://cms.math.ca/cmb/v9/;
                 https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/gvl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian mathematical bulletin = Bulletin canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cmb/",
}

@InProceedings{Kahan:1972:SEA,
  author =       "W. Kahan",
  booktitle =    "Proc. IFIP Congress, Ljubljana",
  title =        "A Survey of Error Analysis",
  publisher =    pub-NH # ", " # pub-NH:adr,
  pages =        "1214--1239",
  year =         "1972",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Information Processing 71",
}

@TechReport{Kahan:1973:IAL,
  author =       "W. Kahan",
  title =        "Implementation of Algorithms (Lecture Notes by {W. S.
                 Haugeland} and {D. Hough})",
  type =         "Technical Report",
  number =       "20",
  institution =  inst-Berkeley-CS,
  address =      inst-Berkeley:adr,
  year =         "1973",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Kahan:1980:IAO,
  author =       "W. Kahan",
  editor =       "Karl L. E. Nickel",
  booktitle =    "Interval Mathematics 1980",
  title =        "Interval Arithmetic Options in the Proposed {IEEE}
                 Floating Point Arithmetic Standard",
  publisher =    pub-AP # ", " # pub-AP:adr-NY,
  pages =        "99--128",
  year =         "1980",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Kahan:1981:WDW,
  author =       "W. Kahan",
  title =        "Why Do We Need a Floating-Point Arithmetic Standard?",
  type =         "Technical Report",
  institution =  inst-Berkeley,
  address =      inst-Berkeley:adr,
  pages =        "41",
  month =        feb,
  year =         "1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Kahan:1983:MWS,
  author =       "W. Kahan",
  booktitle =    "Statistical Computing Section, Proceedings of the
                 American Statistical Association, Toronto",
  title =        "Mathematics Written in Sand---The {HP-15C}, {Intel}
                 8087, etc.",
  pages =        "12--26",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Kahan:1986:SRC,
  author =       "W. Kahan",
  title =        "To Solve a Real Cubic Equation",
  type =         "Technical Report",
  number =       "PAM-352",
  institution =  "Center for Pure and Applied Mathematics, University of
                 California",
  address =      inst-Berkeley:adr,
  pages =        "20",
  month =        nov,
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Kahan:1987:BCC,
  author =       "W. Kahan",
  editor =       "A. Iserles and M. J. D. Powell",
  booktitle =    "The State of the Art in Numerical Analysis",
  title =        "Branch Cuts for Complex Elementary Functions or Much
                 Ado About Nothing's Sign Bit",
  publisher =    pub-OUP,
  pages =        "165--211",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Unpublished{Kahan:1987:DPI,
  author =       "W. Kahan",
  title =        "Doubled-Precision {IEEE} Standard 754 Floating-Point
                 Arithmetic",
  month =        feb,
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Manuscript",
}

@Unpublished{Kahan:1990:HCA,
  author =       "W. Kahan",
  title =        "How {Cray}'s Arithmetic Hurts Scientific Computation
                 (and What Might be Done About It)",
  pages =        "42",
  month =        jun,
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Manuscript prepared for the Cray User Group meeting in
                 Toronto",
}

@Article{Kahan:1991:ARL,
  author =       "W. Kahan",
  title =        "Analysis and Refutation of the {LCAS}",
  journal =      j-SIGNUM,
  volume =       "26",
  number =       "3",
  pages =        "2--15",
  year =         "1991",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J690",
}

@Unpublished{Kahan:1994:CBV,
  author =       "W. Kahan",
  title =        "Computer Benchmarks Versus Accuracy",
  month =        jun,
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Draft manuscript",
}

@Unpublished{Kahan:1996:IPE,
  author =       "W. Kahan",
  title =        "The Improbability of Probabilistic Error Analyses for
                 Numerical Computations",
  pages =        "34",
  month =        mar,
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Manuscript",
}

@Unpublished{Kahan:1996:LNS,
  author =       "W. Kahan",
  title =        "Lecture Notes on the Status of {IEEE Standard} 754 for
                 Binary Floating-Point Arithmetic",
  pages =        "30",
  month =        may,
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Manuscript",
}

@Unpublished{Kahan:1997:MAA,
  author =       "W. Kahan",
  title =        "Miscalculating Area and Angles of a Needle-Like
                 Triangle",
  pages =        "20",
  month =        jul,
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Manuscript",
}

@InProceedings{Kahan:1985:AIA,
  author =       "W. Kahan and E. LeBlanc",
  editor =       "Kai Hwang",
  booktitle =    "Proceedings of the 7th Symposium on Computer
                 Arithmetic",
  title =        "Anomalies in the {IBM ACRITH} Package",
  publisher =    "IEEE Computer Society Press, Silver Spring, MD, USA",
  pages =        "322--331",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Karp:1997:HPD,
  author =       "Alan H. Karp and Peter Markstein",
  title =        "High-Precision Division and Square Root",
  journal =      j-TOMS,
  volume =       "23",
  number =       "4",
  pages =        "561--589",
  year =         "1997",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Karatsuba:1963:MMN,
  author =       "A. Karatsuba and Yu. Ofman",
  title =        "Multiplication of Multidigit Numbers on Automata",
  journal =      j-SOVIET-PHYS-DOKL,
  volume =       "7",
  number =       "7",
  pages =        "595--596",
  month =        jan,
  year =         "1963",
  CODEN =        "SPHDA9",
  ISSN =         "0038-5689",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Soviet Physics---Doklady",
}

@Article{Kahan:1979:PFP,
  author =       "W. Kahan and J. Palmer",
  title =        "On a Proposed Floating-Point Standard",
  journal =      j-SIGNUM,
  volume =       "14",
  pages =        "13--21",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J690",
}

@Article{Kaagstrom:1992:DSM,
  author =       "Bo K{\aa}gstr{\"o}m and Peter Poromaa",
  title =        "Distributed and Shared Memory Block Algorithms for the
                 Triangular {Sylvester} Equation with {${\rm sep}^{-1}$}
                 Estimators",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "90--101",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kaagstrom:1996:LSA,
  author =       "Bo K{\aa}gstr{\"o}m and Peter Poromaa",
  title =        "{LAPACK}-Style Algorithms and Software for Solving the
                 Generalized {Sylvester} Equation and Estimating the
                 Separation Between Regular Matrix Pairs",
  journal =      j-TOMS,
  volume =       "22",
  number =       "1",
  pages =        "78--103",
  year =         "1996",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Kaagstrom:1996:CES,
  author =       "Bo K{\aa}gstr{\"o}m and Peter Poromaa",
  title =        "Computing Eigenspaces with Specified Eigenvalues of a
                 Regular Matrix Pair {$(A,B)$} and Condition Estimation:
                 {Theory}, Algorithms and Software",
  journal =      j-NUM-ALG,
  volume =       "12",
  pages =        "369--407",
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kaporin:1999:PAF,
  author =       "Igor Kaporin",
  title =        "A Practical Algorithm for Faster Matrix
                 Multiplication",
  journal =      j-NLAA,
  volume =       "6",
  pages =        "687--700",
  year =         "1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Karasalo:1974:CTD,
  author =       "Ilkka Karasalo",
  title =        "A Criterion for Truncation of the {$QR$}-Decomposition
                 Algorithm for the Singular Linear Least Squares
                 Problem",
  journal =      j-BIT,
  volume =       "14",
  pages =        "156--166",
  year =         "1974",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Book{Karlin:1968:TP,
  author =       "Samuel Karlin",
  title =        "Total Positivity",
  volume =       "1",
  publisher =    "Stanford University Press",
  address =      inst-U-STANFORD:adr,
  year =         "1968",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Karpinski:1985:PFP,
  author =       "Richard Karpinski",
  title =        "Paranoia: {A} Floating-Point Benchmark",
  journal =      j-BYTE,
  volume =       "10",
  number =       "2",
  pages =        "223--235",
  month =        feb,
  year =         "1985",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BYTE Magazine",
}

@Book{Kato:1976:PTL,
  author =       "Tosio Kato",
  title =        "Perturbation Theory for Linear Operators",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  edition =      "Second",
  pages =        "xxi + 619",
  year =         "1976",
  ISBN =         "3-540-97588-5",
  ISBN-13 =      "978-3-540-97588-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kaufman:1983:MMQ,
  author =       "Linda Kaufman",
  title =        "Matrix Methods for Queuing Problems",
  journal =      j-SISSC,
  volume =       "4",
  number =       "3",
  pages =        "525--552",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kao:2000:LTA,
  author =       "Ming-Yang Kao and Jie Wang",
  title =        "Linear-Time Approximation Algorithms for Computing
                 Numerical Summation with Provably Small Errors",
  journal =      j-SICOMP,
  volume =       "29",
  number =       "5",
  pages =        "1568--1576",
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Karlson:1997:EOB,
  author =       "Rune Karlson and Bertil Wald{\'e}n",
  title =        "Estimation of Optimal Backward Perturbation Bounds for
                 the Linear Least Squares Problem",
  journal =      j-BIT,
  volume =       "37",
  number =       "4",
  pages =        "862--869",
  year =         "1997",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Kaagstrom:1989:GSM,
  author =       "Bo K{\aa}gstr{\"o}m and Lars Westin",
  title =        "Generalized {Schur} Methods with Condition Estimators
                 for Solving the Generalized {Sylvester} Equation",
  journal =      j-IEEE-AC,
  volume =       "AC-34",
  number =       "7",
  pages =        "745--751",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kearfott:1996:AIF,
  author =       "R. Baker Kearfott",
  title =        "Algorithm 763: {INTERVAL\_ARITHMETIC}: {A Fortran 90}
                 Module for an Interval Data Type",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "385--392",
  year =         "1996",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Kearfott:1996:ICI,
  author =       "R. Baker Kearfott",
  title =        "Interval Computations: {Introduction}, Uses, and
                 Resources",
  journal =      j-EUROMATH-BULL,
  volume =       "2",
  number =       "1",
  pages =        "95--112",
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "\path|http://interval.louisiana.edu/preprints.html|",
  fjournal =     "Euromath Bulletin",
}

@Book{Kennedy:1980:SC,
  author =       "William J. {Kennedy, Jr.} and James E. Gentle",
  title =        "Statistical Computing",
  publisher =    "Marcel Dekker",
  address =      "New York",
  pages =        "xi + 591",
  year =         "1980",
  ISBN =         "0-8247-6898-1",
  ISBN-13 =      "978-0-8247-6898-0",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kenney:1990:SAD,
  author =       "Charles Kenney and Gary Hewer",
  title =        "The Sensitivity of the Algebraic and Differential
                 {Riccati} Equations",
  journal =      j-SICOPT,
  volume =       "28",
  number =       "1",
  pages =        "50--69",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kenney:1988:CSR,
  author =       "Charles Kenney and Alan J. Laub",
  title =        "Controllability and Stability Radii for Companion Form
                 Systems",
  journal =      j-MATH-CONTROL-SIGNALS-SYST,
  volume =       "1",
  pages =        "239--256",
  year =         "1988",
  CODEN =        "MCSYE8",
  ISSN =         "0932-4194 (print), 1435-568x (electronic)",
  ISSN-L =       "0932-4194",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Mathematics of control, signals, and systems: MCSS",
}

@Article{Kenney:1994:SSS,
  author =       "Charles S. Kenney and Alan J. Laub",
  title =        "Small-Sample Statistical Condition Estimates for
                 General Matrix Functions",
  journal =      j-SISC,
  volume =       "15",
  number =       "1",
  pages =        "36--61",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Keller:1965:SSS,
  author =       "Herbert B. Keller",
  title =        "On the Solution of Singular and Semidefinite Linear
                 Systems by Iteration",
  journal =      j-SINUM,
  volume =       "2",
  number =       "2",
  pages =        "281--290",
  year =         "1965",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Kelley:1995:IML,
  author =       "C. T. Kelley",
  title =        "Iterative Methods for Linear and Nonlinear Equations",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xiii + 165",
  year =         "1995",
  ISBN =         "0-89871-352-8",
  ISBN-13 =      "978-0-89871-352-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Kelley:1999:IMO,
  author =       "C. T. Kelley",
  title =        "Iterative Methods for Optimization",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xv + 180",
  year =         "1999",
  ISBN =         "0-89871-433-8",
  ISBN-13 =      "978-0-89871-433-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kerr:1990:FCT,
  author =       "Thomas H. Kerr",
  title =        "Fallacies in Computational Testing of Matrix Positive
                 Definiteness/Semidefiniteness",
  journal =      j-IEEE-TRANS-AEROSP-ELECTRON-SYST,
  volume =       "26",
  number =       "2",
  pages =        "415--421",
  year =         "1990",
  CODEN =        "IEARAX",
  ISSN =         "0018-9251 (print), 1557-9603 (electronic)",
  ISSN-L =       "0018-9251",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "IEEE Transactions on Aerospace and Electronic Systems",
}

@InProceedings{Krishnan:2001:PEM,
  author =       "Shankar Krishnan and Mark Foskey and Tim Culver and
                 John Keyser and Dinesh Manocha",
  editor =       "David Eppstein and Dan Halperin and Dinesh Manocha",
  booktitle =    "Proc. ACM Symposium on Computational Geometry",
  title =        "{PRECISE}: {Efficient} Multiprecision Evaluation of
                 Algebraic Roots and Predicates for Reliable Geometric
                 Computation",
  publisher =    "ACM Press",
  pages =        "274--283",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kielbasinski:1973:SAC,
  author =       "Andrzej Kie{\l}basi{\'n}ski",
  title =        "Summation algorithm with corrections and some of its
                 applications",
  journal =      j-MATH-STOS,
  volume =       "1",
  pages =        "22--41",
  year =         "1973",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "(In Polish, cited in \cite{Jankowski:1983:NFP} and
                 \cite{Jankowski:1985:ASC})",
  fjournal =     "Math. Stos.",
}

@Article{Kielbasinski:1981:IRL,
  author =       "Andrzej Kie{\l}basi{\'n}ski",
  title =        "Iterative Refinement for Linear Systems in
                 Variable-Precision Arithmetic",
  journal =      j-BIT,
  volume =       "21",
  pages =        "97--103",
  year =         "1981",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Kielbasinski:1987:NRE,
  author =       "Andrzej Kie{\l}basi{\'n}ski",
  title =        "A Note on Rounding-Error Analysis of {Cholesky}
                 Factorization",
  journal =      j-LAA,
  volume =       "88/89",
  pages =        "487--494",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Kielbasinski:1988:NLA,
  author =       "Andrzej Kie{\l}basi{\'n}ski and Hubert Schwetlick",
  title =        "Numerische Lineare Algebra: {Eine} Computerorientierte
                 Einf{\"u}hrung",
  publisher =    "VEB Deutscher",
  address =      "Berlin",
  pages =        "472",
  year =         "1988",
  ISBN =         "3-87144-999-7",
  ISBN-13 =      "978-3-87144-999-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Kielbasinski:1992:NAL,
  author =       "Andrzej Kie{\l}basi{\'n}ski and Hubert Schwetlick",
  title =        "Numeryczna Algebra Liniowa: {Wprowadzenie} do
                 Oblicze{\'n} Zautomatyzowanych",
  publisher =    "Wydawnictwa Naukowo-Techniczne",
  address =      "Warszawa",
  pages =        "502",
  year =         "1992",
  ISBN =         "83-204-1260-9",
  ISBN-13 =      "978-83-204-1260-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kittaneh:1995:SVC,
  author =       "Fuad Kittaneh",
  title =        "Singular Values of Companion Matrices and Bounds on
                 Zeros of Polynomials",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "1",
  pages =        "333--340",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Klatte:1993:CXC,
  author =       "R. Klatte and U. W. Kulisch and C. Lawo and M. Rauch
                 and A. Wiethoff",
  title =        "{C-XSC}: {A} {C++} Class Library for Extended
                 Scientific Computing",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1993",
  ISBN =         "0-387-56328-8",
  ISBN-13 =      "978-0-387-56328-2",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Klatte:1992:PXL,
  author =       "R. Klatte and U. W. Kulisch and M. Neaga and D. Ratz
                 and Ch. Ullrich",
  title =        "{PASCAL-XSC}---{Language} Reference with Examples",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kenney:1992:MSA,
  author =       "Charles S. Kenney and Alan J. Laub and Philip M.
                 Papadopoulos",
  title =        "Matrix-Sign Algorithms for {Riccati} Equations",
  journal =      "IMA J. Math. Control Inform.",
  volume =       "9",
  pages =        "331--344",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kenney:1998:SCEa,
  author =       "Charles Kenney and Alan J. Laub and M. S. Reese",
  title =        "Statistical Condition Estimation for Linear Systems",
  journal =      j-SISC,
  volume =       "19",
  number =       "2",
  pages =        "566--583",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kenney:1998:SCEb,
  author =       "Charles Kenney and Alan J. Laub and M. S. Reese",
  title =        "Statistical Condition Estimation for Linear Least
                 Squares",
  journal =      j-SIMAX,
  volume =       "19",
  number =       "4",
  pages =        "906--923",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Kahaner:1989:NMS,
  author =       "David K. Kahaner and Cleve B. Moler and Stephen G.
                 Nash",
  title =        "Numerical Methods and Software",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 495",
  year =         "1989",
  ISBN =         "0-13-627258-4",
  ISBN-13 =      "978-0-13-627258-8",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@PhdThesis{Knight:1993:EAS,
  author =       "Philip A. Knight",
  title =        "Error Analysis of Stationary Iteration and Associated
                 Problems",
  school =       inst-U-Manchester,
  address =      inst-U-Manchester:adr,
  pages =        "135",
  month =        sep,
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Knight:1995:FRM,
  author =       "Philip A. Knight",
  title =        "Fast Rectangular Matrix Multiplication and {$QR$}
                 Decomposition",
  journal =      j-LAA,
  volume =       "221",
  pages =        "69--81",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Knuth:1962:EPC,
  author =       "Donald E. Knuth",
  title =        "Evaluation of polynomials by computer",
  journal =      j-CACM,
  volume =       "5",
  number =       "12",
  pages =        "595--599",
  month =        dec,
  year =         "1962",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355580.369074",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68.00 (12.00)",
  MRnumber =     "27 #970",
  bibdate =      "Thu Dec 08 11:11:03 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 MathSciNet database",
  note =         "See letter \cite{Knuth:1963:LEE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  remark =       "The author that Motzkin (1962) showed that Horner's
                 rule for polynomial evaluation may not be optimal, and
                 develops the idea further for arbitrary polynomials,
                 but also observes that the coefficients of the revised
                 polynomials may be difficult to find. He also asks
                 about, but does not answer, the question of error
                 analysis of the various methods.",
}

@Article{Knuth:1992:TNN,
  author =       "Donald E. Knuth",
  title =        "Two Notes on Notation",
  journal =      j-AMM,
  volume =       "99",
  number =       "5",
  pages =        "403--422",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Knuth:1999:DT,
  author =       "Donald E. Knuth",
  title =        "Digital Typography",
  publisher =    "Center for the Study of Language and Information",
  address =      "Stanford University, Stanford, CA, USA",
  pages =        "xv + 685",
  year =         "1999",
  ISBN =         "0-575-86010-4",
  ISBN-13 =      "978-0-575-86010-0",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "CSLI Lecture Notes Number 78",
}

@Book{Knuth:1997:FA,
  author =       "Donald E. Knuth",
  title =        "Fundamental Algorithms",
  volume =       "1",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Third",
  pages =        "xix + 650",
  year =         "1997",
  ISBN =         "0-201-89683-4",
  ISBN-13 =      "978-0-201-89683-1",
  LCCN =         "QA76.6 .K64 1997",
  bibdate =      "Fri Jul 11 15:41:22 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
  price =        "US\$49.50",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  keywords =     "computer algorithms; electronic digital computers --
                 programming",
  tableofcontents = "1: Basic Concepts / 1 \\
                 1.1. Algorithms / 1 \\
                 1.2. Mathematical Preliminaries / 10 \\
                 1.2.1. Mathematical Induction / 11 \\
                 1.2.2. Numbers, Powers, and Logarithms / 21 \\
                 1.2.3. Sums and Products / 27 \\
                 1.2.4. Integer Functions and Elementary Number Theory /
                 39 \\
                 1.2.5. Permutations and Factorials / 45 \\
                 1.2.6. Binomial Coefficients / 52 \\
                 1.2.7. Harmonic Numbers / 75 \\
                 1.2.8. Fibonacci Numbers / 79 \\
                 1.2.9. Generating Functions / 87 \\
                 1.2.10. Analysis of an Algorithm / 96 \\
                 * 1.2.11. Asymptotic Representations / 107 \\
                 *1.2.11.1. The $O$-notation / 107 \\
                 *1.2.11.2. Euler's summation formula / 111 \\
                 *1.2.11.3. Some asymptotic calculations / 116 \\
                 1.3. MIX / 124 \\
                 1.3.1. Description of MIX / 124 \\
                 1.3.2. The MIX Assembly Language / 144 \\
                 1.3.3. Applications to Permutations / 164 \\
                 1.4. Some Fundamental Programming Techniques / 186 \\
                 1.4.1. Subroutines / 186 \\
                 1.4.2. Coroutines / 193 \\
                 1.4.3. Interpretive Routines / 200 \\
                 1.4.3.1. A MIX simulator / 202 \\
                 *1.4.3.2. Trace routines / 212 \\
                 1.4.4. Input and Output / 215 \\
                 1.4.5. History and Bibliography / 229 \\
                 2: Information Structures / 232 \\
                 2.1. Introduction / 232 \\
                 2.2. Linear Lists / 238 \\
                 2.2.1. Stacks, Queues, and Deques / 238 \\
                 2.2.2. Sequential Allocation / 244 \\
                 2.2.3. Linked Allocation / 254 \\
                 2.2.4. Circular Lists / 273 \\
                 2.2.5. Doubly Linked Lists / 280 \\
                 2.2.6. Arrays and Orthogonal Lists / 298 \\
                 2.3. Trees / 308 \\
                 2.3.1. Traversing Binary Trees / 318 \\
                 2.3.2. Binary Tree Representation of Trees / 334 \\
                 2.3.3. Other Representations of Trees / 348 \\
                 2.3.4. Basic Mathematical Properties of Trees / 362 \\
                 2.3.4.1. Free trees / 363 \\
                 2.3.4.2. Oriented trees / 372 \\
                 *2.3.4.3. The ``infinity lemma'' / 382 \\
                 *2.3.4.4. Enumeration of trees / 386 \\
                 2.3.4.5. Path length / 399 \\
                 *2.3.4.6. History and bibliography / 406 \\
                 2.3.5. Lists and Garbage Collection / 408 \\
                 2.4. Multilinked Structures / 424 \\
                 2.5. Dynamic Storage Allocation / 435 \\
                 2.6. History and Bibliography / 457 \\
                 Answers to Exercises / 466 \\
                 Appendix A: Tables of Numerical Quantities / 619 \\
                 1. Fundamental Constants (decimal) / 619 \\
                 2. Fundamental Constants (octal) / 620 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 621 \\
                 Appendix B: Index to Notations / 623 \\
                 Appendix C: Index to Algorithms and Theorems / 628 \\
                 Index and Glossary / 630",
}

@Book{Knuth:1998:SA,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Third",
  pages =        "xiii + 762",
  year =         "1998",
  ISBN =         "0-201-89684-2",
  ISBN-13 =      "978-0-201-89684-8",
  LCCN =         "QA76.6 .K64 1997",
  bibdate =      "Fri Jul 11 15:41:22 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/css.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
  price =        "US\$52.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  tableofcontents = "3: Random Numbers / 1 \\
                 3.1. Introduction / 1 \\
                 3.2. Generating Uniform Random Numbers / 10 \\
                 3.2.1. The Linear Congruential Method / 10 \\
                 3.2 1.1. Choice of modulus / 12 \\
                 3.2.1.2 Choice of multiplier / 16 \\
                 3.2.1.3. Potency / 23 \\
                 3.2.2. Other Methods / 26 \\
                 3.3. Statistical Tests / 41 \\
                 3.3.1. General Test Procedures for Studying Random Data
                 / 41 \\
                 3.3.2. Empirical Tests / 61 \\
                 *3.3.3. Theoretical Tests / 80 \\
                 3.3.4. The Spectral Test / 93 \\
                 3.4. Other Types of Random Quantities / 119 \\
                 3.4 1. Numerical Distributions / 119 \\
                 3.4.2. Random Sampling and Shuffling / 142 \\
                 *3.5. What Is a Random Sequence? / 149 \\
                 3.6. Summary / 184 \\
                 4: Arithmetic / 194 \\
                 4.1. Positional Number Systems / 195 \\
                 4.2. Floating Point Arithmetic / 214 \\
                 4.2.1. Single-Precision Calculations / 214 \\
                 4.2 2. Accuracy of Floating Point Arithmetic / 229 \\
                 *4.2.3. Double-Precision Calculations / 246 \\
                 4.2.4. Distribution of Floating Point Numbers / 253 \\
                 4.3 Multiple Precision Arithmetic / 265 \\
                 4.3.1. The Classical Algorithms / 265 \\
                 *4.3.2. Modular Arithmetic / 284 \\
                 *4.3.3. How Fast Can We Multiply? / 294 \\
                 4.4. Radix Conversion / 319 \\
                 4.5. Rational Arithmetic / 330 \\
                 4.5.1. Fractions / 330 \\
                 4.5.2. The Greatest Common Divisor / 333 \\
                 *4.5.3. Analysis of Euclid's Algorithm / 356 \\
                 4.5.4. Factoring into Primes / 379 \\
                 4.6. Polynomial Arithmetic / 418 \\
                 4.6.1. Division of Polynomials / 420 \\
                 *4.6.2. Factorization of Polynomials / 439 \\
                 4.6.3. Evaluation of Powers / 461 \\
                 4.6.4. Evaluation of Polynomials / 485 \\
                 *4.7. Manipulation of Power Series / 525 \\
                 Answers to Exercises / 538 \\
                 Appendix A: Tables of Numerical Quantities / 726 \\
                 1. Fundamental Constants (decimal) / 726 \\
                 2; Fundamental Constants ( octal) / 727 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 728 \\
                 Appendix B: Index to Notations / 730 \\
                 Index and Glossary / 735",
}

@Book{Korner:1988:FA,
  author =       "T. W. K{\"o}rner",
  title =        "Fourier Analysis",
  publisher =    pub-CUP,
  address =      pub-CUP:adr,
  pages =        "xii + 591",
  year =         "1988",
  ISBN =         "0-521-38991-7",
  ISBN-13 =      "978-0-521-38991-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kosowski:2000:CUT,
  author =       "Przemys{\l}aw Kosowski and Alicja Smoktunowicz",
  title =        "On Constructing Unit Triangular Matrices with
                 Prescribed Singular Values",
  journal =      j-COMPUTING,
  volume =       "64",
  pages =        "279--285",
  year =         "2000",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Kostlan:1992:SGM,
  author =       "Eric Kostlan",
  title =        "On the Spectra of {Gaussian} Matrices",
  journal =      j-LAA,
  volume =       "162--164",
  pages =        "385--388",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kovarik:1976:CAS,
  author =       "Z. V. Kovarik",
  title =        "Compatibility of Approximate Solutions of Inaccurate
                 Linear Equations",
  journal =      j-LAA,
  volume =       "15",
  pages =        "217--225",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Kreczmar:1976:MRS,
  author =       "Antoni Kreczmar",
  title =        "On Memory Requirements of {Strassen's} Algorithms",
  volume =       "45",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "404--407",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Computer Science",
}

@InProceedings{Kubota:1991:PFP,
  author =       "Koichi Kubota",
  editor =       "Andreas Griewank and George F. Corliss",
  booktitle =    "Automatic Differentiation of Algorithms: {Theory},
                 Implementation, and Application",
  title =        "{PADRE2}, a {Fortran} Precompiler Yielding Error
                 Estimates and Second Derivatives",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "251--262",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kuki:1973:SSA,
  author =       "H. Kuki and W. J. Cody",
  title =        "A Statistical Study of the Accuracy of Floating Point
                 Number Systems",
  journal =      j-CACM,
  volume =       "16",
  number =       "4",
  pages =        "223--230",
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Book{Kulisch:1981:CAT,
  author =       "Ulrich W. Kulisch and Willard L. Miranker",
  title =        "Computer Arithmetic in Theory and in Practice",
  publisher =    pub-AP,
  address =      pub-AP:adr-NY,
  pages =        "xiii + 249",
  year =         "1981",
  ISBN =         "0-12-428650-X",
  ISBN-13 =      "978-0-12-428650-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kulisch:1986:ADC,
  author =       "Ulrich W. Kulisch and Willard L. Miranker",
  title =        "The Arithmetic of the Digital Computer: {A} New
                 Approach",
  journal =      j-SIREV,
  volume =       "28",
  number =       "1",
  pages =        "1--40",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Kuperman:1971:ALA,
  author =       "I. B. Kuperman",
  title =        "Approximate Linear Algebraic Equations",
  publisher =    "Van Nostrand Reinhold",
  address =      "London",
  pages =        "xi + 225",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Kuczynski:1992:ELE,
  author =       "J. Kuczy{\'n}ski and H. Wo{\'z}niakowski",
  title =        "Estimating the Largest Eigenvalue by the Power and
                 {Lanczos} Algorithms with a Random Start",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "4",
  pages =        "1094--1122",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Laderman:1976:NAM,
  author =       "J. D. Laderman",
  title =        "A Noncommutative Algorithm for Multiplying {$3 \times
                 3$} Matrices Using 23 Multiplications",
  journal =      j-BAMS,
  volume =       "82",
  number =       "1",
  pages =        "126--128",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Lawson:1995:SLS,
  author =       "Charles L. Lawson and Richard J. Hanson",
  title =        "Solving Least Squares Problems",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xii + 337",
  year =         "1995",
  ISBN =         "0-89871-356-0",
  ISBN-13 =      "978-0-89871-356-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Revised republication of work first published in 1974
                 by Prentice-Hall",
}

@Article{Laszlo:1994:ALB,
  author =       "Lajos L{\'a}szl{\'o}",
  title =        "An Attainable Lower Bound for the Best Normal
                 Approximation",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "3",
  pages =        "1035--1043",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Lay-Yong:1989:MSL,
  author =       "Lam Lay-Yong and Shen Kangshen",
  title =        "Methods of Solving Linear Equations in Traditional
                 {China}",
  journal =      j-HIST-MATH,
  volume =       "16",
  number =       "2",
  pages =        "107--122",
  month =        may,
  year =         "1989",
  CODEN =        "HIMADS",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:18:18 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0315086089900335",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
}

@Book{Lanczos:1956:AA,
  author =       "Cornelius Lanczos",
  title =        "Applied Analysis",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xx + 539",
  year =         "1956",
  ISBN =         "0-486-65656-X",
  ISBN-13 =      "978-0-486-65656-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted by Dover, New York, 1988",
}

@Article{Lancaster:1966:EAN,
  author =       "Peter Lancaster",
  title =        "Error Analysis for the {Newton--Raphson} Method",
  journal =      j-NUM-MATH,
  volume =       "9",
  pages =        "55--68",
  year =         "1966",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Lancaster:1970:ESL,
  author =       "Peter Lancaster",
  title =        "Explicit Solutions of Linear Matrix Equations",
  journal =      j-SIREV,
  volume =       "12",
  number =       "4",
  pages =        "544--566",
  year =         "1970",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Langlois:2001:ALC,
  author =       "Philippe Langlois",
  title =        "Automatic Linear Correction of Rounding Errors",
  journal =      j-BIT,
  volume =       "41",
  number =       "3",
  pages =        "515--539",
  year =         "2001",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Larson:1978:ECE,
  author =       "John L. Larson and Ahmed H. Sameh",
  title =        "Efficient Calculation of the Effects of Roundoff
                 Errors",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "228--236",
  year =         "1978",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Errata 5(3):372, 1979",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Larson:1980:ARE,
  author =       "John L. Larson and Ahmed H. Sameh",
  title =        "Algorithms for Roundoff Error Analysis---{A} Relative
                 Error Approach",
  journal =      j-COMPUTING,
  volume =       "24",
  pages =        "275--297",
  year =         "1980",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Laub:1979:SMS,
  author =       "Alan J. Laub",
  title =        "A {Schur} Method for Solving Algebraic {Riccati}
                 Equations",
  journal =      j-IEEE-AC,
  volume =       "AC-24",
  number =       "6",
  pages =        "913--921",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Lauchli:1961:JEA,
  author =       "Peter L{\"a}uchli",
  title =        "{Jordan-Elimination} und {Ausgleichung} nach kleinsten
                 {Quadraten}",
  journal =      j-NUM-MATH,
  volume =       "3",
  pages =        "226--240",
  year =         "1961",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Porte:1974:ESE,
  author =       "M. La Porte and J. Vignes",
  title =        "Etude Statistique des Erreurs Dans l'Arithm\'etique
                 des Ordinateurs; Application au Contr{\^o}le des
                 {R}\'esultats d'Algorithmes Num\'eriques",
  journal =      j-NUM-MATH,
  volume =       "23",
  pages =        "63--72",
  year =         "1974",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Book{Lavington:1980:EBC,
  author =       "Simon Lavington",
  title =        "Early {British} Computers: {The} Story of Vintage
                 Computers and the People Who Built Them",
  publisher =    "Manchester University Press",
  pages =        "139",
  year =         "1980",
  ISBN =         "0-7190-0803-4",
  ISBN-13 =      "978-0-7190-0803-0",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Li:2000:DIT,
  author =       "X. S. Li and J. W. Demmel and D. H. Bailey and G.
                 Henry and Y. Hida and J. Iskandar and W. Kahan and A.
                 Kapur and M. C. Martin and T. Tung and D. J. Yoo",
  title =        "Design, Implementation and Testing of {Extended and
                 Mixed Precision BLAS}",
  type =         "Technical Report",
  number =       "CS-00-451",
  institution =  inst-CS-U-Tenn,
  address =      inst-CS-U-Tenn:adr,
  pages =        "61",
  month =        oct,
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "LAPACK Working Note 149",
}

@Article{Lehmer:1943:TMP,
  author =       "D. H. Lehmer",
  title =        "Tables to Many Places of Decimals",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "1",
  number =       "1",
  pages =        "30--31",
  year =         "1943",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Lehoucq:1996:CEU,
  author =       "R. B. Lehoucq",
  title =        "The Computation of Elementary Unitary Matrices",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "393--400",
  year =         "1996",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Lemeire:1975:BCN,
  author =       "Frans Lemeire",
  title =        "Bounds for Condition Numbers of Triangular and
                 Trapezoid Matrices",
  journal =      j-BIT,
  volume =       "15",
  pages =        "58--64",
  year =         "1975",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@InProceedings{Lefevre:2001:WCC,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller",
  editor =       "",
  booktitle =    "Proc. 15th IEEE Symposium on Computer Arithmetic",
  title =        "Worst Cases for Correct Rounding of the Elementary
                 Functions in Double Precision",
  publisher =    "IEEE Computer Society Press, Los Alamitos, CA, USA",
  pages =        "",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Leuprecht:1982:PAR,
  author =       "H. Leuprecht and W. Oberaigner",
  title =        "Parallel Algorithms for the Rounding Exact Summation
                 of Floating Point Numbers",
  journal =      j-COMPUTING,
  volume =       "28",
  pages =        "89--104",
  year =         "1982",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Lawson:1979:BLA,
  author =       "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F.
                 T. Krogh",
  title =        "Basic Linear Algebra Subprograms for {Fortran} Usage",
  journal =      j-TOMS,
  volume =       "5",
  number =       "3",
  pages =        "308--323",
  year =         "1979",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Book{LIA94,
  key =          "IEC",
  title =        "{ISO\slash IEC \upshape 10967-1 (1994-12)}:
                 {Information} Technology---Language Independent
                 Arithmetic---Part {$1$}: {Integer} and Floating Point
                 Arithmetic",
  publisher =    pub-IEC,
  address =      pub-IEC:adr,
  pages =        "92",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Lickteig:1987:CCD,
  author =       "Thomas Lickteig",
  title =        "The Computational Complexity of Division in Quadratic
                 Extension Fields",
  journal =      j-SICOMP,
  volume =       "16",
  number =       "2",
  pages =        "278--311",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Li:1998:MSG,
  author =       "Xiaoye S. Li and James W. Demmel",
  booktitle =    "Proceedings of SC98: High Performance Networking and
                 Computing Conference, Orlando, Florida",
  title =        "Making Sparse {Gaussian} Elimination Scalable by
                 Static Pivoting",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "CD ROM",
}

@Article{Linnainmaa:1974:ASK,
  author =       "Seppo Linnainmaa",
  title =        "Analysis of Some Known Methods of Improving the
                 Accuracy of Floating-Point Sums",
  journal =      j-BIT,
  volume =       "14",
  pages =        "167--202",
  year =         "1974",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Linnainmaa:1975:TAS,
  author =       "Seppo Linnainmaa",
  title =        "Towards Accurate Statistical Estimation of Rounding
                 Errors in Floating-Point Computations",
  journal =      j-BIT,
  volume =       "15",
  pages =        "165--173",
  year =         "1975",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Linnainmaa:1976:TEA,
  author =       "Seppo Linnainmaa",
  title =        "Taylor Expansion of the Accumulated Rounding Error",
  journal =      j-BIT,
  volume =       "16",
  pages =        "146--160",
  year =         "1976",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Linnainmaa:1981:SDP,
  author =       "Seppo Linnainmaa",
  title =        "Software for Doubled-Precision Floating-Point
                 Computations",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "272--283",
  year =         "1981",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Linz:1970:AFP,
  author =       "Peter Linz",
  title =        "Accurate Floating-Point Summation",
  journal =      j-CACM,
  volume =       "13",
  number =       "6",
  pages =        "361--362",
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Linzer:1992:STB,
  author =       "Elliot Linzer",
  title =        "On the Stability of Transform-Based Circular
                 Deconvolution",
  journal =      j-SINUM,
  volume =       "29",
  number =       "5",
  pages =        "1482--1492",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Liu:1987:PPS,
  author =       "Joseph W. H. Liu",
  title =        "A Partial Pivoting Strategy for Sparse Symmetric
                 Matrix Decomposition",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "173--182",
  year =         "1987",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Li:1992:HDA,
  author =       "T. Y. Li and Zhonggang Zeng",
  title =        "Homotopy-Determinant Algorithm for Solving
                 Nonsymmetric Eigenvalue Problems",
  journal =      j-MATH-COMP,
  volume =       "59",
  number =       "200",
  pages =        "483--502",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Lefevre:1998:TCR,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller and Arnaud
                 Tisserand",
  title =        "Toward Correctly Rounded Transcendentals",
  journal =      j-IEEE-C,
  volume =       "47",
  number =       "11",
  pages =        "1235--1243",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Loizou:1969:NJC,
  author =       "Georghios Loizou",
  title =        "Nonnormality and {Jordan} Condition Numbers of
                 Matrices",
  journal =      j-ACM,
  volume =       "16",
  number =       "4",
  pages =        "580--584",
  year =         "1969",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Longley:1967:ALS,
  author =       "J. W. Longley",
  title =        "An Appraisal of Least Squares Programs for the
                 Electronic Computer from the Point of View of the
                 User",
  journal =      j-ASA,
  volume =       "62",
  pages =        "819--841",
  year =         "1967",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Laderman:1992:PAA,
  author =       "Julian Laderman and Victor Pan and Xuan-He Sha",
  title =        "On Practical Algorithms for Accelerated Matrix
                 Multiplication",
  journal =      j-LAA,
  volume =       "162--164",
  pages =        "557--588",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Larson:1983:ASR,
  author =       "John L. Larson and Mary E. Pasternak and John A.
                 Wisniewski",
  title =        "Algorithm 594: {Software} for Relative Error
                 Analysis",
  journal =      j-TOMS,
  volume =       "9",
  number =       "1",
  pages =        "125--130",
  year =         "1983",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Lagarias:1998:CPN,
  author =       "Jeffrey C. Lagarias and James A. Reeds and Margaret H.
                 Wright and Paul E. Wright",
  title =        "Convergence Properties of the {Nelder--Mead} Simplex
                 Method in Low Dimensions",
  journal =      j-SIOPT,
  volume =       "9",
  number =       "1",
  pages =        "112--147",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Lewis:2000:DSM,
  author =       "Robert Michael Lewis and Virginia J. Torczon and
                 Michael W. Trossett",
  title =        "Direct Search Methods: {Then} and Now",
  journal =      j-JCAM,
  volume =       "124",
  pages =        "191--207",
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Lu:1994:FSC,
  author =       "Hao Lu",
  title =        "Fast Solution of Confluent {Vandermonde} Linear
                 Systems",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "4",
  pages =        "1277--1289",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Lu:1995:FAC,
  author =       "Hao Lu",
  title =        "Fast Algorithms for Confluent {Vandermonde} Linear
                 Systems and Generalized {Trummer's} Problem",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "2",
  pages =        "655--674",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Lu:1996:SVL,
  author =       "Hao Lu",
  title =        "Solution of {Vandermonde}-Like Systems and Confluent
                 {Vandermonde}-Like Systems",
  journal =      j-SIMAX,
  volume =       "17",
  number =       "1",
  pages =        "127--138",
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Barker:2001:LUG,
  author =       "V. A. Barker and L. S. Blackford and J. J. Dongarra
                 and J. J. Du Croz and S. J. Hammarling and M. Marinova
                 and J. Wa{\'s}niewski and P. Yalamov",
  title =        "{LAPACK95} Users' Guide",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xviii + 258",
  year =         "2001",
  ISBN =         "0-89871-504-0",
  ISBN-13 =      "978-0-89871-504-0",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Anderson:1999:LUG,
  author =       "E. Anderson and Z. Bai and C. H. Bischof and S.
                 Blackford and J. W. Demmel and J. J. Dongarra and J. J.
                 Du Croz and A. Greenbaum and S. J. Hammarling and A.
                 McKenney and D. C. Sorensen",
  title =        "{LAPACK} Users' Guide",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  edition =      "Third",
  pages =        "xxvi + 407",
  year =         "1999",
  ISBN =         "0-89871-447-8",
  ISBN-13 =      "978-0-89871-447-0",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Lyness:1976:CNA,
  author =       "J. N. Lyness and J. J. Kaganove",
  title =        "Comments on the Nature of Automatic Quadrature
                 Routines",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "65--81",
  year =         "1976",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Lyness:1966:VMS,
  author =       "J. N. Lyness and C. B. Moler",
  title =        "{Van der Monde} Systems and Numerical
                 Differentiation",
  journal =      j-NUM-MATH,
  volume =       "8",
  pages =        "458--464",
  year =         "1966",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Lynn:1964:REM,
  author =       "M. Stuart Lynn",
  title =        "On the Round-Off Error in the Method of Successive
                 Over-Relaxation",
  journal =      j-MATH-COMP,
  volume =       "18",
  number =       "85",
  pages =        "36--49",
  year =         "1964",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Macleod:1989:SSG,
  author =       "Allan J. Macleod",
  title =        "Some Statistics on {Gaussian} Elimination with Partial
                 Pivoting",
  journal =      j-SIGNUM,
  volume =       "24",
  number =       "2/3",
  pages =        "10--14",
  year =         "1989",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J690",
}

@Book{Maindonald:1984:SC,
  author =       "J. H. Maindonald",
  title =        "Statistical Computation",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  pages =        "xviii + 370",
  year =         "1984",
  ISBN =         "0-471-86452-8",
  ISBN-13 =      "978-0-471-86452-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Matsui:1981:OUF,
  author =       "Shouichi Matsui and Masao Iri",
  title =        "An Overflow/Underflow-Free Floating-Point
                 Representation of Numbers",
  journal =      j-J-INF-PROCESS,
  volume =       "4",
  number =       "3",
  pages =        "123--133",
  year =         "1981",
  CODEN =        "JIPRDE",
  ISSN =         "0387-6101",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Journal of Information Processing",
}

@Article{Makhoul:1991:TDP,
  author =       "John Makhoul",
  title =        "{Toeplitz} Determinants and Positive
                 Semidefiniteness",
  journal =      j-IEEE-SP,
  volume =       "39",
  number =       "3",
  pages =        "743--746",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Matula:1985:FPR,
  author =       "David W. Matula and Peter Kornerup",
  title =        "Finite Precision Rational Arithmetic: {Slash} Number
                 Systems",
  journal =      j-IEEE-C,
  volume =       "C-34",
  number =       "1",
  pages =        "3--18",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Malcolm:1971:AFP,
  author =       "Michael A. Malcolm",
  title =        "On Accurate Floating-Point Summation",
  journal =      j-CACM,
  volume =       "14",
  number =       "11",
  pages =        "731--736",
  month =        nov,
  year =         "1971",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/362854.362889",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65G05 (68-XX)",
  MRnumber =     "47 4434",
  MRreviewer =   "P. Brock",
  bibdate =      "Mon Jan 22 07:01:06 MST 2001",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#Malcolm71;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Stanford Univ., CA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "accurate floating-point summation; digital arithmetic;
                 error analysis",
  oldlabel =     "Malcolm71",
  treatment =    "P Practical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Malcolm71",
}

@Article{Malcolm:1972:ARP,
  author =       "Michael A. Malcolm",
  title =        "Algorithms to Reveal Properties of Floating-Point
                 Arithmetic",
  journal =      j-CACM,
  volume =       "15",
  number =       "11",
  pages =        "949--951",
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Malyshev:2000:NSG,
  author =       "Alexander N. Malyshev",
  title =        "A Note on the Stability of {Gauss--Jordan} Elimination
                 for Diagonally Dominant Matrices",
  journal =      j-COMPUTING,
  volume =       "65",
  number =       "3",
  pages =        "281--284",
  year =         "2000",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Malyshev:2001:OBP,
  author =       "Alexander N. Malyshev",
  title =        "Optimal Backward Perturbation Bounds for the {LSS}
                 Problem",
  journal =      j-BIT,
  volume =       "41",
  number =       "2",
  pages =        "430--432",
  year =         "2001",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Magnus:1979:CMS,
  author =       "Jan R. Magnus and Heinz Neudecker",
  title =        "The Commutation Matrix: {Some} Properties and
                 Applications",
  journal =      j-ANN-STAT,
  volume =       "7",
  number =       "2",
  pages =        "381--394",
  year =         "1979",
  CODEN =        "ASTSC7",
  ISSN =         "0090-5364 (print), 2168-8966 (electronic)",
  ISSN-L =       "0090-5364",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Annals of Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aos/",
}

@Book{Magnus:1999:MDC,
  author =       "Jan R. Magnus and Heinz Neudecker",
  title =        "Matrix Differential Calculus with Applications in
                 Statistics and Econometrics",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr-C,
  edition =      "Revised",
  pages =        "xviii + 395",
  year =         "1999",
  ISBN =         "0-471-98633-X",
  ISBN-13 =      "978-0-471-98633-1",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Manteuffel:1981:IAA,
  author =       "Thomas A. Manteuffel",
  title =        "An Interval Analysis Approach to Rank Determination in
                 Linear Least Squares Problems",
  journal =      j-SISSC,
  volume =       "2",
  number =       "3",
  pages =        "335--348",
  year =         "1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Malcolm:1974:FMS,
  author =       "Michael A. Malcolm and John Palmer",
  title =        "A Fast Method for Solving a Class of Tridiagonal
                 Linear Systems",
  journal =      j-CACM,
  volume =       "17",
  number =       "1",
  pages =        "14--17",
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Book{maple,
  key =          "Maple",
  title =        "Maple",
  publisher =    "Waterloo Maple Inc.",
  address =      "Waterloo, Ontario, Canada",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "\path|http://www.maplesoft.com|",
}

@Book{Char:1991:MVL,
  author =       "Bruce W. Char and Keith O. Geddes and Gaston H. Gonnet
                 and Benton L. Leong and Michael B. Monagan and Stephen
                 M. Watt",
  title =        "Maple {V} Library Reference Manual",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "xxv + 698",
  year =         "1991",
  ISBN =         "3-540-97592-6",
  ISBN-13 =      "978-3-540-97592-2",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Markoff:1994:CFC,
  author =       "John Markoff",
  title =        "Circuit Flaw Causes {Pentium} Chip to Miscalculate,
                 {Intel} Admits",
  journal =      j-NY-TIMES,
  year =         "1994",
  CODEN =        "NYTIAO",
  ISSN =         "0362-4331 (print), 1542-667X, 1553-8095",
  ISSN-L =       "0362-4331",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "24 November",
  fjournal =     "New York Times",
  journal-URL =  "http://www.nytimes.com/",
}

@Article{Malyshev:2002:COB,
  author =       "Alexander N. Malyshev and Miloud Sadkane",
  title =        "Computation of Optimal Backward Perturbation Bounds
                 for Large Sparse Linear Least Squares Problems",
  journal =      j-BIT,
  volume =       "41",
  number =       "4",
  pages =        "739--747",
  year =         "2002",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Mathias:1992:MPD,
  author =       "Roy Mathias",
  title =        "Matrices with Positive Definite {Hermitian} Part:
                 {Inequalities} and Linear Systems",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "2",
  pages =        "640--654",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Mathias:1995:AEC,
  author =       "Roy Mathias",
  title =        "Accurate Eigensystem Computations by {Jacobi}
                 Methods",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "3",
  pages =        "977--1003",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Mathias:1995:IPP,
  author =       "Roy Mathias",
  title =        "The Instability of Parallel Prefix Matrix
                 Multiplication",
  journal =      j-SISC,
  volume =       "16",
  number =       "4",
  pages =        "956--973",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Mathias:1996:AAO,
  author =       "Roy Mathias",
  title =        "Analysis of Algorithms for Orthogonalizing Products of
                 Unitary Matrices",
  journal =      j-NLAA,
  volume =       "3",
  number =       "2",
  pages =        "125--145",
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{mathematica,
  key =          "Mathematica",
  title =        "Mathematica",
  publisher =    "Wolfram Research, Inc.",
  address =      "Champaign, IL, USA",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "\path|http://www.wolfram.com|",
}

@Book{matlab,
  key =          "MathWorks, Inc.",
  title =        "{MATLAB}",
  publisher =    "The MathWorks, Inc.",
  address =      "Natick, MA, USA",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "\path|http://www.mathworks.com|",
}

@Book{matlab:SMT,
  key =          "MathWorks, Inc.",
  title =        "Symbolic Math Toolbox Version {$2$}: {User's} Guide",
  publisher =    "The MathWorks, Inc.",
  address =      "Natick, MA, USA",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Online version",
}

@Article{Mattheij:1984:SLD,
  author =       "R. M. M. Mattheij",
  title =        "The Stability of {LU}-Decompositions of Block
                 Tridiagonal Matrices",
  journal =      j-BULL-AUSTRAL-MATH-SOC,
  volume =       "29",
  pages =        "177--205",
  year =         "1984",
  CODEN =        "ALNBAB",
  ISSN =         "0004-9727 (print), 1755-1633 (electronic)",
  ISSN-L =       "0004-9727",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Bulletin of the Australian Mathematical Society",
}

@Article{Mattheij:1984:SBD,
  author =       "R. M. M. Mattheij",
  title =        "Stability of Block {$LU$}-Decompositions of Matrices
                 Arising From {BVP}",
  journal =      j-SIAD,
  volume =       "5",
  number =       "3",
  pages =        "314--331",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Matula:1968:C,
  author =       "David W. Matula",
  title =        "In-and-Out Conversions",
  journal =      j-CACM,
  volume =       "11",
  number =       "1",
  pages =        "47--50",
  month =        jan,
  year =         "1968",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/362851.362887",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.80",
  MRnumber =     "39\#2360",
  bibdate =      "Fri Nov 25 18:20:17 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
  note =         "See also \cite{Goldberg:1967:BED,Matula:1968:BCT}",
  abstract =     "By an in-and-out conversion we mean that a
                 floating-point number in one base is converted into a
                 floating-point number in another base and then
                 converted back to a floating-point number in the
                 original base. For all combinations of rounding and
                 truncation conversions the question is considered of
                 how many significant digits are needed in the
                 intermediate base to allow such in-and-out conversions
                 to return the original number (when possible), or at
                 least significant digit.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "floating-point numbers; number base conversion;
                 rounding error; significance; truncation error",
}

@Article{Matula:1970:FFP,
  author =       "David W. Matula",
  title =        "A Formalization of Floating-Point Numeric Base
                 Conversion",
  journal =      j-IEEE-C,
  volume =       "C-19",
  number =       "8",
  pages =        "681--692",
  year =         "1970",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{McCracken:1964:NMF,
  author =       "Daniel D. McCracken and William S. Dorn",
  title =        "Numerical Methods and {Fortran} Programming: {With}
                 Applications in Science and Engineering",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  pages =        "xii + 457",
  year =         "1964",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{McKeeman:1962:ACE,
  author =       "William Marshall McKeeman",
  title =        "Algorithm 135: {Crout} with Equilibration and
                 Iteration",
  journal =      j-CACM,
  volume =       "5",
  pages =        "553--555",
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{McKinnon:1998:CNM,
  author =       "K. I. M. McKinnon",
  title =        "Convergence of the {Nelder--Mead} Simplex Method to a
                 Nonstationary Point",
  journal =      j-SIOPT,
  volume =       "9",
  number =       "1",
  pages =        "148--158",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{McCullagh:1989:GLM,
  author =       "P. McCullagh and J. A. Nelder",
  title =        "Generalized Linear Models",
  publisher =    "Chapman and Hall",
  address =      "London",
  edition =      "Second",
  pages =        "xix + 511",
  year =         "1989",
  ISBN =         "0-412-31760-5",
  ISBN-13 =      "978-0-412-31760-6",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{McCarthy:1974:OCM,
  author =       "Charles McCarthy and Gilbert Strang",
  title =        "Optimal Conditioning of Matrices",
  journal =      j-SINUM,
  volume =       "10",
  number =       "2",
  pages =        "370--388",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{McCullough:1999:NRE,
  author =       "B. D. McCullough and H. D. Vinod",
  title =        "The Numerical Reliability of Econometric Software",
  journal =      j-J-ECON-LIT,
  volume =       "37",
  pages =        "633--665",
  year =         "1999",
  CODEN =        "JECLB3",
  ISSN =         "0022-0515 (print), 1547-1101 (electronic)",
  ISSN-L =       "0022-0515",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Journal of Economic Literature",
}

@Article{Meyer:1957:MIL,
  author =       "H. I. Meyer and B. J. Hollingsworth",
  title =        "A Method of Inverting Large Matrices of Special Form",
  journal =      j-MTAC,
  volume =       "11",
  pages =        "94--97",
  year =         "1957",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Meinguet:1969:ES,
  author =       "Jean Meinguet",
  editor =       "Elden Hansen",
  booktitle =    "Topics in Interval Analysis",
  title =        "On the Estimation of Significance",
  publisher =    pub-OUP,
  pages =        "47--64",
  year =         "1969",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Meinguet:1983:REA,
  author =       "Jean Meinguet",
  title =        "Refined Error Analyses of {Cholesky} Factorization",
  journal =      j-SINUM,
  volume =       "20",
  number =       "6",
  pages =        "1243--1250",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Mendelsohn:1956:SEP,
  author =       "N. S. Mendelsohn",
  title =        "Some Elementary Properties of Ill Conditioned Matrices
                 and Linear Equations",
  journal =      j-AMM,
  volume =       "63",
  number =       "5",
  pages =        "285--295",
  year =         "1956",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Meyer:1977:CPM,
  author =       "Carl D. {Meyer, Jr.} and R. J. Plemmons",
  title =        "Convergent Powers of a Matrix With Applications to
                 Iterative Methods for Singular Linear Systems",
  journal =      j-SINUM,
  volume =       "14",
  number =       "4",
  pages =        "699--705",
  year =         "1977",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Metcalf:1999:FE,
  author =       "Michael Metcalf and John K. Reid",
  title =        "Fortran 90/95 Explained",
  publisher =    pub-OUP,
  edition =      "Second",
  pages =        "358",
  year =         "1999",
  ISBN =         "0-19-850558-2",
  ISBN-13 =      "978-0-19-850558-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Metropolis:1977:MSA,
  author =       "N. Metropolis",
  editor =       "David A. H. Jacobs",
  booktitle =    "The State of the Art in Numerical Analysis",
  title =        "Methods of Significance Arithmetic",
  publisher =    pub-AP # ", " # pub-AP:adr-L,
  pages =        "179--192",
  year =         "1977",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Meurant:1992:RIS,
  author =       "G{\'e}rard Meurant",
  title =        "A Review on the Inverse of Symmetric Tridiagonal and
                 Block Tridiagonal Matrices",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "3",
  pages =        "707--728",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Milenkovic:1988:VIG,
  author =       "Victor J. Milenkovic",
  title =        "Verifiable Implementations of Geometric Algorithms
                 Using Finite Precision Arithmetic",
  journal =      j-ART-INTELL,
  volume =       "37",
  pages =        "377--401",
  year =         "1988",
  CODEN =        "AINTBB",
  ISSN =         "0004-3702 (print), 1872-7921 (electronic)",
  ISSN-L =       "0004-3702",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Artificial Intelligence",
}

@Article{Miller:1975:CCN,
  author =       "Webb Miller",
  title =        "Computational Complexity and Numerical Stability",
  journal =      j-SICOMP,
  volume =       "4",
  number =       "2",
  pages =        "97--107",
  year =         "1975",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Miller:1975:SRA,
  author =       "Webb Miller",
  title =        "Software for Roundoff Analysis",
  journal =      j-TOMS,
  volume =       "1",
  number =       "2",
  pages =        "108--128",
  year =         "1975",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Miller:1976:GTR,
  author =       "Webb Miller",
  title =        "Graph Transformations for Roundoff Analysis",
  journal =      j-SICOMP,
  volume =       "5",
  number =       "2",
  pages =        "204--216",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Miller:1984:ENS,
  author =       "Webb Miller",
  title =        "The Engineering of Numerical Software",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "viii + 167",
  year =         "1984",
  ISBN =         "0-13-279043-2",
  ISBN-13 =      "978-0-13-279043-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Miller:1988:ISM,
  author =       "D. F. Miller",
  title =        "The Iterative Solution of the Matrix Equation
                 {$XA+BX+C=0$}",
  journal =      j-LAA,
  volume =       "105",
  pages =        "131--137",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Mirsky:1961:ILA,
  author =       "L. Mirsky",
  title =        "An Introduction to Linear Algebra",
  publisher =    pub-OUP,
  pages =        "viii + 440",
  year =         "1961",
  ISBN =         "0-486-66434-1",
  ISBN-13 =      "978-0-486-66434-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted by Dover, New York, 1990",
}

@Article{Miller:19xx:SRA,
  author =       "Webb Miller and David Spooner",
  title =        "Software for Roundoff Analysis, {II}",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "369--387",
  year =         "{\noopsort{a}}1978",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Miller:19xx:ASR,
  author =       "Webb Miller and David Spooner",
  title =        "Algorithm 532: {Software} for Roundoff Analysis",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "388--390",
  year =         "{\noopsort{b}}1978",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Mitchell:1948:IMO,
  author =       "Herbert F. {Mitchell, Jr.}",
  title =        "Inversion of a Matrix of Order 38",
  journal =      j-MTAC,
  volume =       "3",
  pages =        "161--166",
  year =         "1948",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Miller:1980:SRA,
  author =       "Webb Miller and Celia Wrathall",
  title =        "Software for Roundoff Analysis of Matrix Algorithms",
  publisher =    pub-AP,
  address =      pub-AP:adr-NY,
  pages =        "x + 151",
  year =         "1980",
  ISBN =         "0-12-497250-0",
  ISBN-13 =      "978-0-12-497250-6",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Moore:1998:MCP,
  author =       "J. Strother Moore and Thomas W. Lynch and Matt
                 Kaufmann",
  title =        "A Mechanically Checked Proof of the
                 {$\mathrm{AMD}5_K86$} Floating-Point Division Program",
  journal =      j-IEEE-C,
  volume =       "47",
  number =       "9",
  pages =        "913--926",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Moler:1967:IRF,
  author =       "Cleve B. Moler",
  title =        "Iterative Refinement in Floating Point",
  journal =      j-ACM,
  volume =       "14",
  number =       "2",
  pages =        "316--321",
  year =         "1967",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Moler:1972:MCF,
  author =       "Cleve B. Moler",
  title =        "Matrix Computations with {Fortran} and Paging",
  journal =      j-CACM,
  volume =       "15",
  number =       "4",
  pages =        "268--270",
  year =         "1972{\noopsort{a}}",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Moler:1972:ALE,
  author =       "Cleve B. Moler",
  title =        "Algorithm 423: {Linear} Equation Solver",
  journal =      j-CACM,
  volume =       "15",
  number =       "4",
  pages =        "274",
  year =         "1972{\noopsort{b}}",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Moler:1974:CRS,
  author =       "Cleve B. Moler",
  title =        "Cramer's Rule on 2-by-2 Systems",
  journal =      j-SIGNUM,
  volume =       "9",
  number =       "4",
  pages =        "13--14",
  year =         "1974",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J690",
}

@InCollection{Moler:1978:TRP,
  author =       "Cleve B. Moler",
  editor =       "G. H. Golub and J. Oliger",
  booktitle =    "Numerical Analysis",
  title =        "Three Research Problems in Numerical Linear Algebra",
  volume =       "22",
  publisher =    pub-AMS # ", " # pub-AMS:adr,
  pages =        "1--18",
  year =         "1978",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Proceedings of Symposia in Applied Mathematics",
}

@Article{Moler:1990:TND,
  author =       "Cleve B. Moler",
  title =        "Technical Note: {Double-rounding} and Implications for
                 Numeric Computations",
  journal =      j-MATHWORKS-NEWSLETTER,
  volume =       "4",
  pages =        "6",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "The MathWorks Newsletter",
}

@Article{Moler:1990:CCW,
  author =       "Cleve B. Moler",
  title =        "Cleve's Corner: {The} World's Simplest Impossible
                 Problem",
  journal =      j-MATHWORKS-NEWSLETTER,
  volume =       "4",
  number =       "2",
  pages =        "6--7",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "The MathWorks Newsletter",
}

@Article{Moler:1995:TTN,
  author =       "Cleve B. Moler",
  title =        "A Tale of Two Numbers",
  journal =      j-SIAM-NEWS,
  volume =       "28",
  pages =        "1,16",
  month =        jan,
  year =         "1995",
  ISSN =         "0036-1437",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Also in \emph{MATLAB News and Notes}, Winter 1995,
                 10--12",
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@Article{Moller:1965:QDP,
  author =       "Ole M{\o}ller",
  title =        "Quasi Double-Precision in Floating Point Addition",
  journal =      j-BIT,
  volume =       "5",
  pages =        "37--50",
  year =         "1965",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "See also \cite{Moller:1965:NQD} for remarks on this
                 article",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Moller:1965:NQD,
  author =       "Ole M{\o}ller",
  title =        "Note on Quasi Double-Precision",
  journal =      j-BIT,
  volume =       "5",
  pages =        "251--255",
  year =         "1965",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Moler:1983:RSR,
  author =       "Cleve B. Moler and Donald Morrison",
  title =        "Replacing Square Roots by {Pythagorean} Sums",
  journal =      j-IBM-JRD,
  volume =       "27",
  number =       "6",
  pages =        "577--581",
  year =         "1983",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@Article{Moler:1983:SVA,
  author =       "Cleve B. Moler and Donald Morrison",
  title =        "Singular Value Analysis of Cryptograms",
  journal =      j-AMM,
  volume =       "90",
  pages =        "78--87",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Moore:1966:IA,
  author =       "Ramon E. Moore",
  title =        "Interval Analysis",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xi + 145",
  year =         "1966",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Moore:1979:MAI,
  author =       "Ramon E. Moore",
  title =        "Methods and Applications of Interval Analysis",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xi + 190",
  year =         "1979",
  ISBN =         "0-89871-161-4",
  ISBN-13 =      "978-0-89871-161-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Moler:1978:NDW,
  author =       "Cleve B. Moler and Charles F. {Van Loan}",
  title =        "Nineteen Dubious Ways to Compute the Exponential of a
                 Matrix",
  journal =      j-SIREV,
  volume =       "20",
  number =       "4",
  pages =        "801--836",
  year =         "1978",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Martin:1966:IRS,
  author =       "R. S. Martin and G. Peters and J. H. Wilkinson",
  title =        "Iterative Refinement of the Solution of a Positive
                 Definite System of Equations",
  journal =      j-NUM-MATH,
  volume =       "8",
  pages =        "203--216",
  year =         "1966",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Also in \cite[pp.~31--44]{Wilkinson:1971:LA},
                 Contribution I/2",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Mead:2001:SPS,
  author =       "J. L. Mead and R. E. Renaut and B. D. Welfert",
  title =        "Stability of a Pivoting Strategy for Parallel
                 {Gaussian} Elimination",
  journal =      j-BIT,
  volume =       "41",
  number =       "3",
  pages =        "633--639",
  year =         "2001",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Book{Muirhead:1982:AMS,
  author =       "Robb J. Muirhead",
  title =        "Aspects of Multivariate Statistical Theory",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  pages =        "xix + 673",
  year =         "1982",
  ISBN =         "0-471-09442-0",
  ISBN-13 =      "978-0-471-09442-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Muller:1983:REA,
  author =       "K. H. M{\"u}ller",
  title =        "Rounding Error Analysis of {Horner's} Scheme",
  journal =      j-COMPUTING,
  volume =       "30",
  pages =        "285--303",
  year =         "1983",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Book{Muller:1989:AO,
  author =       "Jean-Michel Muller",
  title =        "Arithm{\'e}tique des Ordinateurs",
  publisher =    "Masson",
  address =      "Paris",
  pages =        "214",
  year =         "1989",
  ISBN =         "2-225-81689-1",
  ISBN-13 =      "978-2-225-81689-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "In French. Cited in \cite{Francois:1991:SPM}",
}

@Book{Muller:1997:EFA,
  author =       "Jean-Michel Muller",
  title =        "Elementary Functions: {Algorithms} and
                 Implementation",
  publisher =    pub-BH,
  address =      pub-BH:adr,
  pages =        "xv + 204",
  year =         "1997",
  ISBN =         "0-8176-3990-X",
  ISBN-13 =      "978-0-8176-3990-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Merikoski:1997:BUB,
  author =       "Jorma Kaarlo Merikoski and Uoti Arpala and Ari
                 Virtanen and Tin-Yau Tam and Frank Uhlig",
  title =        "A Best Upper Bound for the 2-Norm Condition Number of
                 a Matrix",
  journal =      j-LAA,
  volume =       "254",
  pages =        "355--365",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Nashed:1976:ABG,
  author =       "M. Zuhair Nashed and L. B. Rall",
  editor =       "M. Zuhair Nashed",
  booktitle =    "Generalized Inverses and Applications",
  title =        "Annotated Bibliography on Generalized Inverses and
                 Applications",
  publisher =    pub-AP # ", " # pub-AP:adr-NY,
  pages =        "771--1041",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Nelson:1998:PDM,
  editor =       "David Nelson",
  title =        "The Penguin Dictionary of Mathematics",
  publisher =    pub-Penguin,
  address =      pub-Penguin:adr-L,
  edition =      "Second",
  pages =        "461",
  year =         "1998",
  ISBN =         "0-14-051342-6",
  ISBN-13 =      "978-0-14-051342-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Nelder:1965:SMF,
  author =       "J. A. Nelder and R. Mead",
  title =        "A Simplex Method for Function Minimization",
  journal =      j-COMP-J,
  volume =       "7",
  pages =        "308--313",
  year =         "1965",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Neumann:1984:BEA,
  author =       "M. Neumann and R. J. Plemmons",
  title =        "Backward Error Analysis for Linear Systems Associated
                 with Inverses of {$H$}-Matrices",
  journal =      j-BIT,
  volume =       "24",
  pages =        "102--112",
  year =         "1984",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Neal:1992:GAG,
  author =       "Larry Neal and George Poole",
  title =        "A Geometric Analysis of {Gaussian} Elimination. {II}",
  journal =      j-LAA,
  volume =       "173",
  pages =        "239--264",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Newman:1958:EMI,
  author =       "Morris Newman and John Todd",
  title =        "The Evaluation of Matrix Inversion Programs",
  journal =      j-SIAM,
  volume =       "6",
  number =       "4",
  pages =        "466--476",
  year =         "1958",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Neumaier:1974:REV,
  author =       "A. Neumaier",
  title =        "Rundungsfehleranalyse einiger {Verfahren zur Summation
                 endlicher Summen}",
  journal =      j-ZAMM,
  volume =       "54",
  pages =        "39--51",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Neumaier:1985:IPR,
  author =       "A. Neumaier",
  title =        "Inner Product Rounding Error Analysis in the Presence
                 of Underflow",
  journal =      j-COMPUTING,
  volume =       "34",
  pages =        "365--373",
  year =         "1985",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Neumaier:1986:CMM,
  author =       "A. Neumaier",
  title =        "On the Comparison of {$H$}-Matrices with
                 {$M$}-Matrices",
  journal =      j-LAA,
  volume =       "83",
  pages =        "135--141",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Newbery:1973:EAF,
  author =       "A. C. R. Newbery",
  title =        "Error Analysis for {Fourier} Series Evaluation",
  journal =      j-MATH-COMP,
  volume =       "27",
  number =       "123",
  pages =        "639--644",
  year =         "1973",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Newbery:1974:EAP,
  author =       "A. C. R. Newbery",
  title =        "Error Analysis for Polynomial Evaluation",
  journal =      j-MATH-COMP,
  volume =       "28",
  number =       "127",
  pages =        "789--793",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Newcomb:1881:NFU,
  author =       "Simon Newcomb",
  title =        "Note on the Frequency of Use of the Different Digits
                 in Natural Numbers",
  journal =      j-AM-J-MATH,
  volume =       "4",
  pages =        "39--40",
  year =         "1881",
  CODEN =        "AJMAAN",
  ISSN =         "0002-9327 (print), 1080-6377 (electronic)",
  ISSN-L =       "0002-9327",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "American Journal of Mathematics",
}

@InCollection{Newman:1962:MC,
  author =       "Morris Newman",
  editor =       "John Todd",
  booktitle =    "Survey of Numerical Analysis",
  title =        "Matrix Computations",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  pages =        "222--254",
  year =         "1962",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Nickel:1970:KBS,
  author =       "K. Nickel",
  title =        "Das {Kahan-Babu\u{s}kasche Summierungsverfahren in
                 Triplex-ALGOL} 60",
  journal =      j-ZAMM,
  volume =       "50",
  pages =        "369--373",
  year =         "1970",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Nickel:1977:IA,
  author =       "Karl Nickel",
  editor =       "David A. H. Jacobs",
  booktitle =    "The State of the Art in Numerical Analysis",
  title =        "Interval-Analysis",
  publisher =    pub-AP # ", " # pub-AP:adr-L,
  pages =        "193--225",
  year =         "1977",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Notay:1993:CRC,
  author =       "Yvan Notay",
  title =        "On the Convergence Rate of the Conjugate Gradients in
                 Presence of Rounding Errors",
  journal =      j-NUM-MATH,
  volume =       "65",
  pages =        "301--317",
  year =         "1993",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Book{Nocedal:1999:NO,
  author =       "Jorge Nocedal and Stephen J. Wright",
  title =        "Numerical Optimization",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-NY,
  pages =        "xx + 636",
  year =         "1999",
  ISBN =         "0-387-98793-2",
  ISBN-13 =      "978-0-387-98793-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Oettli:1964:CAS,
  author =       "W. Oettli and W. Prager",
  title =        "Compatibility of Approximate Solution of Linear
                 Equations With Given Error Bounds for Coefficients and
                 Right-Hand Sides",
  journal =      j-NUM-MATH,
  volume =       "6",
  pages =        "405--409",
  year =         "1964",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Oettli:1965:SSL,
  author =       "W. Oettli",
  title =        "On the Solution Set of a Linear System with Inaccurate
                 Coefficients",
  journal =      j-SINUM,
  volume =       "2",
  number =       "1",
  pages =        "115--118",
  year =         "1965",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{OLeary:1980:EMC,
  author =       "Dianne Prost O'Leary",
  title =        "Estimating Matrix Condition Numbers",
  journal =      j-SISSC,
  volume =       "1",
  number =       "2",
  pages =        "205--209",
  year =         "1980",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Oliver:1977:EAM,
  author =       "J. Oliver",
  title =        "An Error Analysis of the Modified {Clenshaw} Method
                 for Evaluating {Chebyshev} and {Fourier} Series",
  journal =      j-JIMA,
  volume =       "20",
  pages =        "379--391",
  year =         "1977",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Oliver:1979:REP,
  author =       "J. Oliver",
  title =        "Rounding Error Propagation in Polynomial Evaluation
                 Schemes",
  journal =      j-JCAM,
  volume =       "5",
  number =       "2",
  pages =        "85--97",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Olver:1978:NAE,
  author =       "F. W. J. Olver",
  title =        "A New Approach to Error Arithmetic",
  journal =      j-SINUM,
  volume =       "15",
  number =       "2",
  pages =        "368--393",
  year =         "1978",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Olver:1983:EAC,
  author =       "F. W. J. Olver",
  booktitle =    "Computational Aspects of Complex Analysis",
  title =        "Error Analysis of Complex Arithmetic",
  volume =       "102",
  publisher =    pub-reidel # ", " # pub-reidel:adr,
  pages =        "279--292",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "NATO Advanced Study Institute Series C",
  editors =      "H. Werner and L. Wuytack and E. Ng. and H. J.
                 B{\"u}nger",
}

@Article{Olver:1986:EBP,
  author =       "F. W. J. Olver",
  title =        "Error Bounds for Polynomial Evaluation and Complex
                 Arithmetic",
  journal =      j-IMAJNA,
  volume =       "6",
  pages =        "373--379",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Olver:1982:PEB,
  author =       "F. W. J. Olver and J. H. Wilkinson",
  title =        "{\em A posteriori\/} Error Bounds for {Gaussian}
                 Elimination",
  journal =      j-IMAJNA,
  volume =       "2",
  pages =        "377--406",
  year =         "1982",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Oettli:1965:ASL,
  author =       "W. Oettli and W. Prager and J. H. Wilkinson",
  title =        "Admissible Solutions of Linear Systems With Not
                 Sharply Defined Coefficients",
  journal =      j-SINUM,
  volume =       "2",
  number =       "2",
  pages =        "291--299",
  year =         "1965",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ortega:1963:EAH,
  author =       "James M. Ortega",
  title =        "An Error Analysis of {Householder's} Method for the
                 Symmetric Eigenvalue Problem",
  journal =      j-NUM-MATH,
  volume =       "5",
  pages =        "211--225",
  year =         "1963",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Book{Ortega:1972:NAS,
  author =       "James M. Ortega",
  title =        "Numerical Analysis: {A} Second Course",
  publisher =    pub-AP,
  address =      pub-AP:adr-NY,
  pages =        "xiii + 201",
  year =         "1972",
  ISBN =         "0-89871-250-5 (original), 0-89871-250-5 (SIAM)",
  ISBN-13 =      "978-0-89871-250-6 (original), 978-0-89871-250-6
                 (SIAM)",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Republished by SIAM (1990).",
}

@Book{Ostrowski:1973:SEE,
  author =       "A. M. Ostrowski",
  title =        "Solution of Equations in {Euclidean and Banach}
                 Spaces",
  publisher =    pub-AP,
  address =      pub-AP:adr-NY,
  pages =        "xx + 412",
  year =         "1973",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Third edition of Solution of Equations and Systems of
                 Equations",
}

@Book{Overton:2001:NCI,
  author =       "Michael L. Overton",
  title =        "Numerical Computing with {IEEE} Floating Point
                 Arithmetic, Including One Theorem, One Rule of Thumb,
                 and One Hundred and One Exercises",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xiv + 104",
  year =         "2001",
  ISBN =         "0-89871-482-6 (hardcover), 0-89871-571-7 (paperback),
                 0-89871-807-4 (ebook)",
  ISBN-13 =      "978-0-89871-482-1 (hardcover), 978-0-89871-571-2
                 (print), 978-0-89871-807-2 (e-book)",
  LCCN =         "QA76.9.M35 O94 2001",
  MRclass =      "65-02 (65G30 68M07 68N99)",
  MRnumber =     "MR1828597 (2003b:65002)",
  MRreviewer =   "Jesse L. Barlow",
  bibdate =      "Fri Apr 27 16:50:46 2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2000.bib",
  price =        "US\$40.00",
  URL =          "http://www.cs.nyu.edu/cs/faculty/overton/book/;
                 http://www.siam.org/catalog/mcc07/ot76.htm",
  abstract =     "Are you familiar with the IEEE floating point
                 arithmetic standard? Would you like to understand it
                 better? This book gives a broad overview of numerical
                 computing, in a historical context, with a special
                 focus on the IEEE standard for binary floating point
                 arithmetic. Key ideas are developed step by step,
                 taking the reader from floating point representation,
                 correctly rounded arithmetic, and the IEEE philosophy
                 on exceptions, to an understanding of the crucial
                 concepts of conditioning and stability, explained in a
                 simple yet rigorous context. It gives technical details
                 that are not readily available elsewhere and includes
                 challenging exercises that go beyond the topics covered
                 in the text. Numerical Computing with IEEE Floating
                 Point Arithmetic provides an easily accessible yet
                 detailed discussion of IEEE Std 754-1985, arguably the
                 most important standard in the computer industry. The
                 result of an unprecedented cooperation between academic
                 computer scientists and the cutting edge of industry,
                 it is supported by virtually every modern computer.
                 Other topics include the floating point architecture of
                 the Intel microprocessors and a discussion of
                 programming language support for the standard.",
  acknowledgement = ack-nhfb,
  tableofcontents = "1: Introduction \\
                 2: The real numbers \\
                 3: Computer representation of numbers \\
                 4: IEEE floating point representation \\
                 5: Rounding \\
                 6: Correctly rounded floating point operations \\
                 7: Exceptions \\
                 8: The Intel microprocessors \\
                 9: Programming languages \\
                 10: Floating point in C \\
                 11: Cancellation \\
                 12: Conditioning of problems \\
                 13: Stability of algorithms \\
                 14: Conclusion",
}

@Article{Parlett:2000:RRR,
  author =       "Beresford N. Parlett and Inderjit S. Dhillon",
  title =        "Relatively Robust Representations of Symmetric
                 Tridiagonals",
  journal =      j-LAA,
  volume =       "309",
  pages =        "121--151",
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Patterson:1998:COD,
  author =       "David A. Patterson and John L. Hennessy",
  title =        "Computer Organization and Design: {The}
                 Hardware/Software Interface",
  publisher =    "Morgan Kaufmann",
  address =      "San Francisco, CA, USA",
  edition =      "Second",
  pages =        "xxix + 759 + appendices",
  year =         "1998",
  ISBN =         "1-55860-428-6",
  ISBN-13 =      "978-1-55860-428-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Paige:1973:EAM,
  author =       "C. C. Paige",
  title =        "An Error Analysis of a Method for Solving Matrix
                 Equations",
  journal =      j-MATH-COMP,
  volume =       "27",
  number =       "122",
  pages =        "355--359",
  year =         "1973",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Paige:1990:SAG,
  author =       "C. C. Paige",
  editor =       "M. G. Cox and S. J. Hammarling",
  booktitle =    "Reliable Numerical Computation",
  title =        "Some Aspects of Generalized {QR} Factorizations",
  publisher =    pub-OUP,
  pages =        "73--91",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Pan:2000:ECR,
  author =       "C.-T. Pan",
  title =        "On the Existence and Computation of Rank-Revealing
                 {LU} Factorizations",
  journal =      j-LAA,
  volume =       "316",
  pages =        "199--222",
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Pan:2001:SMP,
  author =       "Victor Y. Pan",
  title =        "Structured Matrices and Polynomials: {Unified}
                 Superfast Algorithms",
  publisher =    pub-BH,
  address =      pub-BH:adr,
  pages =        "xxiv + 278",
  year =         "2001",
  ISBN =         "0-8176-4240-4",
  ISBN-13 =      "978-0-8176-4240-2",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Pan:1978:SAO,
  author =       "Victor Y. Pan",
  booktitle =    "Proc. 19th Annual Symposium on the Foundations of
                 Computer Science",
  title =        "Strassen Algorithm is Not Optimal. {Trilinear}
                 Technique of Aggregating, Uniting and Canceling for
                 Constructing Fast Algorithms for Matrix
                 Multiplication",
  publisher =    "Ann Arbor, MI, USA",
  pages =        "166--176",
  year =         "1978",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Pan:1984:HCW,
  author =       "Victor Y. Pan",
  title =        "How Can We Speed up Matrix Multiplication?",
  journal =      j-SIREV,
  volume =       "26",
  number =       "3",
  pages =        "393--415",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Parhami:2000:CAA,
  author =       "Behrooz Parhami",
  title =        "Computer Arithmetic: Algorithms and Hardware Designs",
  publisher =    pub-OUP,
  address =      pub-OUP:adr-NY,
  pages =        "xx + 490",
  year =         "2000",
  ISBN =         "0-19-512583-5 (hardcover), 3-540-04907-X (print),
                 3-540-36246-0 (e-book)",
  ISBN-13 =      "978-0-19-512583-2 (hardcover), 978-3-540-04907-4
                 (print), 978-3-540-36246-3 (e-book)",
  LCCN =         "QA76.9.C62P37 1999",
  bibdate =      "Sat Jun 17 12:26:40 2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$85.00",
  abstract =     "The field of digital computer architecture has grown
                 explosively in the past two decades. Through a steady
                 stream of experimental research, tool-building efforts,
                 and theoretical studies, the design of an
                 instruction-set architecture has been transformed into
                 one of the most quantitative branches of computer
                 technology. However, this explosive growth has led to
                 unprecedented hardware complexity and almost
                 intolerable development costs. The challenge faxing
                 current and future computer designers is to institute
                 simplicity where we now have complexity; to use
                 fundamental theories being developed in this area to
                 gain performance and ease-of-use benefits from simpler
                 circuits; to understand the interplay between
                 technological capabilities/limitations and sound
                 architectural decisions. Computer arithmetic plays a
                 key role in the computer designers' quest for
                 user-friendliness, compactness, simplicity, high
                 performance, low cost, and low power. Parhami's
                 Computer Architecture emphasizes both the underlying
                 theory and actual hardware designs. and links computer
                 arithmetic to other subfields of computing. It is the
                 first computer arithmetic book to cover all topics
                 important for a balanced and complete view of the
                 field. IT will be accompanied by an instructor's
                 manual, with problem solutions and enlarged versions of
                 the figures/charts, suitable for reproduction as
                 transparencies. This is a textbook for senior/graduate
                 level courses in departments of computer science and
                 electrical and computer engineering. The course is
                 commonly called Computer Arithmetic. Students wishing
                 to enroll will usually have taken courses in computer
                 organization and advanced digital design before
                 enrolling. Computer Arithmetic is a sub-field of
                 digital computer organization. It deals with the
                 hardware realization of arithmetic functions to support
                 various computer architectures, as well as arithmetic
                 algorithms for firmware or software implementations. A
                 major thrust of digital computer arithmetic is the
                 design of hardware algorithms and circuits to enhance
                 the speed of numeric operations. Thus much of what is
                 presented in this book complements the architectural
                 and algorithmic speedup techniques studied in the
                 context of high performance computer architecture and
                 parallel processing.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Part I: Number Representation \\
                 1: Numbers and Arithmetic \\
                 2: Representing Signed Numbers \\
                 3: Redundant Number Systems \\
                 4: Residue Number Systems \\
                 Part II: Addition/Subtraction \\
                 5: Basic Addition and Counting \\
                 6: Carry-Lookahead Adders \\
                 7: Variations in Fast Adders \\
                 8: Multioperand Addition \\
                 Part III: Multiplication \\
                 9: Basic Multiplication Schemes \\
                 10: High-Radix Multipliers \\
                 11: Tree and Array Multipliers \\
                 12: Variations in Multipliers \\
                 Part IV: Division \\
                 13: Basic Division Schemes \\
                 14: High-Radix Dividers \\
                 15: Variations in Dividers \\
                 16: Division by Convergence \\
                 Part V: Real Arithmetic \\
                 17: Floating-Point Representations \\
                 18: Floating-Point Operations \\
                 19: Errors and Error Control",
}

@Article{Parlett:1964:LMA,
  author =       "Beresford N. Parlett",
  title =        "{Laguerre's} Method Applied to the Matrix Eigenvalue
                 Problem",
  journal =      j-MATH-COMP,
  volume =       "18",
  pages =        "464--485",
  year =         "1964",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Parlett:1965:MEP,
  author =       "Beresford N. Parlett",
  title =        "Matrix Eigenvalue Problems",
  journal =      j-AMM,
  volume =       "72",
  number =       "2",
  pages =        "59--66",
  month =        feb,
  year =         "1965",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Parlett:1971:AAR,
  author =       "Beresford N. Parlett",
  title =        "Analysis of Algorithms for Reflections in Bisectors",
  journal =      j-SIREV,
  volume =       "13",
  number =       "2",
  pages =        "197--208",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Parlett:1990:CJH,
  author =       "Beresford N. Parlett",
  editor =       "Stephen G. Nash",
  booktitle =    "A History of Scientific Computing",
  title =        "The Contribution of {J. H. Wilkinson} to Numerical
                 Analysis",
  publisher =    pub-AW # ", " # pub-AW:adr,
  pages =        "17--30",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Parlett:1998:SEP,
  author =       "Beresford N. Parlett",
  title =        "The Symmetric Eigenvalue Problem",
  volume =       "20",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xxiv + 398",
  year =         "1998",
  DOI =          "https://doi.org/10.1137/1.9781611971163",
  ISBN =         "0-89871-402-8 (paperback), 1-61197-116-0 (e-book)",
  ISBN-13 =      "978-0-89871-402-9 (paperback), 978-1-61197-116-3
                 (e-book)",
  LCCN =         "QA188 .P37 1998",
  MRclass =      "65F15 (15A18)",
  MRnumber =     "MR1490034 (99c:65072)",
  MRreviewer =   "F. Szidarovszky",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Corrected reprint \cite{Parlett:1980:SEP}.",
  series =       "Classics in Applied Mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0708/97040623-d.html",
  ZMnumber =     "0885.65039",
  abstract =     "According to Parlett, ``Vibrations are everywhere, and
                 so too are the eigenvalues associated with them. As
                 mathematical models invade more and more disciplines,
                 we can anticipate a demand for eigenvalue calculations
                 in an ever richer variety of contexts''. Anyone who
                 performs these calculations will welcome the reprinting
                 of Parlett's book (originally published in 1980). In
                 this unabridged, amended version, Parlett covers
                 aspects of the problem that are not easily found
                 elsewhere. The chapter titles convey the scope of the
                 material succinctly. The aim of the book is to present
                 mathematical knowledge that is needed in order to
                 understand the art of computing eigenvalues of real
                 symmetric matrices, either all of them or only a few.
                 The author explains why the selected information really
                 matters and he is not shy about making judgments. The
                 commentary is lively but the proofs are terse. The
                 first nine chapters are based on a matrix on which it
                 is possible to make similarity transformations
                 explicitly. The only source of error is inexact
                 arithmetic. The last five chapters turn to large sparse
                 matrices and the task of making approximations and
                 judging them.",
  acknowledgement = ack-njh # " and " # ack-nhfb # " and " # ack-rah,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 15A18
                 Eigenvalues of matrices, etc. 15A23 Factorization of
                 matrices 15A57 Other types of matrices 15-02 Research
                 monographs (linear algebra) 65-02 Research monographs
                 (numerical analysis) 65F25 Orthogonalization (numerical
                 linear algebra)",
  keywords =     "bandmatrices; bounds for eigenvalues; eigenvalues;
                 generalized eigenvalue problem; Krylov sequences;
                 localization of eigenvalues; orthogonal
                 transformations; tridiagonal matrices; vector
                 iteration",
  libnote =      "Not yet in my library.",
  remark =       "Unabridged, corrected republication of the original
                 edition (1980; Zbl 0431.65017)",
  tableofcontents = "Convergence theory for the Rayleigh quotient
                 iteration \\
                 Eigenvectors of tridiagonals \\
                 Convergence theory, simpler than Wilkinson's, for
                 Wilkinson's shift strategy in $Q L$ and $Q R$ \\
                 New proofs and sharper results for error bounds \\
                 Optimal properties of Rayleigh--Ritz approximations \\
                 Approximation theory from Krylov subspaces, Paige's
                 theorem for noisy Lanczos algorithms, and
                 semiorthogonality among Lanczos vectors \\
                 Four flavors of subspace iteration",
}

@Article{Pan:1991:INI,
  author =       "Victor Y. Pan and Robert Schreiber",
  title =        "An Improved {Newton} Iteration for the Generalized
                 Inverse of a Matrix, with Applications",
  journal =      j-SISSC,
  volume =       "12",
  number =       "5",
  pages =        "1109--1130",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Paterson:1973:NNM,
  author =       "Michael S. Paterson and Larry J. Stockmeyer",
  title =        "On the Number of Nonscalar Multiplications Necessary
                 to Evaluate Polynomials",
  journal =      j-SICOMP,
  volume =       "2",
  number =       "1",
  pages =        "60--66",
  year =         "1973",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{patriot92,
  key =          "United States General Accounting Office",
  title =        "Patriot Missile Defense: {Software} Problem Led to
                 System Failure at {Dhahran}, {Saudi Arabia}",
  type =         "Report",
  number =       "GAO/IMTEC-92-26",
  institution =  "Information Management and Technology Division, United
                 States General Accounting Office",
  address =      "Washington, D.C.",
  pages =        "16",
  month =        feb,
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Paige:1994:HGC,
  author =       "C. C. Paige and M. Wei",
  title =        "History and Generality of the {CS} Decomposition",
  journal =      j-LAA,
  volume =       "208/209",
  pages =        "303--326",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Unpublished{Paxson:1991:PTI,
  author =       "Vern Paxson",
  title =        "A Program for Testing {IEEE} Decimal--Binary
                 Conversion",
  pages =        "40",
  month =        may,
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Manuscript.
                 \path|ftp://ftp.ee.lbl.gov/testbase-report.ps.Z|",
}

@Article{Pan:2001:CNC,
  author =       "Victor Y. Pan and Y. Yu",
  title =        "Certification of Numerical Computation of the Sign of
                 the Determinant of a Matrix",
  journal =      j-ALGORITHMICA,
  volume =       "30",
  number =       "4",
  pages =        "708--724",
  year =         "2001",
  CODEN =        "ALGOEJ",
  ISSN =         "0178-4617 (print), 1432-0541 (electronic)",
  ISSN-L =       "0178-4617",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Algorithmica",
  journal-URL =  "http://link.springer.com/journal/453",
}

@InCollection{Pan:1999:NIS,
  author =       "Victor Y. Pan and Sheryl Branham and Rhys E. Rosholt
                 and Ai-Long Zheng",
  editor =       "Thomas Kailath and Ali H. Sayed",
  booktitle =    "Fast Reliable Algorithms for Matrices with Structure",
  title =        "Newton's Iteration for Structured Matrices",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "189--210",
  year =         "1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Pena:1996:PSL,
  author =       "J. M. Pe{\~n}a",
  title =        "Pivoting Strategies Leading to Small Bounds of the
                 Errors for Certain Linear Systems",
  journal =      j-IMAJNA,
  volume =       "16",
  number =       "2",
  pages =        "141--153",
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Pena:1998:PSL,
  author =       "J. M. Pe{\~n}a",
  title =        "Pivoting Strategies Leading to Diagonal Dominance by
                 Rows",
  journal =      j-NUM-MATH,
  volume =       "81",
  pages =        "293--304",
  year =         "1998",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Penzl:1998:NSG,
  author =       "Thilo Penzl",
  title =        "Numerical Solution of Generalized {Lyapunov}
                 Equations",
  journal =      j-Adv-Comp-Math,
  volume =       "8",
  pages =        "33--48",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Percival:2002:RMM,
  author =       "Colin Percival",
  title =        "Rapid Multiplication Modulo the Sum and Difference of
                 Highly Composite Numbers",
  journal =      j-MATH-COMP,
  volume =       "",
  number =       "",
  pages =        "",
  year =         "2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "To appear",
}

@Book{Petersen:1981:ET,
  author =       "Karl Petersen",
  title =        "Ergodic Theory",
  publisher =    pub-CUP,
  address =      pub-CUP:adr,
  pages =        "xi + 329",
  year =         "1981",
  ISBN =         "0-521-23632-0",
  ISBN-13 =      "978-0-521-23632-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Peters:1970:LSP,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "The Least Squares Problem and Pseudo-Inverses",
  journal =      j-COMP-J,
  volume =       "13",
  number =       "3",
  pages =        "309--316",
  year =         "1970",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Peters:1971:PPA,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "Practical Problems Arising in the Solution of
                 Polynomial Equations",
  journal =      j-JIMA,
  volume =       "8",
  pages =        "16--35",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Peters:1975:SGJ,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "On the Stability of {Gauss--Jordan} Elimination With
                 Pivoting",
  journal =      j-CACM,
  volume =       "18",
  number =       "1",
  pages =        "20--24",
  year =         "1975",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Tao:1984:CSM,
  author =       "Pham Dinh Tao",
  title =        "Convergence of a Subgradient Method for Computing the
                 Bound Norm of Matrices",
  journal =      j-LAA,
  volume =       "62",
  pages =        "163--182",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "In French",
}

@Article{Tao:1984:SMC,
  author =       "Pham Dinh Tao",
  title =        "Some Methods for Computing the Maximum of Quadratic
                 Form on the Unit Ball of the Maximum Norm",
  journal =      j-NUM-MATH,
  volume =       "45",
  pages =        "377--401",
  year =         "1984",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "In French",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Pichat:1972:CSA,
  author =       "M. Pichat",
  title =        "Correction d'une Somme en Arithm\'etique \`a Virgule
                 Flottante",
  journal =      j-NUM-MATH,
  volume =       "19",
  pages =        "400--406",
  year =         "1972",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Pierce:1992:FAC,
  author =       "Daniel J. Pierce and Robert J. Plemmons",
  title =        "Fast Adaptive Condition Estimation",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "274--291",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Peitgen:1992:FCP,
  author =       "Heinz-Otto Peitgen and Hartmut J{\"u}rgens and Dietmar
                 Saupe",
  title =        "Fractals for the Classroom. Part One: Introduction to
                 Fractals and Chaos",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-NY,
  pages =        "xiv + 450",
  year =         "1992",
  ISBN =         "0-387-97041-X",
  ISBN-13 =      "978-0-387-97041-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Plauger:1988:PFP,
  author =       "P. J. Plauger",
  title =        "Properties of Floating-Point Arithmetic",
  journal =      j-COMP-LANG-MAG,
  volume =       "5",
  number =       "3",
  pages =        "17--22",
  year =         "1988",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computer Language Magazine",
}

@Article{Plemmons:1974:LLS,
  author =       "Robert J. Plemmons",
  title =        "Linear Least Squares by Elimination and {MGS}",
  journal =      j-ACM,
  volume =       "21",
  number =       "4",
  pages =        "581--585",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Plemmons:1976:RSD,
  author =       "R. J. Plemmons",
  title =        "Regular Splittings and the Discrete {Neumann}
                 Problem",
  journal =      j-NUM-MATH,
  volume =       "25",
  pages =        "153--161",
  year =         "1976",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Polman:1987:IBF,
  author =       "Ben Polman",
  title =        "Incomplete Blockwise Factorizations of (Block)
                 {$H$}-Matrices",
  journal =      j-LAA,
  volume =       "90",
  pages =        "119--132",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Poole:2000:RPS,
  author =       "George Poole and Larry Neal",
  title =        "The Rook's Pivoting Strategy",
  journal =      j-JCAM,
  volume =       "123",
  pages =        "353--369",
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Powell:1969:AHT,
  author =       "M. J. D. Powell and J. K. Reid",
  booktitle =    "Proc. IFIP Congress 1968",
  title =        "On Applying {Householder} Transformations to Linear
                 Least Squares Problems",
  publisher =    pub-NH # ", " # pub-NH:adr,
  pages =        "122--126",
  year =         "1969",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Poljak:1993:CRN,
  author =       "Svatopluk Poljak and Ji{\v{r}}{\'\i} Rohn",
  title =        "Checking Robust Nonsingularity is {NP}-Hard",
  journal =      j-MATH-CONTROL-SIGNALS-SYST,
  volume =       "6",
  pages =        "1--9",
  year =         "1993",
  CODEN =        "MCSYE8",
  ISSN =         "0932-4194 (print), 1435-568x (electronic)",
  ISSN-L =       "0932-4194",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Mathematics of control, signals, and systems: MCSS",
}

@Article{Powell:1970:SNM,
  author =       "M. J. D. Powell",
  title =        "A Survey of Numerical Methods for Unconstrained
                 Optimization",
  journal =      j-SIREV,
  volume =       "12",
  number =       "1",
  pages =        "79--97",
  year =         "1970",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Powell:1975:VUM,
  author =       "M. J. D. Powell",
  title =        "A View of Unconstrained Minimization Algorithms That
                 Do Not Require Derivatives",
  journal =      j-TOMS,
  volume =       "1",
  number =       "2",
  pages =        "97--107",
  year =         "1975",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Power:1986:CDH,
  author =       "Stephen Power",
  title =        "The {Cholesky} Decomposition in {Hilbert} Space",
  journal =      j-IMA-BULL,
  volume =       "22",
  number =       "11/12",
  pages =        "186--187",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "IMA Bulletin",
}

@Article{Powell:1998:DSA,
  author =       "M. J. D. Powell",
  title =        "Direct Search Algorithms for Optimization
                 Calculations",
  journal =      j-ACTA-NUMERICA,
  volume =       "7",
  pages =        "287--336",
  year =         "1998",
  CODEN =        "ANUMFU",
  DOI =          "https://doi.org/10.1017/S0962492900002841",
  ISBN =         "0-521-64316-3",
  ISBN-13 =      "978-0-521-64316-0",
  ISSN =         "0962-4929 (print), 1474-0508 (electronic)",
  ISSN-L =       "0962-4929",
  bibdate =      "Sat Sep 24 10:23:37 MDT 2011",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Acta Numer.",
  fjournal =     "Acta Numerica",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANU",
  onlinedate =   "07 November 2008",
}

@InProceedings{Priest:1991:AAP,
  author =       "Douglas M. Priest",
  editor =       "Peter Kornerup and David W. Matula",
  booktitle =    "Proc. 10th IEEE Symposium on Computer Arithmetic",
  title =        "Algorithms for Arbitrary Precision Floating Point
                 Arithmetic",
  publisher =    "IEEE Computer Society Press, Los Alamitos, CA, USA",
  pages =        "132--143",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@PhdThesis{Priest:1992:PFP,
  author =       "Douglas M. Priest",
  title =        "On Properties of Floating Point Arithmetics:
                 {Numerical} Stability and the Cost of Accurate
                 Computations",
  school =       "Mathematics Department, University of California",
  address =      inst-Berkeley:adr,
  pages =        "126",
  month =        nov,
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "\path|ftp://ftp.icsi.berkeley.edu/pub/theory/priest-thesis.ps.Z|",
}

@Article{Pryce:1981:REA,
  author =       "J. D. Pryce",
  title =        "Round-Off Error Analysis with Fewer Tears",
  journal =      j-IMA-BULL,
  volume =       "17",
  pages =        "40--47",
  year =         "1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "IMA Bulletin",
}

@Article{Pryce:1984:NMR,
  author =       "J. D. Pryce",
  title =        "A New Measure of Relative Error for Vectors",
  journal =      j-SINUM,
  volume =       "21",
  number =       "1",
  pages =        "202--215",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Pryce:1985:MEA,
  author =       "J. D. Pryce",
  title =        "Multiplicative Error Analysis of Matrix Transformation
                 Algorithms",
  journal =      j-IMAJNA,
  volume =       "5",
  pages =        "437--445",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Misc{Embree:19xx:PG,
  author =       "Mark Embree and Lloyd N. Trefethen",
  title =        "Pseudospectra Gateway",
  year =         "19xx",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "\path|http://www.comlab.ox.ac.uk/pseudospectra/|",
}

@Book{Press:1992:NRF,
  author =       "William H. Press and Saul A. Teukolsky and William T.
                 Vetterling and Brian P. Flannery",
  title =        "Numerical Recipes in {FORTRAN}: {The} Art of
                 Scientific Computing",
  publisher =    pub-CUP,
  edition =      "Second",
  pages =        "xxvi + 963",
  year =         "1992",
  ISBN =         "0-521-43064-X",
  ISBN-13 =      "978-0-521-43064-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Puschmann:1983:CPR,
  author =       "Heinrich Puschmann and Joaqu{\'\i}n Cort\'es",
  title =        "The Coordinex Problem and its Relation to the
                 Conjecture of {Wilkinson}",
  journal =      j-NUM-MATH,
  volume =       "42",
  pages =        "291--297",
  year =         "1983",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Puglisi:1992:MHM,
  author =       "Chiara Puglisi",
  title =        "Modification of the {Householder} Method Based on the
                 Compact {WY} Representation",
  journal =      j-SISSC,
  volume =       "13",
  number =       "3",
  pages =        "723--726",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Puschmann:1985:ZUV,
  author =       "Heinrich Puschmann and Marcelo Nordio",
  title =        "Zwei {Unzal{\"a}ssige} {Verst{\"a}rkungen} der
                 {Vermutung} von {Wilkinson}",
  journal =      j-LAA,
  volume =       "72",
  pages =        "167--176",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "In German",
}

@Article{Quintana:2001:NPM,
  author =       "Enrique S. Quintana and Gregorio Quintana and Xiaobai
                 Sun and Robert van de Geijn",
  title =        "A Note on Parallel Matrix Inversion",
  journal =      j-SISC,
  volume =       "22",
  number =       "5",
  pages =        "1762--1771",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Quinn:1991:TMY,
  author =       "Thomas R. Quinn and Scott Tremaine and Martin Duncan",
  title =        "A Three Million Year Integration of the Earth's
                 Orbit",
  journal =      j-ASTRON-J,
  volume =       "101",
  number =       "6",
  pages =        "2287--2305",
  year =         "1991",
  CODEN =        "ANJOAA",
  ISSN =         "0004-6256 (print), 1538-3881 (electronic)",
  ISSN-L =       "0004-6256",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Astronomical Journal",
  journal-URL =  "http://iopscience.iop.org/1538-3881",
}

@Article{Quinn:1983:EPR,
  author =       "Kevin Quinn",
  title =        "Ever Had Problems Rounding Off Figures? {This} Stock
                 Exchange Has",
  journal =      j-WALL-ST-J,
  year =         "1983",
  CODEN =        "WSJOAF",
  ISSN =         "0099-9660",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "8 November",
  fjournal =     "Wall Street Journal",
  page =         "37",
}

@Article{Quinlan:1994:REL,
  author =       "Gerald D. Quinlan",
  title =        "Round-Off Error in Long-Term Orbital Integrations
                 Using Multistep Methods",
  journal =      j-CELEST-MECH-DYN-ASTR,
  volume =       "58",
  pages =        "339--351",
  year =         "1994",
  CODEN =        "CLMCAV",
  ISSN =         "0923-2958 (print), 1572-9478 (electronic)",
  ISSN-L =       "0923-2958",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Celestial Mechanics and Dynamical Astronomy",
}

@Article{Quinn:1990:REL,
  author =       "Thomas Quinn and Scott Tremaine",
  title =        "Roundoff Error in Long-Term Planetary Orbit
                 Integrations",
  journal =      j-ASTRON-J,
  volume =       "99",
  number =       "3",
  pages =        "1016--1023",
  year =         "1990",
  CODEN =        "ANJOAA",
  ISSN =         "0004-6256 (print), 1538-3881 (electronic)",
  ISSN-L =       "0004-6256",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Astronomical Journal",
  journal-URL =  "http://iopscience.iop.org/1538-3881",
}

@Article{Raimi:1969:PDF,
  author =       "Ralph A. Raimi",
  title =        "The Peculiar Distribution of First Digits",
  journal =      j-SCI-AMER,
  volume =       "221",
  number =       "6",
  pages =        "109--120",
  year =         "1969",
  CODEN =        "SCAMAC",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}

@Article{Raimi:1976:FDP,
  author =       "Ralph A. Raimi",
  title =        "The First Digit Problem",
  journal =      j-AMM,
  volume =       "83",
  pages =        "521--538",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Rall:1981:ADT,
  author =       "Louis B. Rall",
  title =        "Automatic Differentiation: {Techniques} and
                 Applications",
  volume =       "120",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "viii + 165",
  year =         "1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Computer Science",
}

@InProceedings{Rall:1991:TMC,
  author =       "Louis B. Rall",
  editor =       "Kenneth R. Meyer and Dieter S. Schmidt",
  booktitle =    "Computer Aided Proofs in Analysis",
  title =        "Tools for Mathematical Computation",
  volume =       "28",
  publisher =    pub-Springer # ", " # pub-Springer:adr-NY,
  pages =        "217--228",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "IMA Volumes in Mathematics and Its Applications",
}

@Article{Ramos:1971:REA,
  author =       "George U. Ramos",
  title =        "Roundoff Error Analysis of the Fast {Fourier}
                 Transform",
  journal =      j-MATH-COMP,
  volume =       "25",
  number =       "116",
  pages =        "757--768",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Randell:1975:ODC,
  editor =       "Brian Randell",
  title =        "The Origins of Digital Computers: {Selected} Papers",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  edition =      "Third",
  pages =        "xvi + 580",
  year =         "1975",
  ISBN =         "3-540-11319-3",
  ISBN-13 =      "978-3-540-11319-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Rath:1982:FGR,
  author =       "Wolfgang Rath",
  title =        "Fast {Givens} Rotations for Orthogonal Similarity
                 Transformations",
  journal =      j-NUM-MATH,
  volume =       "40",
  pages =        "47--56",
  year =         "1982",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Reichel:1990:NIL,
  author =       "Lothar Reichel",
  title =        "Newton Interpolation at {Leja} Points",
  journal =      j-BIT,
  volume =       "30",
  pages =        "332--346",
  year =         "1990",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Reichel:1991:FQD,
  author =       "Lothar Reichel",
  title =        "Fast {QR} Decomposition of {Vandermonde}-Like Matrices
                 and Polynomial Least Squares Approximation",
  journal =      j-SIMAX,
  volume =       "12",
  number =       "3",
  pages =        "552--564",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Reid:2000:ISL,
  author =       "J. K. Reid",
  title =        "Implicit Scaling of Linear Least Squares Problems",
  journal =      j-BIT,
  volume =       "40",
  number =       "1",
  pages =        "146--157",
  year =         "2000",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Reid:1971:NSG,
  author =       "J. K. Reid",
  title =        "A Note on the Stability of {Gaussian} Elimination",
  journal =      j-JIMA,
  volume =       "8",
  pages =        "374--375",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Reid:1987:SM,
  author =       "J. K. Reid",
  editor =       "A. Iserles and M. J. D. Powell",
  booktitle =    "The State of the Art in Numerical Analysis",
  title =        "Sparse Matrices",
  publisher =    pub-OUP,
  pages =        "59--85",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Reiser:1975:EDF,
  author =       "John F. Reiser and Donald E. Knuth",
  title =        "Evading the Drift in Floating-Point Addition",
  journal =      j-INFPL,
  volume =       "3",
  number =       "3",
  pages =        "84--87",
  year =         "1975",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Reichel:1991:CVS,
  author =       "Lothar Reichel and Gerhard Opfer",
  title =        "{Chebyshev--Vandermonde} Systems",
  journal =      j-MATH-COMP,
  volume =       "57",
  number =       "196",
  pages =        "703--721",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Reichel:1992:EPE,
  author =       "Lothar Reichel and Lloyd N. Trefethen",
  title =        "Eigenvalues and Pseudo-Eigenvalues of {Toeplitz}
                 Matrices",
  journal =      j-LAA,
  volume =       "162--164",
  pages =        "153--185",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Reddy:1992:SML,
  author =       "Satish C. Reddy and Lloyd N. Trefethen",
  title =        "Stability of the Method of Lines",
  journal =      j-NUM-MATH,
  volume =       "62",
  pages =        "235--267",
  year =         "1992",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Rheinboldt:1976:MIC,
  author =       "Werner C. Rheinboldt",
  title =        "On Measures of Ill-Conditioning for Nonlinear
                 Equations",
  journal =      j-MATH-COMP,
  volume =       "30",
  number =       "133",
  pages =        "104--111",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Rice:1966:TC,
  author =       "John R. Rice",
  title =        "A Theory of Condition",
  journal =      j-SINUM,
  volume =       "3",
  number =       "2",
  pages =        "287--310",
  year =         "1966",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Rice:1966:EGS,
  author =       "John R. Rice",
  title =        "Experiments on {Gram--Schmidt} Orthogonalization",
  journal =      j-MATH-COMP,
  volume =       "20",
  pages =        "325--328",
  year =         "1966",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Rigal:1967:CGS,
  author =       "J. L. Rigal and J. Gaches",
  title =        "On the Compatibility of a Given Solution with the Data
                 of a Linear System",
  journal =      j-ACM,
  volume =       "14",
  number =       "3",
  pages =        "543--548",
  year =         "1967",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Roberts:1980:LMR,
  author =       "J. D. Roberts",
  title =        "Linear Model Reduction and Solution of the Algebraic
                 {Riccati} Equation by Use of the Sign Function",
  journal =      j-IJC,
  volume =       "32",
  number =       "4",
  pages =        "677--687",
  year =         "1980",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "First issued as report CUED/B-Control/TR13, Department
                 of Engineering, University of Cambridge, 1971",
}

@Article{Rohn:1989:NCN,
  author =       "Ji{\v{r}}{\'\i} Rohn",
  title =        "New Condition Numbers for Matrices and Linear
                 Systems",
  journal =      j-COMPUTING,
  volume =       "41",
  pages =        "167--169",
  year =         "1989",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Rohn:1989:SLI,
  author =       "Ji{\v{r}}{\'\i} Rohn",
  title =        "Systems of Linear Interval Equations",
  journal =      j-LAA,
  volume =       "126",
  pages =        "39--78",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Rohn:1990:NUD,
  author =       "Ji{\v{r}}{\'\i} Rohn",
  title =        "Nonsingularity Under Data Rounding",
  journal =      j-LAA,
  volume =       "139",
  pages =        "171--174",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Rohn:1995:NHR,
  author =       "Ji{\v{r}}{\'\i} Rohn",
  title =        "{NP}-Hardness Results for Some Linear and Quadratic
                 Problems",
  type =         "Technical Report",
  number =       "No. 619",
  institution =  "Institute of Computer Science, Academy of Sciences of
                 the Czech Republic",
  address =      "Prague",
  pages =        "11",
  month =        jan,
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Robertazzi:1988:BOF,
  author =       "T. G. Robertazzi and S. C. Schwartz",
  title =        "Best ``Ordering'' for Floating-Point Addition",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "101--110",
  year =         "1988",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Ross:1965:RTE,
  author =       "D. R. Ross",
  title =        "Reducing Truncation Errors Using Cascading
                 Accumulators",
  journal =      j-CACM,
  volume =       "8",
  number =       "1",
  pages =        "32--33",
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@PhdThesis{Rowan:1990:FSA,
  author =       "Thomas Harvey Rowan",
  title =        "Functional Stability Analysis of Numerical
                 Algorithms",
  school =       "University of Texas at Austin",
  address =      "Austin, TX, USA",
  pages =        "xii + 205",
  month =        may,
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Routh:1977:PSM,
  author =       "M. W. Routh and P. A. Swartz and M. B. Denton",
  title =        "Performance of the Super Modified Simplex",
  journal =      j-ANAL-CHEM,
  volume =       "49",
  number =       "9",
  pages =        "1422--1428",
  year =         "1977",
  CODEN =        "ANCHAM",
  ISSN =         "0003-2700 (print), 1520-6882 (electronic)",
  ISSN-L =       "0003-2700",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Analytical Chemistry (Washington, DC, USA)",
  journal-URL =  "http://pubs.acs.org/journal/ancham",
}

@Article{Ruhe:1983:NAG,
  author =       "Axel Ruhe",
  title =        "Numerical Aspects of {Gram--Schmidt} Orthogonalization
                 of Vectors",
  journal =      j-LAA,
  volume =       "52/53",
  pages =        "591--601",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Rump:2001:SVM,
  author =       "Siegfried M. Rump",
  title =        "Self-Validating Methods",
  journal =      j-LAA,
  volume =       "324",
  pages =        "3--13",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Rump:2002:OSN,
  author =       "Siegfried M. Rump",
  title =        "Optimal Scaling for {$P$}-norms and Componentwise
                 Distance to Singularity",
  journal =      j-IMAJNA,
  volume =       "",
  number =       "",
  pages =        "",
  year =         "2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "To appear",
}

@Article{Rump:1998:SPS,
  author =       "Siegfried M. Rump",
  title =        "Structured Perturbations and Symmetric Matrices",
  journal =      j-LAA,
  volume =       "278",
  pages =        "121--132",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Rump:1999:ICM,
  author =       "Siegfried M. Rump",
  title =        "Ill-Conditioned Matrices Are Componentwise Near to
                 Singularity",
  journal =      j-SIREV,
  volume =       "41",
  number =       "1",
  pages =        "102--112",
  year =         "1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InCollection{Rump:1999:IIL,
  author =       "Siegfried M. Rump",
  editor =       "Tibor Csendes",
  booktitle =    "Developments~in~Reliable Computing",
  title =        "{INTLAB---INTerval LABoratory}",
  publisher =    pub-Kluwer,
  address =      pub-Kluwer:adr,
  pages =        "77--104",
  year =         "1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Rump:1999:FPI,
  author =       "Siegfried M. Rump",
  title =        "Fast and Parallel Interval Arithmetic",
  journal =      j-BIT,
  volume =       "39",
  number =       "3",
  pages =        "534--554",
  year =         "1999",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Russinoff:1998:MCP,
  author =       "David M. Russinoff",
  title =        "A Mechanically Checked Proof of {IEEE} Compliance of
                 the Floating Point Multiplication, Division and Square
                 Root Algorithms of the {AMD-K7} Processor",
  journal =      "LMS J. Computer Math.",
  volume =       "1",
  pages =        "148--200",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Rutherford:1947:SCD,
  author =       "D. E. Rutherford",
  title =        "Some Continuant Determinants Arising in Physics and
                 Chemistry",
  journal =      j-PROC-R-SOC-EDINB,
  volume =       "62,A",
  pages =        "229--236",
  year =         "1947",
  CODEN =        "PRSEAE",
  ISSN =         "0080-4541 (print), 2053-5902 (electronic)",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Proceedings of the Royal Society of Edinburgh",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PRE",
}

@Article{Rutherford:1952:SCD,
  author =       "D. E. Rutherford",
  title =        "Some Continuant Determinants Arising in Physics and
                 Chemistry---{II}",
  journal =      j-PROC-R-SOC-EDINB,
  volume =       "63,A",
  pages =        "232--241",
  year =         "1952",
  CODEN =        "PRSEAE",
  ISSN =         "0080-4541 (print), 2053-5902 (electronic)",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Proceedings of the Royal Society of Edinburgh",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PRE",
}

@InCollection{Rutishauser:1958:SEP,
  author =       "Heinz Rutishauser",
  booktitle =    "Further Contributions to the Solution of Simultaneous
                 Linear Equations and the Determination of Eigenvalues",
  title =        "Solution of Eigenvalue Problems With the
                 {LR}-Transformation",
  number =       "49",
  publisher =    "National Bureau of Standards, United States Department
                 of Commerce",
  address =      "Washington, D. C.",
  pages =        "47--81",
  year =         "1958",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Applied Mathematics Series",
}

@InProceedings{Rutishauser:1968:TM,
  author =       "H. Rutishauser",
  booktitle =    "Programmation en Math{\'e}matiques Num{\'e}riques,
                 Besan{\c{c}}on, 1966",
  title =        "On Test Matrices",
  volume =       "7 (no. 165)",
  pages =        "349--365",
  year =         "1968",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "{\'E}ditions Centre Nat. Recherche Sci., Paris",
}

@Article{Samelson:1953:ORR,
  author =       "Klaus Samelson and Friedrich L. Bauer",
  title =        "{Optimale Rechengenauigkeit} bei {Rechenanlagen} mit
                 gleitendem {Komma}",
  journal =      j-ZAMP,
  volume =       "4",
  pages =        "312--316",
  year =         "1953",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Sameh:1977:STS,
  author =       "Ahmed H. Sameh and Richard P. Brent",
  title =        "Solving Triangular Systems on a Parallel Computer",
  journal =      j-SINUM,
  volume =       "14",
  number =       "6",
  pages =        "1101--1113",
  year =         "1977",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Sanz-Serna:1993:SCS,
  author =       "J. M. Sanz-Serna and S. Larsson",
  title =        "Shadows, Chaos, and Saddles",
  journal =      j-APP-NUM-MATH,
  volume =       "13",
  pages =        "181--190",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InCollection{Savage:1954:TIF,
  author =       "I. Richard Savage and Eugene Lukacs",
  editor =       "Olga Taussky",
  booktitle =    "Contributions to the Solution of Systems of Linear
                 Equations and the Determination of Eigenvalues",
  title =        "Tables of Inverse of Finite Segments of the {Hilbert}
                 Matrix",
  number =       "39",
  publisher =    "National Bureau of Standards, United States Department
                 of Commerce",
  address =      "Washington, D. C.",
  pages =        "105--108",
  year =         "1954",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Applied Mathematics Series",
}

@TechReport{Saunders:1972:LSL,
  author =       "M. A. Saunders",
  title =        "Large-Scale Linear Programming Using the {Cholesky}
                 Factorization",
  type =         "Report",
  number =       "CS 252",
  institution =  inst-CS-U-STANFORD,
  month =        jan,
  year =         "1972",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Sautter:1978:EAG,
  author =       "Werner Sautter",
  title =        "Error Analysis of {Gauss} Elimination for the Best
                 Least Squares Problem",
  journal =      j-NUM-MATH,
  volume =       "30",
  pages =        "165--184",
  year =         "1978",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  germantitle =  "Fehleranalyse f{\"ur} die {Gau\ss}-Elimination zur
                 Berechnung der L{\"o}sung minimaler L{\"a}nge",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Book{Smith:1976:MER,
  author =       "B. T. Smith and J. M. Boyle and J. J. Dongarra and B.
                 S. Garbow and Y. Ikebe and V. C. Klema and C. B.
                 Moler",
  title =        "Matrix Eigensystem Routines---{EISPACK} Guide",
  volume =       "6",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  edition =      "Second",
  pages =        "vii + 551",
  year =         "1976",
  ISBN =         "3-540-06710-8",
  ISBN-13 =      "978-3-540-06710-8",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Computer Science",
}

@Book{Scarborough:1950:NMA,
  author =       "James B. Scarborough",
  title =        "Numerical Mathematical Analysis",
  publisher =    pub-JH,
  address =      pub-JH:adr,
  edition =      "Second",
  pages =        "xviii + 511",
  year =         "1950",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Schatzman:1996:ADF,
  author =       "James C. Schatzman",
  title =        "Accuracy of the Discrete {Fourier} Transform and the
                 Fast {Fourier} Transform",
  journal =      j-SISC,
  volume =       "17",
  number =       "5",
  pages =        "1150--1166",
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Schelin:1983:CFA,
  author =       "Charles W. Schelin",
  title =        "Calculator Function Approximation",
  journal =      j-AMM,
  volume =       "90",
  number =       "5",
  pages =        "317--325",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Schryer:1981:TCF,
  author =       "N. L. Schryer",
  title =        "A Test of a Computer's Floating-Point Arithmetic
                 Unit",
  type =         "Computing Science Technical Report",
  number =       "No. 89",
  institution =  inst-ATT,
  address =      inst-ATT:adr,
  year =         "1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Schryer:1984:DCF,
  author =       "N. L. Schryer",
  editor =       "Wayne R. Cowell",
  booktitle =    "Sources and Development of Mathematical Software",
  title =        "Determination of Correct Floating-Point Model
                 Parameters",
  publisher =    pub-PH # ", " # pub-PH:adr,
  pages =        "360--366",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Schreiber:1988:BAP,
  author =       "Robert S. Schreiber",
  editor =       "M. H. Schultz",
  booktitle =    "Numerical Algorithms for Modern Parallel Computer
                 Architectures",
  title =        "Block Algorithms for Parallel Machines",
  number =       "13",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "197--207",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "IMA Volumes In Mathematics and Its Applications",
}

@Article{Schreiber:1989:HRS,
  author =       "Robert S. Schreiber",
  title =        "{Hough's} Random Story Explained",
  journal =      j-NA-DIGEST,
  volume =       "Volume 89, Issue 3",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "NA Digest",
}

@Article{schu33,
  author =       "G{\"u}nther Schulz",
  title =        "{Iterative Berechnung} der Reziproken {Matrix}",
  journal =      j-ZAMM,
  volume =       "13",
  pages =        "57--59",
  year =         "1933",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Schreiber:1988:BRT,
  author =       "Robert S. Schreiber and Beresford N. Parlett",
  title =        "Block Reflectors: {Theory} and Computation",
  journal =      j-SINUM,
  volume =       "25",
  number =       "1",
  pages =        "189--205",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Schonfelder:1980:ECP,
  author =       "J. L. Schonfelder and M. Razaz",
  title =        "Error Control with Polynomial Approximations",
  journal =      j-IMAJNA,
  volume =       "1",
  pages =        "105--114",
  year =         "1980",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Schneider:1962:CTS,
  author =       "Hans Schneider and W. Gilbert Strang",
  title =        "Comparison Theorems for Supremum Norms",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "15--20",
  year =         "1962",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Schreiber:1989:SEW,
  author =       "Robert S. Schreiber and Charles F. {Van Loan}",
  title =        "A Storage Efficient {WY} Representation for Products
                 of {Householder} Transformations",
  journal =      j-SISSC,
  volume =       "10",
  pages =        "53--57",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Schneider:1998:MWN,
  author =       "Hans Schneider and Hans F. Weinberger",
  title =        "On Matrices for Which Norm Bounds Are Attained",
  journal =      j-LAA,
  volume =       "275--276",
  pages =        "563--577",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Scherer:1980:SNR,
  author =       "R. Scherer and K. Zeller",
  title =        "Shorthand Notation for Rounding Errors",
  journal =      j-COMPUTING,
  volume =       "Suppl. 2",
  pages =        "165--168",
  year =         "1980",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Book{Sedgewick:1988:A,
  author =       "Robert Sedgewick",
  title =        "Algorithms",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xii + 657",
  year =         "1988",
  ISBN =         "0-201-06673-4",
  ISBN-13 =      "978-0-201-06673-9",
  LCCN =         "QA76.6 .S435 1988",
  MRclass =      "68-01, 68N01, 68P05, 68P10, 68Q25, 68W10, 68W99",
  bibdate =      "Wed Dec 15 10:41:37 1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/hash.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
  price =        "US\$34.95",
  ZMnumber =     "0717.68005",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
  remark =       prep-tex,
}

@Misc{Severance:1998:IOM,
  author =       "Charles Severance",
  title =        "An Interview with the Old Man of Floating-Point.
                 {Reminiscences} Elicited from {William Kahan by Charles
                 Severance}",
  month =        feb,
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "\path|http://www.cs.berkeley.edu/~wkahan/ieee754status/754story.html|.
                 A shortened version appears in \emph{Computer},
                 31(3):114--115, March 1998.",
}

@Book{shal73,
  author =       "Lawrence F. Shampine and Richard C. {Allen, Jr.}",
  title =        "Numerical Computing: {An} Introduction",
  publisher =    "W. B. Saunders",
  address =      "Philadelphia, PA, USA",
  pages =        "vii + 258",
  year =         "1973",
  ISBN =         "0-7216-8150-6",
  ISBN-13 =      "978-0-7216-8150-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Shampine:1994:NSO,
  author =       "Lawrence F. Shampine",
  title =        "Numerical Solution of Ordinary Differential
                 Equations",
  publisher =    pub-CH,
  address =      pub-CH:adr-NY,
  pages =        "x + 484",
  year =         "1994",
  ISBN =         "0-412-05151-6",
  ISBN-13 =      "978-0-412-05151-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Shapiro:1982:OSM,
  author =       "Alexander Shapiro",
  title =        "Optimally Scaled Matrices, Necessary and Sufficient
                 Conditions",
  journal =      j-NUM-MATH,
  volume =       "39",
  pages =        "239--245",
  year =         "1982",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Shapiro:1985:OBD,
  author =       "Alexander Shapiro",
  title =        "Optimal Block Diagonal {$l_2$}-Scaling of Matrices",
  journal =      j-SINUM,
  volume =       "22",
  number =       "1",
  pages =        "81--94",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Shapiro:1991:UBN,
  author =       "Alexander Shapiro",
  title =        "Upper Bounds for Nearly Optimal Diagonal Scaling of
                 Matrices",
  journal =      j-LMA,
  volume =       "29",
  pages =        "147--147",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Sharangpani:1994:SAF,
  author =       "H. P. Sharangpani and M. L. Barton",
  title =        "Statistical Analysis of Floating Point Flaw in the
                 {Pentium} Processor (1994)",
  institution =  "Intel Corporation",
  pages =        "31",
  month =        nov,
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Shroff:1992:ACE,
  author =       "Gautam M. Shroff and Christian H. Bischof",
  title =        "Adaptive Condition Estimation for Rank-One Updates of
                 {QR} Factorizations",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "4",
  pages =        "1264--1278",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Shewchuk:1997:APF,
  author =       "Jonathan Richard Shewchuk",
  title =        "Adaptive Precision Floating-Point Arithmetic and Fast
                 Robust Geometric Predicates",
  journal =      j-DISCRETE-COMPUT-GEOM,
  volume =       "18",
  number =       "3",
  pages =        "305--363",
  year =         "1997",
  CODEN =        "DCGEER",
  ISSN =         "0179-5376 (print), 1432-0444 (electronic)",
  ISSN-L =       "0179-5376",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Discrete and Computational Geometry",
  journal-URL =  "http://link.springer.com/journal/454",
}

@Article{Shampine:1997:MOS,
  author =       "Lawrence F. Shampine and Mark W. Reichelt",
  title =        "The {MATLAB} {ODE} Suite",
  journal =      j-SISC,
  volume =       "18",
  number =       "1",
  pages =        "1--22",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Shepherd:1989:MCW,
  author =       "David Shepherd and Greg Wilson",
  title =        "Making Chips that Work",
  journal =      j-NEW-SCIENTIST,
  pages =        "61--64",
  year =         "1989",
  CODEN =        "NWSCAL",
  ISSN =         "0262-4079, 0028-6664",
  ISSN-L =       "0262-4079",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "13 May",
  fjournal =     "New Scientist",
  journal-URL =  "http://www.sciencedirect.com/science/journal/02624079",
}

@Article{Skeel:1979:SNS,
  author =       "Robert D. Skeel",
  title =        "Scaling for Numerical Stability in {Gaussian}
                 Elimination",
  journal =      j-ACM,
  volume =       "26",
  number =       "3",
  pages =        "494--526",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Skeel:1980:IRI,
  author =       "Robert D. Skeel",
  title =        "Iterative Refinement Implies Numerical Stability for
                 {Gaussian} Elimination",
  journal =      j-MATH-COMP,
  volume =       "35",
  number =       "151",
  pages =        "817--832",
  year =         "1980",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Skeel:1981:EER,
  author =       "Robert D. Skeel",
  title =        "Effect of Equilibration on Residual Size for Partial
                 Pivoting",
  journal =      j-SINUM,
  volume =       "18",
  number =       "3",
  pages =        "449--454",
  year =         "1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Skeel:1989:SNB,
  author =       "Robert D. Skeel",
  title =        "Safety in Numbers: {The} Boundless Errors of Numerical
                 Computation",
  type =         "Working Document",
  number =       "89-3",
  institution =  "Department of Computer Science, University of
                 Illinois",
  address =      "Urbana, IL, USA",
  pages =        "9",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Skeel:1993:ENC,
  author =       "Robert D. Skeel and Jerry B. Keiper",
  title =        "Elementary Numerical Computing with {Mathematica}",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  pages =        "xiv + 434",
  year =         "1993",
  ISBN =         "0-07-057820-6",
  ISBN-13 =      "978-0-07-057820-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Blackford:1997:SUG,
  author =       "L. S. Blackford and J. Choi and A. Cleary and E.
                 D'Azevedo and J. Demmel and I. Dhillon and J. Dongarra
                 and S. Hammarling and G. Henry and A. Petitet and K.
                 Stanley and D. Walker and R. C. Whaley",
  title =        "{ScaLAPACK} Users' Guide",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xxvi + 325",
  year =         "1997",
  ISBN =         "0-89871-397-8",
  ISBN-13 =      "978-0-89871-397-8",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Smale:1990:SRF,
  author =       "Steve Smale",
  title =        "Some Remarks on the Foundations of Numerical
                 Analysis",
  journal =      j-SIREV,
  volume =       "32",
  number =       "2",
  pages =        "211--220",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Smith:1962:ACD,
  author =       "Robert L. Smith",
  title =        "Algorithm 116: {Complex} Division",
  journal =      j-CACM,
  volume =       "5",
  number =       "8",
  pages =        "435",
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Smith:1965:ASO,
  author =       "Francis J. Smith",
  title =        "An Algorithm for Summing Orthogonal Polynomial Series
                 and their Derivatives with Applications to
                 Curve-Fitting and Interpolation",
  journal =      j-MATH-COMP,
  volume =       "19",
  pages =        "33--36",
  year =         "1965",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Smith:1975:SAP,
  author =       "Jon M. Smith",
  title =        "Scientific Analysis on the Pocket Calculator",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  pages =        "xii + 380",
  year =         "1975",
  ISBN =         "0-471-79997-1",
  ISBN-13 =      "978-0-471-79997-9",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Smith:1991:AFP,
  author =       "David M. Smith",
  title =        "Algorithm 693: {A} {FORTRAN} Package for
                 Floating-Point Multiple-Precision Arithmetic",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "273--283",
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Smith:1998:AMP,
  author =       "David M. Smith",
  title =        "Algorithm 786: {Multiple}-Precision Complex Arithmetic
                 and Functions",
  journal =      j-TOMS,
  volume =       "24",
  number =       "4",
  pages =        "359--367",
  year =         "1998",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Smoktunowicz:1995:NSC,
  author =       "Alicja Smoktunowicz",
  title =        "A Note on the Strong Componentwise Stability of
                 Algorithms for Solving Symmetric Linear Systems",
  journal =      j-DEMONSTRATIO-MATHEMATICA,
  volume =       "28",
  number =       "2",
  pages =        "443--448",
  year =         "1995",
  CODEN =        "DEMADO",
  ISSN =         "0420-1213",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Demonstratio Mathematica",
}

@Article{Smoktunowicz:1984:BCI,
  author =       "Alicja Smoktunowicz and Jolanta Sokolnicka",
  title =        "Binary Cascades Iterative Refinement in
                 Doubled-Mantissa Arithmetics",
  journal =      j-BIT,
  volume =       "24",
  pages =        "123--127",
  year =         "1984",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Snyder:1955:ISS,
  author =       "James N. Snyder",
  title =        "On the Improvement of the Solutions to a Set of
                 Simultaneous Linear Equations using the {ILLIAC}",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "9",
  pages =        "177--184",
  year =         "1955",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Sorensen:1985:APP,
  author =       "D. C. Sorensen",
  title =        "Analysis of Pairwise Pivoting in {Gaussian}
                 Elimination",
  journal =      j-IEEE-C,
  volume =       "C-34",
  pages =        "274--278",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Soderstrom:1974:NPI,
  author =       "Torsten S{\"o}derstr{\"o}m and G. W. Stewart",
  title =        "On the Numerical Properties of an Iterative Method for
                 Computing the {Moore--Penrose} Generalized Inverse",
  journal =      j-SINUM,
  volume =       "11",
  number =       "1",
  pages =        "61--74",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Spiess:1976:UZD,
  author =       "J. Spie{\ss}",
  title =        "Untersuchungen des {Zeitgewinns} durch neue
                 {Algorithmen} zur {Matrix-Multiplikation}",
  journal =      j-COMPUTING,
  volume =       "17",
  pages =        "23--36",
  year =         "1976",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Stegun:1956:PC,
  author =       "Irene A. Stegun and Milton Abramowitz",
  title =        "Pitfalls in Computation",
  journal =      j-SIAM,
  volume =       "4",
  number =       "4",
  pages =        "207--219",
  year =         "1956",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Stoer:1980:INA,
  author =       "Josef Stoer and R. Bulirsch",
  title =        "Introduction to Numerical Analysis",
  publisher =    "Springer-Verlag",
  address =      "New York",
  pages =        "ix + 609",
  year =         "1980",
  ISBN =         "0-387-90420-4",
  ISBN-13 =      "978-0-387-90420-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Sterbenz:1974:FPC,
  author =       "Pat H. Sterbenz",
  title =        "Floating-Point Computation",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xiv + 316",
  year =         "1974",
  ISBN =         "0-13-322495-3",
  ISBN-13 =      "978-0-13-322495-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stewart:1971:EAA,
  author =       "G. W. Stewart",
  title =        "Error Analysis of the Algorithm for Shifting the Zeros
                 of a Polynomial by Synthetic Division",
  journal =      j-MATH-COMP,
  volume =       "25",
  number =       "113",
  pages =        "135--139",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Stewart:1973:IMC,
  author =       "G. W. Stewart",
  title =        "Introduction to Matrix Computations",
  publisher =    pub-AP,
  address =      pub-AP:adr-NY,
  pages =        "xiii + 441",
  year =         "1973",
  ISBN =         "0-12-670350-7",
  ISBN-13 =      "978-0-12-670350-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stewart:1973:EPB,
  author =       "G. W. Stewart",
  title =        "Error and Perturbation Bounds for Subspaces Associated
                 with Certain Eigenvalue Problems",
  journal =      j-SIREV,
  volume =       "15",
  number =       "4",
  pages =        "727--764",
  year =         "1973",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stewart:1974:MPE,
  author =       "G. W. Stewart",
  title =        "Modifying Pivot Elements in {Gaussian} Elimination",
  journal =      j-MATH-COMP,
  volume =       "28",
  number =       "126",
  pages =        "537--542",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stewart:1977:PPI,
  author =       "G. W. Stewart",
  title =        "On the Perturbation of Pseudo-Inverses, Projections
                 and Linear Least Squares Problems",
  journal =      j-SIREV,
  volume =       "19",
  number =       "4",
  pages =        "634--662",
  year =         "1977",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stewart:1977:PBF,
  author =       "G. W. Stewart",
  title =        "Perturbation Bounds for the {$QR$} Factorization of a
                 Matrix",
  journal =      j-SINUM,
  volume =       "14",
  number =       "3",
  pages =        "509--518",
  year =         "1977",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Stewart:1977:RDL,
  author =       "G. W. Stewart",
  editor =       "John R. Rice",
  booktitle =    "Mathematical Software {III}",
  title =        "Research, Development, and {LINPACK}",
  publisher =    pub-AP # ", " # pub-AP:adr-NY,
  pages =        "1--14",
  year =         "1977",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stewart:1980:EGR,
  author =       "G. W. Stewart",
  title =        "The Efficient Generation of Random Orthogonal Matrices
                 With an Application to Condition Estimators",
  journal =      j-SINUM,
  volume =       "17",
  number =       "3",
  pages =        "403--409",
  year =         "1980",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stewart:1985:NCD,
  author =       "G. W. Stewart",
  title =        "A Note on Complex Division",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "238--241",
  year =         "1985",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Stewart:1990:SPT,
  author =       "G. W. Stewart",
  title =        "Stochastic Perturbation Theory",
  journal =      j-SIREV,
  volume =       "32",
  number =       "4",
  pages =        "579--610",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Stewart:1992:NGS,
  author =       "G. W. Stewart",
  title =        "Note on a Generalized {Sylvester} Equation",
  type =         "IMA Preprint Series",
  number =       "\#985",
  institution =  inst-IMA,
  address =      inst-IMA:adr,
  pages =        "3",
  month =        may,
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stewart:1993:PLC,
  author =       "G. W. Stewart",
  title =        "On the Perturbation of {LU}, {Cholesky}, and {QR}
                 Factorizations",
  journal =      j-SIMAX,
  volume =       "14",
  number =       "4",
  pages =        "1141--1145",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stewart:1993:EHS,
  author =       "G. W. Stewart",
  title =        "On the Early History of the Singular Value
                 Decomposition",
  journal =      j-SIREV,
  volume =       "35",
  number =       "4",
  pages =        "551--566",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Gauss:1995:TCO,
  author =       "Carl Friedrich Gauss",
  title =        "Theory of the Combination of Observations Least
                 Subject to Errors. {Part} One, Part Two, Supplement",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xi + 241",
  year =         "1995",
  ISBN =         "0-89871-347-1",
  ISBN-13 =      "978-0-89871-347-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Translated from the Latin by G. W. Stewart",
}

@Article{Stewart:1995:GSG,
  author =       "G. W. Stewart",
  title =        "{Gauss}, Statistics, and {Gaussian} Elimination",
  journal =      j-COMPUT-GRAPH-STAT,
  volume =       "4",
  number =       "1",
  pages =        "1--11",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stewart:1997:PCF,
  author =       "G. W. Stewart",
  title =        "On the Perturbation of {$LU$} and {Cholesky} Factors",
  journal =      j-IMAJNA,
  volume =       "17",
  number =       "1",
  pages =        "1--6",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stewart:1997:TMG,
  author =       "G. W. Stewart",
  title =        "The Triangular Matrices of {Gaussian} Elimination and
                 Related Decompositions",
  journal =      j-IMAJNA,
  volume =       "17",
  number =       "1",
  pages =        "7--16",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stewart:1997:MCS,
  author =       "G. W. Stewart",
  title =        "On {Markov} Chains with Sluggish Transients",
  journal =      "Communication in Statistics, Stochastic Models",
  volume =       "13",
  pages =        "85--95",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stewart:1998:AM,
  author =       "G. W. Stewart",
  title =        "On the Adjugate Matrix",
  journal =      j-LAA,
  volume =       "283",
  pages =        "151--164",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stewart:1997:CFS,
  author =       "Michael Stewart",
  title =        "{Cholesky} Factorization of Semidefinite {Toeplitz}
                 Matrices",
  journal =      j-LAA,
  volume =       "254",
  pages =        "497--525",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Stewart:2001:MAV,
  author =       "G. W. Stewart",
  title =        "Matrix Algorithms. {Volume II}: Eigensystems",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xix + 469",
  year =         "2001",
  ISBN =         "0-89871-503-2",
  ISBN-13 =      "978-0-89871-503-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Starke:1991:S,
  author =       "Gerhard Starke and Wilhelm Niethammer",
  title =        "{SOR} for {$AX-XB=C$}",
  journal =      j-LAA,
  volume =       "154--156",
  pages =        "355--375",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Stoer:1972:ENM,
  author =       "Josef Stoer",
  title =        "Einf{\"u}hrung in die Numerische Mathematik {I}",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "ix + 250",
  year =         "1972",
  ISBN =         "0-387-05750-1",
  ISBN-13 =      "978-0-387-05750-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stone:1962:BPR,
  author =       "Betty Jane Stone",
  title =        "Best Possible Ratios of Certain Matrix Norms",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "114--116",
  year =         "1962",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Stoutemyer:1977:AEA,
  author =       "David R. Stoutemyer",
  title =        "Automatic Error Analysis Using Computer Algebraic
                 Manipulation",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "26--43",
  year =         "1977",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Stoutemyer:1991:CMC,
  author =       "David R. Stoutemyer",
  title =        "Crimes and Misdemeanours in the Computer Algebra
                 Trade",
  journal =      j-NAMS,
  volume =       "38",
  number =       "7",
  pages =        "778--785",
  year =         "1991",
  CODEN =        "AMNOAN",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
}

@Article{Strassen:1969:GEO,
  author =       "V. Strassen",
  title =        "Gaussian Elimination is Not Optimal",
  journal =      j-NUM-MATH,
  volume =       "13",
  pages =        "354--356",
  year =         "1969",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Strang:1986:PTM,
  author =       "Gilbert Strang",
  title =        "A Proposal for {Toeplitz} Matrix Calculations",
  journal =      j-STUDIES-APPL-MATH,
  volume =       "74",
  pages =        "171--176",
  year =         "1986",
  CODEN =        "SAPMB6",
  ISSN =         "0022-2526 (print), 1467-9590 (electronic)",
  ISSN-L =       "0022-2526",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Studies in Applied Mathematics",
}

@Book{Strang:1993:ILA,
  author =       "Gilbert Strang",
  title =        "Introduction to Linear Algebra",
  publisher =    pub-Wellesley,
  address =      pub-Wellesley:adr,
  pages =        "viii + 472",
  year =         "1993",
  ISBN =         "0-9614088-5-5",
  ISBN-13 =      "978-0-9614088-5-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Stewart:1990:MPT,
  author =       "Gilbert Wright (Gilbert W.) Stewart and {Ji-guang}
                 Sun",
  title =        "Matrix Perturbation Theory",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xv + 365",
  year =         "1990",
  ISBN =         "0-12-670230-6 (hardcover)",
  ISBN-13 =      "978-0-12-670230-9 (hardcover)",
  LCCN =         "QA871 .S775 1990",
  bibdate =      "Thu May 29 07:15:52 MDT 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Computer science and scientific computing",
  URL =          "http://catalog.hathitrust.org/api/volumes/oclc/21227976.html;
                 http://www.loc.gov/catdir/description/els032/90033378.htm;
                 http://www.loc.gov/catdir/description/els032/90033378.html;
                 http://www.loc.gov/catdir/toc/els031/90033378.htm;
                 http://www.loc.gov/catdir/toc/els031/90033378.html",
  acknowledgement = ack-nhfb,
  GWS-number =   "B3",
  subject =      "Perturbation (Mathematics); Matrices",
  tableofcontents = "I. Preliminaries \\
                 1. Notation \\
                 2. The $QR$ decomposition \\
                 projections \\
                 3. Eigenvalues and eigenvectors \\
                 4. The singular value decomposition \\
                 II. Norms and metrics \\
                 1. Vector norms \\
                 2. Matrix norms \\
                 3. Unitarily invariant norms \\
                 4. Metrics on subspaces of C'n' \\
                 III. Linear systems and least squares problems \\
                 1. The pseudo-inverse and least squares \\
                 2. Inverses and linear systems \\
                 3. The pseudo-inverse \\
                 4. Projections \\
                 5. The Linear least squares problem \\
                 IV. The perturbation of Eigenvalues \\
                 1. General perturbation theorems \\
                 2. Gerschgorin theory: differentiability \\
                 3. Normal and diagonalizable matrices \\
                 4. Hermitian matrices \\
                 5. Some further results \\
                 V. Invariant subspaces \\
                 1. The theory of simple invariant subspaces \\
                 2. Perturbation of invariant subspaces \\
                 3. Hermitian matrices \\
                 4. The singular value decomposition \\
                 VI. Generalized Eigenvalue problems \\
                 1. Background \\
                 2. Regular matrix pairs \\
                 3. Definite matrix pairs \\
                 References \\
                 Notation \\
                 Index",
}

@Article{Stummel:1980:REA,
  author =       "F. Stummel",
  title =        "Rounding Error Analysis of Elementary Numerical
                 Algorithms",
  journal =      j-COMPUTING,
  volume =       "Suppl. 2",
  pages =        "169--195",
  year =         "1980",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Stummel:1981:PTE,
  author =       "F. Stummel",
  title =        "Perturbation Theory For Evaluation Algorithms of
                 Arithmetic Expressions",
  journal =      j-MATH-COMP,
  volume =       "37",
  number =       "156",
  pages =        "435--473",
  year =         "1981",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stummel:1982:OEE,
  author =       "F. Stummel",
  title =        "Optimal Error Estimates For {Gaussian} Elimination in
                 Floating-Point Arithmetic",
  journal =      j-ZAMM,
  volume =       "62",
  pages =        "T355--T357",
  year =         "1982",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Stummel:1985:FEAa,
  author =       "Friedrich Stummel",
  title =        "Forward Error Analysis of {Gaussian} Elimination,
                 {Part I}: {Error} and Residual Estimates",
  journal =      j-NUM-MATH,
  volume =       "46",
  pages =        "365--395",
  year =         "1985",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Stummel:1985:FEAb,
  author =       "Friedrich Stummel",
  title =        "Forward Error Analysis of {Gaussian} Elimination,
                 {Part II}: {Stability} Theorems",
  journal =      j-NUM-MATH,
  volume =       "46",
  pages =        "397--415",
  year =         "1985",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Stummel:1985:SOE,
  author =       "F. Stummel",
  title =        "Strict Optimal Error Estimates for {Gaussian}
                 Elimination",
  journal =      j-ZAMM,
  volume =       "65",
  pages =        "T405--T407",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Steele:1990:HPF,
  author =       "Guy L. {Steele, Jr.} and Jon L. White",
  title =        "How to Print Floating-Point Numbers Accurately",
  journal =      j-SIGPLAN,
  volume =       "25",
  number =       "6",
  pages =        "112--126",
  year =         "1990",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Article{Stoer:1962:TDM,
  author =       "Josef Stoer and C. Witzgall",
  title =        "Transformations by Diagonal Matrices in a Normed
                 Space",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "158--171",
  year =         "1962",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Sun:1995:BKR,
  author =       "Xiaobai Sun and Christian H. Bischof",
  title =        "A Basis-Kernel Representation of Orthogonal Matrices",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "4",
  pages =        "1184--1196",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Sun:1991:PBC,
  author =       "{Ji-guang} Sun",
  title =        "Perturbation Bounds for the {Cholesky} and {$QR$}
                 Factorizations",
  journal =      j-BIT,
  volume =       "31",
  pages =        "341--352",
  year =         "1991",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Sun:1992:REP,
  author =       "{Ji-guang} Sun",
  title =        "Rounding-Error and Perturbation Bounds for the
                 {Cholesky} and {$LDL^T$} Factorizations",
  journal =      j-LAA,
  volume =       "173",
  pages =        "77--97",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Sun:1992:CPB,
  author =       "{Ji-guang} Sun",
  title =        "Componentwise Perturbation Bounds for Some Matrix
                 Decompositions",
  journal =      j-BIT,
  volume =       "32",
  number =       "4",
  pages =        "702--714",
  year =         "1992",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Sun:1995:NBP,
  author =       "{Ji-guang} Sun",
  title =        "A Note on Backward Perturbations for the {Hermitian}
                 Eigenvalue Problem",
  journal =      j-BIT,
  volume =       "35",
  pages =        "385--393",
  year =         "1995",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Sun:1995:PBQ,
  author =       "{Ji-guang} Sun",
  title =        "On Perturbation Bounds for the {QR} Factorization",
  journal =      j-LAA,
  volume =       "215",
  pages =        "95--111",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Sun:1996:OBP,
  author =       "{Ji-guang} Sun",
  title =        "Optimal Backward Perturbation Bounds for the Linear
                 Least-Squares Problem with Multiple Right-Hand Sides",
  journal =      j-IMAJNA,
  volume =       "16",
  number =       "1",
  pages =        "1--11",
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Sun:1997:OBPa,
  author =       "{Ji-guang} Sun",
  title =        "On Optimal Backward Perturbation Bounds for the Linear
                 Least Squares Problem",
  journal =      j-BIT,
  volume =       "37",
  number =       "1",
  pages =        "179--188",
  year =         "1997",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Sun:1998:BSB,
  author =       "{Ji-guang} Sun",
  title =        "Bounds for the Structured Backward Errors of
                 {Vandermonde} Systems",
  journal =      j-SIMAX,
  volume =       "20",
  number =       "1",
  pages =        "45--59",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{sunM92,
  key =          "Sun",
  title =        "{SPARCompiler FORTRAN}: {Numerical} Computation
                 Guide",
  publisher =    "Sun Microsystems, Inc.",
  address =      "Mountain View, CA, USA",
  month =        oct,
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Part No. 800-7097-11, Revision A",
}

@Book{sunM92a,
  key =          "Sun",
  title =        "{SPARCompiler FORTRAN} \textup{2.0.1}: {User's}
                 Guide",
  publisher =    "Sun Microsystems, Inc.",
  address =      "Mountain View, CA, USA",
  month =        oct,
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Part No. 800-6552-11, Revision A",
}

@Article{Sun:1997:OBPb,
  author =       "{Ji-guang} Sun and Zheng Sun",
  title =        "Optimal Backward Perturbation Bounds for
                 Underdetermined Systems",
  journal =      j-SIMAX,
  volume =       "18",
  number =       "2",
  pages =        "393--402",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Sleijpen:2000:DER,
  author =       "Gerard L. G. Sleijpen and Henk A. van der Vorst and
                 Jan Modersitzki",
  title =        "Differences in the Effects of Rounding Errors in
                 {Krylov} Solvers for Symmetric Indefinite Linear
                 Systems",
  journal =      j-SIMAX,
  volume =       "22",
  number =       "3",
  pages =        "726--751",
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Swartzlander:1975:SLN,
  author =       "Earl E. {Swartzlander, Jr.} and Aristides G.
                 Alexopolous",
  title =        "The Sign/Logarithm Number System",
  journal =      j-IEEE-C,
  volume =       "C-24",
  number =       "12",
  pages =        "1238--1242",
  year =         "1975",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Swann:1972:DSM,
  author =       "W. H. Swann",
  editor =       "W. Murray",
  booktitle =    "Numerical Methods for Unconstrained Optimization",
  title =        "Direct Search Methods",
  publisher =    pub-AP # ", " # pub-AP:adr-L,
  pages =        "13--28",
  year =         "1972",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Swann:1974:COD,
  author =       "W. H. Swann",
  editor =       "P. E. Gill and W. Murray",
  booktitle =    "Numerical Methods for Constrained Optimization",
  title =        "Constrained Optimization by Direct Search",
  publisher =    pub-AP # ", " # pub-AP:adr-L,
  pages =        "191--217",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Swartzlander:1980:CA,
  editor =       "Earl E. {Swartzlander, Jr.}",
  title =        "Computer Arithmetic",
  volume =       "21",
  publisher =    "Dowden, Hutchinson and Ross",
  address =      "Stroudsburg, PA, USA",
  year =         "1980",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Benchmark Papers in Electrical Engineering and
                 Computer Science",
}

@Article{Sweeney:1965:AFP,
  author =       "D. W. Sweeney",
  title =        "An Analysis of Floating-Point Addition",
  journal =      j-IBM-SYS-J,
  volume =       "4",
  pages =        "31--42",
  year =         "1965",
  CODEN =        "IBMSA7",
  ISSN =         "0018-8670",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted in
                 \cite[pp.~317--328]{Swartzlander:1980:CA}",
  fjournal =     "IBM Systems Journal",
}

@Book{sylv04,
  key =          "Sylvester, James Joseph",
  title =        "The Collected Mathematical Papers of James Joseph
                 Sylvester",
  volume =       "1 (1837--1853)",
  publisher =    pub-CUP,
  pages =        "xii + 650",
  year =         "1904",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Sylvester:1850:AAN,
  author =       "J. J. Sylvester",
  title =        "Additions to the Articles, ``{On a New Class of
                 Theorems},'' and ``{On Pascal's Theorem}''",
  journal =      j-PHIL-MAGAZINE,
  volume =       "37",
  pages =        "363--370",
  year =         "1850",
  CODEN =        "PHMAA4",
  ISSN =         "0031-8086",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted in \cite[pp.~1451--151]{sylv04}",
}

@Article{Sylvester:1851:RBM,
  author =       "J. J. Sylvester",
  title =        "On the Relation Between the Minor Determinants of
                 Linearly Equivalent Quadratic Functions",
  journal =      j-PHIL-MAGAZINE,
  volume =       "(Fourth Series) 1",
  pages =        "295--305",
  year =         "1851",
  CODEN =        "PHMAA4",
  ISSN =         "0031-8086",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted in \cite[pp.~241--250]{sylv04}",
}

@Article{Sylvester:1884:EM,
  author =       "J. J. Sylvester",
  title =        "Sur l'Equation en Matrices {$px=xq$}",
  journal =      j-C-R-ACAD-SCI,
  pages =        "67--71 and 115--116",
  year =         "1884",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Comptes Rendus de l'Acad{\'e}mie des Sciences",
}

@Article{Tang:1981:BDV,
  author =       "W. P. Tang and G. H. Golub",
  title =        "The Block Decomposition of a {Vandermonde} Matrix and
                 its Applications",
  journal =      j-BIT,
  volume =       "21",
  pages =        "505--517",
  year =         "1981",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@InCollection{Taussky:1962:EFM,
  author =       "Olga Taussky and Marvin Marcus",
  editor =       "John Todd",
  booktitle =    "Survey of Numerical Analysis",
  title =        "Eigenvalues of Finite Matrices",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  pages =        "279--313",
  year =         "1962",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Tang:1989:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Exponential
                 Function in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "15",
  number =       "2",
  pages =        "144--157",
  year =         "1989",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Tang:1990:AET,
  author =       "Ping Tak Peter Tang",
  title =        "Accurate and Efficient Testing of the Exponential and
                 Logarithm Functions",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "185--200",
  year =         "1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Tang:1990:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Logarithm Function
                 in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "378--400",
  year =         "1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@InProceedings{Tang:1991:TLA,
  author =       "Ping Tak Peter Tang",
  editor =       "Peter Kornerup and David W. Matula",
  booktitle =    "Proc. 10th IEEE Symposium on Computer Arithmetic",
  title =        "Table-Lookup Algorithms for Elementary Functions and
                 Their Error Analysis",
  publisher =    "IEEE Computer Society Press, Los Alamitos, CA, USA",
  pages =        "232--236",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Tang:1992:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Expm1 Function in
                 {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "211--222",
  year =         "1992",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Book{Taub:1963:JNC,
  editor =       "A. H. Taub",
  title =        "{John von Neumann} Collected Works",
  volume =       "V, {Design of Computers, Theory of Automata and
                 Numerical Analysis}",
  publisher =    "Pergamon",
  address =      "Oxford",
  pages =        "ix + 784",
  year =         "1963",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Taussky:1949:RCC,
  author =       "Olga Taussky",
  title =        "A Remark Concerning the Characteristic Roots of the
                 Finite Segments of the {Hilbert} Matrix",
  journal =      j-QUART-J-MATH,
  volume =       "20",
  pages =        "80--83",
  year =         "1949",
  CODEN =        "QJMAAT",
  ISSN =         "0033-5606 (print), 1464-3847 (electronic)",
  ISSN-L =       "0033-5606",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Quarterly Journal of Mathematics",
}

@Article{Taussky:1988:HBT,
  author =       "Olga Taussky",
  title =        "How {I} Became a Torchbearer for Matrix Theory",
  journal =      j-AMM,
  volume =       "95",
  number =       "9",
  pages =        "801--812",
  month =        nov,
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Tasche:2001:WAC,
  author =       "Manfred Tasche and Hansmartin Zeuner",
  title =        "Worst and Average Case Roundoff Error Analysis for
                 {FFT}",
  journal =      j-BIT,
  volume =       "41",
  number =       "3",
  pages =        "563--581",
  year =         "2001",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Book{Barrett:1994:TSL,
  author =       "Richard Barrett and Michael Berry and Tony F. Chan and
                 James Demmel and June Donato and Jack Dongarra and
                 Victor Eijkhout and Roldan Pozo and Charles Romine and
                 Henk van der Vorst",
  title =        "Templates for the Solution of Linear Systems:
                 {Building} Blocks for Iterative Methods",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xiii + 112",
  year =         "1994",
  ISBN =         "0-89871-328-5",
  ISBN-13 =      "978-0-89871-328-2",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Thacher:1961:ACP,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Algorithm 43: {Crout} With Pivoting {II}",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "176--177",
  year =         "1961",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Book{Thisted:1988:ESC,
  author =       "Ronald A. Thisted",
  title =        "Elements of Statistical Computing: {Numerical}
                 Computation",
  publisher =    "Chapman and Hall",
  address =      "New York",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Thompson:1942:GFC,
  author =       "D'Arcy Wentworth Thompson",
  title =        "On Growth and Form. {The} Complete Revised Edition",
  publisher =    pub-CUP,
  pages =        "viii + 1116",
  year =         "1942",
  ISBN =         "0-486-67135-6",
  ISBN-13 =      "978-0-486-67135-2",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted by Dover, New York, 1992",
}

@Article{Tienari:1970:SMR,
  author =       "Martti Tienari",
  title =        "A Statistical Model of Roundoff Error for Varying
                 Length Floating-Point Arithmetic",
  journal =      j-BIT,
  volume =       "10",
  pages =        "355--365",
  year =         "1970",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Tisseur:2001:QEP,
  author =       "Fran\c{c}oise Tisseur and Karl Meerbergen",
  title =        "The Quadratic Eigenvalue Problem",
  journal =      j-SIREV,
  volume =       "43",
  number =       "2",
  pages =        "235--286",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Tisseur:2001:NMF,
  author =       "Fran\c{c}oise Tisseur",
  title =        "Newton's Method in Floating Point Arithmetic and
                 Iterative Refinement of Generalized Eigenvalue
                 Problems",
  journal =      j-SIMAX,
  volume =       "22",
  number =       "4",
  pages =        "1038--1057",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InCollection{Todd:1954:CFS,
  author =       "John Todd",
  editor =       "Olga Taussky",
  booktitle =    "Contributions to the Solution of Systems of Linear
                 Equations and the Determination of Eigenvalues",
  title =        "The Condition of the Finite Segments of the {Hilbert}
                 Matrix",
  number =       "39",
  publisher =    "National Bureau of Standards, United States Department
                 of Commerce",
  address =      "Washington, D. C.",
  pages =        "109--116",
  year =         "1954",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Applied Mathematics Series",
}

@Article{Todd:1961:CPC,
  author =       "John Todd",
  title =        "Computational Problems Concerning the {Hilbert}
                 Matrix",
  journal =      j-J-RES-NATL-BUR-STAND-B,
  volume =       "65",
  number =       "1",
  pages =        "19--22",
  year =         "1961",
  CODEN =        "JNBBAU",
  ISSN =         "0022-4340",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Journal of Research of the National Bureau of Standards. Section B, Mathematics and Mathematical Physics",
  journal-URL =  "http://www.nist.gov/nvl/jrespastpapers.cfm",
}

@InProceedings{Todd:1968:CN,
  author =       "J. Todd",
  booktitle =    "Programmation en Math{\'e}matiques Num{\'e}riques,
                 Besan{\c{c}}on, 1966",
  title =        "On Condition Numbers",
  volume =       "7 (no. 165)",
  pages =        "141--159",
  year =         "1968",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "{\'E}ditions Centre Nat. Recherche Sci., Paris",
}

@Book{Todd:1977:BNM,
  author =       "John Todd",
  title =        "Basic Numerical Mathematics, Vol.~2: Numerical
                 Algebra",
  publisher =    "Birkh{\"a}user, Basel, and Academic Press, New York",
  year =         "1977",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Toledo:1997:LRL,
  author =       "Sivan Toledo",
  title =        "Locality of Reference in {LU} Decomposition with
                 Partial Pivoting",
  journal =      j-SIMAX,
  volume =       "18",
  number =       "4",
  pages =        "1065--1081",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@PhdThesis{Torczon:1989:MDS,
  author =       "Virginia J. Torczon",
  title =        "Multi-Directional Search: {A} Direct Search Algorithm
                 for Parallel Machines",
  school =       "Rice University",
  address =      "Houston, TX, USA",
  pages =        "vii + 85",
  month =        may,
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Torczon:1991:CMS,
  author =       "Virginia J. Torczon",
  title =        "On the Convergence of the Multidirectional Search
                 Algorithm",
  journal =      j-SIOPT,
  volume =       "1",
  number =       "1",
  pages =        "123--145",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Torczon:1997:CPS,
  author =       "Virginia J. Torczon",
  title =        "On the Convergence of Pattern Search Algorithms",
  journal =      j-SIOPT,
  volume =       "7",
  number =       "1",
  pages =        "1--25",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Tornheim:1965:MTP,
  author =       "L. Tornheim",
  title =        "Maximum Third Pivot for {Gaussian} Reduction",
  type =         "Technical Report",
  institution =  "Calif. Research Corp.",
  address =      "Richmond, CA",
  year =         "1965",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Cited in \cite{Cryer:1968:PSG}",
}

@Article{Toh:1994:PPP,
  author =       "Kim-Chuan Toh and Lloyd N. Trefethen",
  title =        "Pseudozeros of Polynomials and Pseudospectra of
                 Companion Matrices",
  journal =      j-NUM-MATH,
  volume =       "68",
  number =       "3",
  pages =        "403--425",
  year =         "1994",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Traub:1966:APU,
  author =       "J. F. Traub",
  title =        "Associated Polynomials and Uniform Methods for the
                 Solution of Linear Problems",
  journal =      j-SIREV,
  volume =       "8",
  number =       "3",
  pages =        "277--301",
  year =         "1966",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Trefethen:1997:NLA,
  author =       "Lloyd N. Trefethen and David {Bau III}",
  title =        "Numerical Linear Algebra",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xii + 361",
  year =         "1997",
  ISBN =         "0-89871-361-7",
  ISBN-13 =      "978-0-89871-361-9",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Trefethen:1985:TMG,
  author =       "Lloyd N. Trefethen",
  title =        "Three Mysteries of {Gaussian} Elimination",
  journal =      j-SIGNUM,
  volume =       "20",
  pages =        "2--5",
  year =         "1985",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J690",
}

@InProceedings{Trefethen:1990:ATN,
  author =       "Lloyd N. Trefethen",
  editor =       "J. C. Mason and M. G. Cox",
  booktitle =    "Algorithms for Approximation II",
  title =        "Approximation Theory and Numerical Linear Algebra",
  publisher =    pub-CH # ", " # pub-CH:adr-L,
  pages =        "336--360",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Trefethen:1992:PM,
  author =       "Lloyd N. Trefethen",
  editor =       "D. F. Griffiths and G. A. Watson",
  booktitle =    "Numerical Analysis \textup{1991}, Proceedings of the
                 \textup{14}th Dundee Conference",
  title =        "Pseudospectra of Matrices",
  volume =       "260",
  publisher =    pub-Longman-ST # ", " # pub-Longman-ST:adr,
  pages =        "234--266",
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Pitman Research Notes in Mathematics",
}

@Article{Trefethen:1992:DNA,
  author =       "Lloyd N. Trefethen",
  title =        "The Definition of Numerical Analysis",
  journal =      j-SIAM-NEWS,
  volume =       "25",
  pages =        "6 and 22",
  month =        nov,
  year =         "1992",
  ISSN =         "0036-1437",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@InProceedings{Trefethen:1999:SP,
  author =       "Lloyd N. Trefethen",
  editor =       "Mark Ainsworth and Jeremy Levesley and Marco
                 Marletta",
  booktitle =    "The Graduate Student's Guide to Numerical Analysis
                 '98",
  title =        "Spectra and Pseudospectra",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "217--250",
  year =         "1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Tropp:1984:FA,
  author =       "Henry S. Tropp",
  title =        "{FORTRAN} Anecdotes",
  journal =      j-AHC,
  volume =       "6",
  number =       "1",
  pages =        "59--64",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Tropp:1984:OTE,
  author =       "Henry S. Tropp",
  title =        "Origin of the Term {\emph{Bit}}",
  journal =      j-AHC,
  volume =       "6",
  number =       "2",
  pages =        "152--155",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Trefethen:1990:ACS,
  author =       "Lloyd N. Trefethen and Robert S. Schreiber",
  title =        "Average-Case Stability of {Gaussian} Elimination",
  journal =      j-SIMAX,
  volume =       "11",
  number =       "3",
  pages =        "335--360",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Trefethen:1987:IPS,
  author =       "Lloyd N. Trefethen and Manfred R. Trummer",
  title =        "An Instability Phenomenon in Spectral Methods",
  journal =      j-SINUM,
  volume =       "24",
  number =       "5",
  pages =        "1008--1023",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Tsao:1975:NIH,
  author =       "{Nai-kuan} Tsao",
  title =        "A Note on Implementing the {Householder}
                 Transformation",
  journal =      j-SINUM,
  volume =       "12",
  number =       "1",
  pages =        "53--58",
  year =         "1975",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Tsao:1983:SAE,
  author =       "{Nai-kuan} Tsao",
  title =        "A Simple Approach to the Error Analysis of
                 Division-Free Numerical Algorithms",
  journal =      j-IEEE-C,
  volume =       "C-32",
  number =       "4",
  pages =        "343--351",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Turnbull:1932:ITC,
  author =       "H. W. Turnbull and A. C. Aitken",
  title =        "An Introduction to the Theory of Canonical Matrices",
  publisher =    "Blackie, London and Glasgow",
  pages =        "xiii + 200",
  year =         "1932",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted with appendix, 1952",
}

@Article{Tucker:2002:ROS,
  author =       "Warwick Tucker",
  title =        "A Rigorous {ODE} Solver and {Smale's} 14th Problem",
  journal =      j-FOCM,
  volume =       "2",
  number =       "1",
  pages =        "53--117",
  year =         "2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Turing:1936:CNA,
  author =       "A. M. Turing",
  title =        "On Computable Numbers, with an Application to the
                 {Entscheidungsproblem}",
  journal =      j-PROC-LONDON-MATH-SOC-3,
  volume =       "42",
  pages =        "230--265",
  year =         "1936",
  CODEN =        "PLMTAL",
  ISSN =         "0024-6115 (print), 1460-244x (electronic)",
  ISSN-L =       "0024-6115",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Proceedings of the London Mathematical Society. Third Series",
}

@TechReport{Turing:1945:PDM,
  author =       "A. M. Turing",
  title =        "Proposal for Development in the {Mathematics Division}
                 of an {Automatic Computing Engine} {(ACE)}",
  type =         "{Report E.882, Executive Committee}",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  year =         "1945",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted in \cite[pp.~20-105]{Carpenter:1986:MTA} and
                 \cite[pp.~1--86]{Ince:1992:CWM}",
}

@Article{Turing:1948:REM,
  author =       "A. M. Turing",
  title =        "Rounding-Off Errors in Matrix Processes",
  journal =      j-QJMAM,
  volume =       "1",
  pages =        "287--308",
  year =         "1948",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted in \cite{Britton:1992:CWM} with summary and
                 notes (including corrections)",
}

@Book{Turnbull:1929:TDM,
  author =       "H. W. Turnbull",
  title =        "The Theory of Determinants, Matrices, and Invariants",
  publisher =    "Blackie",
  address =      "London and Glasgow",
  pages =        "xvi + 338",
  year =         "1929",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Turner:1982:DLS,
  author =       "Peter R. Turner",
  title =        "The Distribution of Leading Significant Digits",
  journal =      j-IMAJNA,
  volume =       "2",
  pages =        "407--412",
  year =         "1982",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Turner:1984:FRD,
  author =       "Peter R. Turner",
  title =        "Further Revelations on {L.S.D.}",
  journal =      j-IMAJNA,
  volume =       "4",
  pages =        "225--231",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Turner:1991:WRR,
  author =       "Peter R. Turner",
  title =        "Will the ``Real'' Real Arithmetic Please Stand Up?",
  journal =      j-NAMS,
  volume =       "38",
  number =       "4",
  pages =        "298--304",
  year =         "1991",
  CODEN =        "AMNOAN",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
}

@Article{Tyrtyshnikov:1991:CTM,
  author =       "Evgenij E. Tyrtyshnikov",
  title =        "Cauchy-{Toeplitz} Matrices and Some Applications",
  journal =      j-LAA,
  volume =       "149",
  pages =        "1--18",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Urabe:1968:RED,
  author =       "Minoru Urabe",
  title =        "Roundoff Error Distribution in Fixed-Point
                 Multiplication and a Remark About the Rounding Rule",
  journal =      j-SINUM,
  volume =       "5",
  number =       "2",
  pages =        "202--210",
  year =         "1968",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Uspensky:1948:TE,
  author =       "J. V. Uspensky",
  title =        "Theory of Equations",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  pages =        "vii + 353",
  year =         "1948",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Vanderbei:1995:SQD,
  author =       "Robert J. Vanderbei",
  title =        "Symmetric Quasi-Definite Matrices",
  journal =      j-SIOPT,
  volume =       "5",
  number =       "1",
  pages =        "100--113",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Loan:1979:NEM,
  author =       "Charles F. {Van Loan}",
  title =        "A Note on the Evaluation of Matrix Polynomials",
  journal =      j-IEEE-AC,
  volume =       "AC-24",
  number =       "2",
  pages =        "320--321",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Loan:1985:MWE,
  author =       "Charles F. {Van Loan}",
  title =        "On the Method of Weighting for Equality-Constrained
                 Least-Squares Problems",
  journal =      j-SINUM,
  volume =       "22",
  number =       "5",
  pages =        "851--864",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Loan:1987:ECE,
  author =       "Charles F. {Van Loan}",
  title =        "On Estimating the Condition of Eigenvalues and
                 Eigenvectors",
  journal =      j-LAA,
  volume =       "88/89",
  pages =        "715--732",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Loan:1992:CFF,
  author =       "Charles F. {Van Loan}",
  title =        "Computational Frameworks for the {Fast Fourier
                 Transform}",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xiii + 273",
  year =         "1992",
  DOI =          "https://doi.org/10.1137/1.9781611970999",
  ISBN =         "0-89871-285-8 (paperback), 1-61197-099-7 (e-book)",
  ISBN-13 =      "978-0-89871-285-8 (paperback), 978-1-61197-099-9
                 (e-book)",
  LCCN =         "QA403.5 .V35 1992",
  bibdate =      "Mon Oct 26 07:31:14 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  acknowledgement = ack-nhfb,
  series =       "Frontiers in applied mathematics",
  subject =      "Fourier transformations",
  tableofcontents = "1: The Radix-2 Frameworks: Matrix Notation and
                 Algorithms \\
                 The FFT Idea \\
                 The Cooley--Tukey Factorization \\
                 Weight and Butterfly Computations \\
                 Bit Reversal and Transposition \\
                 The Cooley--Tukey Framework \\
                 The Stockham Autosort Frameworks \\
                 The Pease Framework \\
                 Decimation in Frequency and Inverse FFTs \\
                 2: General Radix Frameworks: The General Radix Ideas
                 \\
                 Index Reversal and Transposition \\
                 Mixed-Radix Factorizations \\
                 Radix-4 and Radix-8 Frameworks \\
                 The Split-Radix Frameworks \\
                 3: High Performance Frameworks: The Multiple DFT
                 Problem \\
                 Matrix Transposition \\
                 The Large Single-Vector FFT Problem \\
                 Multi-Dimensional FFT Problem \\
                 Distributed Memory FFTs \\
                 Shared Memory FFTs \\
                 4: Selected Topics: Prime Factor FFTs \\
                 Convolution \\
                 FFTs of Real Data \\
                 Cosine and Sine Transforms \\
                 Fast Poisson Solvers \\
                 Bibliography \\
                 Index",
}

@Book{Rienen:2001:NMC,
  author =       "Ursula van Rienen",
  title =        "Numerical Methods in Computational Electrodynamics:
                 {Linear} Systems in Practical Applications",
  number =       "12",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "xiii + 375",
  year =         "2001",
  ISBN =         "3-540-67629-5",
  ISBN-13 =      "978-3-540-67629-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Computational Science and
                 Engineering",
}

@Article{Varah:1972:SBT,
  author =       "J. M. Varah",
  title =        "On the Solution of Block-Tridiagonal Systems Arising
                 From Certain Finite-Difference Equations",
  journal =      j-MATH-COMP,
  volume =       "26",
  number =       "120",
  pages =        "859--868",
  year =         "1972",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Varah:1975:LBS,
  author =       "J. M. Varah",
  title =        "A Lower Bound for the Smallest Singular Value of a
                 Matrix",
  journal =      j-LAA,
  volume =       "11",
  pages =        "3--5",
  year =         "1975",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Varah:1979:STM,
  author =       "J. M. Varah",
  title =        "On the Separation of Two Matrices",
  journal =      j-SINUM,
  volume =       "16",
  number =       "2",
  pages =        "216--222",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Varga:1976:DDA,
  author =       "Richard S. Varga",
  title =        "On Diagonal Dominance Arguments for Bounding
                 {$\|A^{-1}\|_\infty$}",
  journal =      j-LAA,
  volume =       "14",
  pages =        "211--217",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Varga:1990:SCM,
  author =       "Richard S. Varga",
  title =        "Scientific Computation on Mathematical Problems and
                 Conjectures",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "vi + 122",
  year =         "1990",
  ISBN =         "0-89871-257-2",
  ISBN-13 =      "978-0-89871-257-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Vavasis:1989:GEP,
  author =       "S. A. Vavasis",
  title =        "Gaussian Elimination with Partial Pivoting is
                 {P}-Complete",
  journal =      j-SIAM-J-DISCR-MATH,
  volume =       "2",
  pages =        "413--423",
  year =         "1989",
  CODEN =        "SJDMEC",
  ISSN =         "0895-4801 (print), 1095-7146 (electronic)",
  ISSN-L =       "0895-4801",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "SIAM Journal on Discrete Mathematics",
  journal-URL =  "http://epubs.siam.org/sidma",
}

@Article{Verdonk:2001:PRIa,
  author =       "Brigitte Verdonk and Annie Cuyt and Dennis
                 Verschaeren",
  title =        "A Precision and Range Independent Tool for Testing
                 Floating-Point Arithmetic {I}: {Basic} Operations,
                 Square Root and Remainder",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "92--118",
  year =         "2001",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Verdonk:2001:PRIb,
  author =       "Brigitte Verdonk and Annie Cuyt and Dennis
                 Verschaeren",
  title =        "A Precision and Range Independent Tool for Testing
                 Floating-Point Arithmetic {II}: {Conversions}",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "119--140",
  year =         "2001",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Sluis:1969:CNE,
  author =       "A. van der Sluis",
  title =        "Condition Numbers and Equilibration of Matrices",
  journal =      j-NUM-MATH,
  volume =       "14",
  pages =        "14--23",
  year =         "1969",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Sluis:1970:CEP,
  author =       "A. van der Sluis",
  title =        "Condition, Equilibration and Pivoting in Linear
                 Algebraic Systems",
  journal =      j-NUM-MATH,
  volume =       "15",
  pages =        "74--86",
  year =         "1970",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Sluis:1975:SSL,
  author =       "A. van der Sluis",
  title =        "Stability of the Solutions of Linear Least Squares
                 Problems",
  journal =      j-NUM-MATH,
  volume =       "23",
  pages =        "241--254",
  year =         "1975",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{vanVeldhuizen:1977:NPP,
  author =       "M. {van Veldhuizen}",
  title =        "A Note on Partial Pivoting and {Gaussian}
                 Elimination",
  journal =      j-NUM-MATH,
  volume =       "29",
  pages =        "1--10",
  year =         "1977",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Verzuh:1949:SSL,
  author =       "Frank M. Verzuh",
  title =        "The Solution of Simultaneous Linear Equations with the
                 Aid of the 602 Calculating Punch",
  journal =      j-MTAC,
  volume =       "3",
  pages =        "453--462",
  year =         "1949",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Vignes:1986:ESM,
  author =       "J. Vignes and R. Alt",
  editor =       "Willard L. Miranker and Richard A. Toupin",
  booktitle =    "Accurate Scientific Computations, Proceedings, 1985",
  title =        "An Efficient Stochastic Method for Round-Off Error
                 Analysis",
  volume =       "235",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "183--205",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Computer Science",
}

@InProceedings{Vitasek:1969:NSS,
  author =       "Emil Vitasek",
  editor =       "J. Ll. Morris",
  booktitle =    "Conference on the Numerical Solution of Differential
                 Equations",
  title =        "The Numerical Stability in Solution of Differential
                 Equations",
  volume =       "109",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "87--111",
  year =         "1969",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Mathematics",
}

@Article{Vitenko:1968:OAA,
  author =       "I. V. Viten'ko",
  title =        "Optimum Algorithms for Adding and Multiplying on
                 Computers with a Floating Point",
  journal =      j-USSR-COMP-MATH-MATH-PHYS,
  volume =       "8",
  number =       "5",
  pages =        "183--195",
  year =         "1968",
  CODEN =        "CMMPA9",
  ISSN =         "0041-5553, 0502-9902",
  ISSN-L =       "0041-5553",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "U.S.S.R. Computational Mathematics and Mathematical Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00415553",
}

@Article{Viswanath:1998:CNR,
  author =       "D. Viswanath and L. N. Trefethen",
  title =        "Condition Numbers of Random Triangular Matrices",
  journal =      j-SIMAX,
  volume =       "19",
  number =       "2",
  pages =        "564--581",
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Neumann:1947:NIM,
  author =       "John von Neumann and Herman H. Goldstine",
  title =        "Numerical Inverting of Matrices of High Order",
  journal =      j-BAMS,
  volume =       "53",
  pages =        "1021--1099",
  year =         "1947",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted in \cite[pp.~479--557]{Taub:1963:JNC}",
}

@InProceedings{vanderVorst:1990:CBP,
  author =       "H. A. van der Vorst",
  editor =       "Owe Axelsson and {Lily Yu.} Kolotilina",
  booktitle =    "Preconditioned Conjugate Gradient Methods",
  title =        "The Convergence Behaviour of Preconditioned {CG} and
                 {CG-S} in the Presence of Rounding Errors",
  volume =       "1457",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "126--136",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Mathematics",
}

@Article{Wachpress:1988:ISL,
  author =       "Eugene L. Wachpress",
  title =        "Iterative Solution of the {Lyapunov} Matrix Equation",
  journal =      j-APPL-MATH-LETT,
  volume =       "1",
  number =       "1",
  pages =        "87--90",
  year =         "1988",
  CODEN =        "AMLEEL",
  ISSN =         "0893-9659 (print), 1873-5452 (electronic)",
  ISSN-L =       "0893-9659",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Applied Mathematics Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08939659",
}

@Book{Wallis:1990:IFP,
  editor =       "Peter J. L. Wallis",
  title =        "Improving Floating-Point Programming",
  publisher =    "Wiley",
  address =      "London",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Wallis:1993:HM,
  author =       "W. D. Wallis",
  editor =       "Richard A. Brualdi and Shmuel Friedland and Victor
                 Klee",
  booktitle =    "Combinatorial and Graph-Theoretical Problems in Linear
                 Algebra",
  title =        "Hadamard Matrices",
  volume =       "50",
  publisher =    pub-Springer # ", " # pub-Springer:adr-NY,
  pages =        "235--243",
  year =         "1993",
  ISBN =         "0-387-94086-3",
  ISBN-13 =      "978-0-387-94086-1",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "IMA Volumes in Mathematics and Its Applications",
}

@Article{Ward:1976:QAH,
  author =       "Robert C. Ward",
  title =        "The {QR} Algorithm and {Hyman's} Method on Vector
                 Computers",
  journal =      j-MATH-COMP,
  volume =       "30",
  number =       "133",
  pages =        "132--142",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Wareeditor:1960:SCT,
  author =       "Willis H. {Ware, editor}",
  title =        "Soviet Computer Technology---1959",
  journal =      j-CACM,
  volume =       "3",
  number =       "3",
  pages =        "131--166",
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Watson:1991:AOS,
  author =       "G. A. Watson",
  title =        "An Algorithm for Optimal {$\ell_2$} Scaling of
                 Matrices",
  journal =      j-IMAJNA,
  volume =       "11",
  pages =        "481--492",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Wedderburn:1934:LM,
  author =       "J. H. M. Wedderburn",
  title =        "Lectures on Matrices",
  volume =       "17",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "vii + 205",
  year =         "1934",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "American Mathematical Society Colloquium
                 Publications",
}

@Article{Wedin:1973:PTP,
  author =       "Per-{\AA}ke Wedin",
  title =        "Perturbation Theory for Pseudo-Inverses",
  journal =      j-BIT,
  volume =       "13",
  pages =        "217--232",
  year =         "1973",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Wei:1990:PLS,
  author =       "Musheng Wei",
  title =        "Perturbation of the Least Squares Problem",
  journal =      j-LAA,
  volume =       "141",
  pages =        "177--182",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Wendroff:1966:TNA,
  author =       "Burton Wendroff",
  title =        "Theoretical Numerical Analysis",
  publisher =    "Academic Press",
  address =      "New York",
  pages =        "xi + 239",
  year =         "1966",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Werner:1984:PIL,
  author =       "Wilhelm Werner",
  title =        "Polynomial Interpolation: {Lagrange} Versus {Newton}",
  journal =      j-MATH-COMP,
  volume =       "43",
  number =       "167",
  pages =        "205--217",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Westlake:1968:HNM,
  author =       "Joan R. Westlake",
  title =        "A Handbook of Numerical Matrix Inversion and Solution
                 of Linear Equations",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  year =         "1968",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Wegert:1994:BNP,
  author =       "Elias Wegert and Lloyd N. Trefethen",
  title =        "From the {Buffon} Needle Problem to the {Kreiss}
                 Matrix Theorem",
  journal =      j-AMM,
  volume =       "101",
  number =       "2",
  pages =        "132--139",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{White:1997:INL,
  author =       "Michael White",
  title =        "{Isaac Newton}: {The} Last Sorcerer",
  publisher =    "Fourth Estate",
  address =      "London",
  pages =        "402",
  year =         "1997",
  ISBN =         "1-85702-706-X",
  ISBN-13 =      "978-1-85702-706-8",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Williams:1989:EBC,
  editor =       "M. R. Williams and Martin Campbell-Kelly",
  title =        "The Early British Computer Conferences",
  volume =       "14",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Charles Babbage Institute Reprint Series for the
                 History of Computing",
}

@Article{Wichmann:1989:TFS,
  author =       "B. A. Wichmann",
  title =        "Towards a Formal Specification of Floating Point",
  journal =      j-COMP-J,
  volume =       "32",
  number =       "",
  pages =        "432--436",
  year =         "1989",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Wichmann:1992:NUF,
  author =       "B. A. Wichmann",
  title =        "A Note on the Use of Floating Point in Critical
                 Systems",
  journal =      j-COMP-J,
  volume =       "35",
  number =       "1",
  pages =        "41--44",
  year =         "1992",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Wijngaarden:1966:NAI,
  author =       "A. van Wijngaarden",
  title =        "Numerical Analysis as an Independent Science",
  journal =      j-BIT,
  volume =       "6",
  pages =        "66--81",
  year =         "1966",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Wilkinson:1948:ACE,
  author =       "J. H. Wilkinson",
  title =        "The {Automatic Computing Engine} at the {National
                 Physical Laboratory}",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "195",
  pages =        "285--286",
  year =         "1948",
  CODEN =        "PRLAAZ",
  ISSN =         "0080-4630",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
}

@TechReport{Wilkinson:1948:PRA,
  author =       "J. H. Wilkinson",
  title =        "Progress Report on the {Automatic Computing Engine}",
  type =         "Report",
  number =       "MA/17/1024",
  institution =  "Mathematics Division, Department of Scientific and
                 Industrial Research, National Physical Laboratory",
  address =      inst-NPL:adr,
  pages =        "127",
  month =        apr,
  year =         "1948",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Wilkinson:1954:PA,
  author =       "J. H. Wilkinson",
  booktitle =    "Automatic Digital Computation",
  title =        "The {Pilot ACE}",
  publisher =    "Her Majesty's Stationery Office, London",
  pages =        "5--14",
  year =         "1954",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Wilkinson:1954:LAP,
  author =       "J. H. Wilkinson",
  booktitle =    "Automatic Digital Computation",
  title =        "Linear Algebra on the {Pilot ACE}",
  publisher =    "Her Majesty's Stationery Office, London",
  year =         "1954",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Wilkinson:1955:UIM,
  author =       "J. H. Wilkinson",
  title =        "The Use of Iterative Methods for Finding the Latent
                 Roots and Vectors of Matrices",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "9",
  pages =        "184--191",
  year =         "1955",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Wilkinson:1960:EAF,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis of Floating-Point Computation",
  journal =      j-NUM-MATH,
  volume =       "2",
  pages =        "319--340",
  year =         "1960",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Wilkinson:1961:EAD,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis of Direct Methods of Matrix Inversion",
  journal =      j-ACM,
  volume =       "8",
  pages =        "281--330",
  year =         "1961",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Wilkinson:1962:EAE,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis of Eigenvalue Techniques Based on
                 Orthogonal Transformations",
  journal =      j-SIAM,
  volume =       "10",
  number =       "1",
  pages =        "162--195",
  year =         "1962",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Wilkinson:1963:REA,
  author =       "J. H. Wilkinson",
  title =        "Rounding Errors in Algebraic Processes",
  publisher =    "Notes on Applied Science No. 32, Her Majesty's
                 Stationery Office",
  address =      "London",
  pages =        "vi + 161",
  year =         "1963",
  ISBN =         "0-486-67999-3",
  ISBN-13 =      "978-0-486-67999-0",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Also published by Prentice-Hall, Englewood Cliffs, NJ,
                 USA. Reprinted by Dover, New York, 1994",
}

@InCollection{Wilkinson:1963:PRF,
  author =       "J. H. Wilkinson",
  booktitle =    "Experimental Arithmetic, High Speed Computing and
                 Mathematics",
  title =        "Plane-Rotations in Floating-Point Arithmetic",
  volume =       "15",
  publisher =    pub-AMS # ", " # pub-AMS:adr,
  pages =        "185--198",
  year =         "1963",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Proceedings of Symposia in Applied Mathematics",
}

@Book{Wilkinson:1965:AEP,
  author =       "J. H. Wilkinson",
  title =        "The Algebraic Eigenvalue Problem",
  publisher =    pub-OUP,
  pages =        "xviii + 662",
  year =         "1965",
  ISBN =         "0-19-853403-5 (\hbk), 0-19-853418-3 (\pbk)",
  ISBN-13 =      "978-0-19-853403-7 (\hbk), 978-0-19-853418-1 (\pbk)",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Wilkinson:1965:EAT,
  author =       "J. H. Wilkinson",
  editor =       "Louis B. Rall",
  booktitle =    "Error in Digital Computation",
  title =        "Error Analysis of Transformations Based on the Use of
                 Matrices of the Form {$I-2ww^H$}",
  volume =       "2",
  publisher =    pub-Wiley # ", " # pub-Wiley:adr,
  pages =        "77--101",
  year =         "1965",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Wilkinson:1967:BZW,
  author =       "J. H. Wilkinson",
  title =        "Bledy Zaokragle{\'n} w Procesach Algebraicznych",
  publisher =    "PWW",
  address =      "Warszawa",
  year =         "1967",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Polish translation of \cite{Wilkinson:1963:REA}",
}

@InProceedings{Wilkinson:1968:PEA,
  author =       "J. H. Wilkinson",
  editor =       "I. G. Petrovsky",
  booktitle =    "Proc. International Congress of Mathematicians, Moscow
                 1966",
  title =        "A Priori Error Analysis of Algebraic Processes",
  publisher =    "Mir Publishers, Moscow",
  pages =        "629--640",
  year =         "1968",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Wilkinson:1969:R,
  author =       "J. H. Wilkinson",
  title =        "Rundungsfehler",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1969",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "German translation of \cite{Wilkinson:1963:REA}",
}

@Book{Wilkinson:1970:AEP,
  author =       "J. H. Wilkinson",
  title =        "The Algebraic Eigenvalue Problem",
  publisher =    "Nauka",
  address =      "U.S.S.R. Academy of Sciences",
  pages =        "564",
  year =         "1970",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Wilkinson:1971:MEA,
  author =       "J. H. Wilkinson",
  title =        "Modern Error Analysis",
  journal =      j-SIREV,
  volume =       "13",
  number =       "4",
  pages =        "548--568",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Wilkinson:1971:SCN,
  author =       "J. H. Wilkinson",
  title =        "Some Comments from a Numerical Analyst",
  journal =      j-ACM,
  volume =       "18",
  number =       "2",
  pages =        "137--147",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Wilkinson:1974:NLA,
  author =       "J. H. Wilkinson",
  title =        "Numerical Linear Algebra on Digital Computers",
  journal =      j-IMA-BULL,
  volume =       "10",
  number =       "9/10",
  pages =        "354--356",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "IMA Bulletin",
}

@Article{Wilkinson:1974:CEA,
  author =       "J. H. Wilkinson",
  title =        "The Classical Error Analyses for the Solution of
                 Linear Systems",
  journal =      j-IMA-BULL,
  volume =       "10",
  number =       "5/6",
  pages =        "175--180",
  year =         "1974",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "IMA Bulletin",
}

@InBook{Evans:1976:IJH,
  author =       "Christopher Evans",
  title =        "Interview with {J}. {H}. Wilkinson",
  number =       "10",
  publisher =    "Science Museum, London",
  year =         "1976",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Pioneers of Computing, 60-Minute Recordings of
                 Interviews",
}

@InCollection{Wilkinson:1980:TWN,
  author =       "J. H. Wilkinson",
  editor =       "N. Metropolis and J. Howlett and Gian-Carlo Rota",
  booktitle =    "A History of Computing in the Twentieth Century: {A}
                 Collection of Essays",
  title =        "Turing's Work at the {National Physical Laboratory}
                 and the Construction of {Pilot ACE}, {DEUCE}, and
                 {ACE}",
  publisher =    "Academic Press",
  address =      "New York",
  pages =        "101--114",
  year =         "1980",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InCollection{Wilkinson:1984:PP,
  author =       "James H. Wilkinson",
  editor =       "G. H. Golub",
  booktitle =    "Studies in Numerical Analysis",
  title =        "The Perfidious Polynomial",
  volume =       "24",
  publisher =    pub-MAA,
  address =      pub-MAA:adr,
  pages =        "1--28",
  year =         "1984",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Studies in Mathematics",
}

@InCollection{Wilkinson:1985:SAE,
  author =       "J. H. Wilkinson",
  booktitle =    "NAG Newsletter 2/85",
  title =        "The State of the Art in Error Analysis",
  publisher =    "Numerical Algorithms Group",
  address =      "Oxford, UK",
  pages =        "5--28",
  month =        nov,
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Wilkinson:1986:EAR,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis Revisited",
  journal =      j-IMA-BULL,
  volume =       "22",
  number =       "11/12",
  pages =        "192--200",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "IMA Bulletin",
}

@Article{Anonymous:1987:JW,
  author =       "Anonymous",
  title =        "{James Wilkinson} (1919--1986)",
  journal =      j-AHC,
  volume =       "9",
  number =       "2",
  pages =        "205--210",
  year =         "1987",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "From the introduction: ``A series of lightly edited
                 extracts from messages that were sent over various
                 computer networks during the period October 5,
                 1986--February 13, 1987''",
}

@Article{Wilkes:1997:AE,
  author =       "M. V. Wilkes",
  title =        "Arithmetic on the {EDSAC}",
  journal =      j-IEEE-AHC,
  volume =       "19",
  number =       "1",
  pages =        "13--15",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Winograd:1968:NAI,
  author =       "S. Winograd",
  title =        "A New Algorithm for Inner Product",
  journal =      j-IEEE-C,
  volume =       "C-18",
  pages =        "693--694",
  year =         "1968",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Winograd:1971:MM,
  author =       "S. Winograd",
  title =        "On Multiplication of {$2 \times 2$} Matrices",
  journal =      j-LAA,
  volume =       "4",
  pages =        "381--388",
  year =         "1971",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Walden:1995:OBP,
  author =       "Bertil Wald{\'e}n and Rune Karlson and {Ji-guang}
                 Sun",
  title =        "Optimal Backward Perturbation Bounds for the Linear
                 Least Squares Problem",
  journal =      j-NLAA,
  volume =       "2",
  number =       "3",
  pages =        "271--286",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Woehr:1997:CWK,
  author =       "Jack Woehr",
  title =        "A Conversation with {William Kahan}",
  journal =      j-DDJ,
  volume =       "271",
  pages =        "18--32",
  month =        nov,
  year =         "1997",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Wolfe:1964:RTE,
  author =       "Jack M. Wolfe",
  title =        "Reducing Truncation Errors by Programming",
  journal =      j-CACM,
  volume =       "7",
  number =       "6",
  pages =        "355--356",
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Book{Wolfram:1999:MB,
  author =       "Stephen Wolfram",
  title =        "The {Mathematica} Book",
  publisher =    "Wolfram Media, Champaign, IL, USA and " # pub-CUP # ",
                 " # pub-CUP:adr,
  edition =      "Fourth",
  pages =        "xxvi + 1470",
  year =         "1999",
  ISBN =         "1-57955-004-5 (Wolfram), 0-521-64314-7 (Cambridge)",
  ISBN-13 =      "978-1-57955-004-2 (Wolfram), 978-0-521-64314-6
                 (Cambridge)",
  bibsource =          "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{wood58,
  author =       "Michael Woodger",
  title =        "The History and Present Use of Digital Computers at
                 the {National Physical Laboratory}",
  journal =      j-PROC-CONTROL-AUTOMATION,
  pages =        "437--442",
  month =        nov,
  year =         "1958",
  CODEN =        "PCAUA3",
  ISSN =         "0552-234X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted in \cite[pp.~125-140]{Carpenter:1986:MTA}.",
  fjournal =     "Process Control and Automation",
}

@Article{Wozniakowski:1977:NSS,
  author =       "H. Wo{\'z}niakowski",
  title =        "Numerical Stability for Solving Nonlinear Equations",
  journal =      j-NUM-MATH,
  volume =       "27",
  pages =        "373--390",
  year =         "1977",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Wozniakowski:1977:NSC,
  author =       "H. Wo{\'z}niakowski",
  title =        "Numerical Stability of the {Chebyshev} Method for the
                 Solution of Large Linear Systems",
  journal =      j-NUM-MATH,
  volume =       "28",
  pages =        "191--209",
  year =         "1977",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Wozniakowski:1978:REA,
  author =       "H. Wo{\'z}niakowski",
  title =        "Roundoff-error analysis of iterations for large linear
                 systems",
  journal =      j-NUM-MATH,
  volume =       "30",
  pages =        "301--314",
  year =         "1978",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Wozniakowski:1980:REA,
  author =       "H. Wo{\'z}niakowski",
  title =        "Roundoff-Error Analysis of a New Class of
                 Conjugate-Gradient Algorithms",
  journal =      j-LAA,
  volume =       "29",
  pages =        "507--529",
  year =         "1980",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Whaley:2001:AEO,
  author =       "R. Clint Whaley and Antoine Petitet and Jack J.
                 Dongarra",
  title =        "Automated Empirical Optimization of Software and the
                 {ATLAS} Project",
  journal =      j-PAR-COMP,
  volume =       "27",
  number =       "1--2",
  pages =        "3--25",
  year =         "2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Wright:1992:IMC,
  author =       "Margaret H. Wright",
  title =        "Interior Methods for Constrained Optimization",
  journal =      j-ACTA-NUMERICA,
  volume =       "1",
  pages =        "341--407",
  year =         "1992",
  CODEN =        "ANUMFU",
  DOI =          "https://doi.org/10.1017/S0962492900002300",
  ISBN =         "0-521-41026-6",
  ISBN-13 =      "978-0-521-41026-7",
  ISSN =         "0962-4929 (print), 1474-0508 (electronic)",
  ISSN-L =       "0962-4929",
  bibdate =      "Sat Sep 24 10:23:30 MDT 2011",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/att.bib;
                 ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/SEL-HPC.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
  URL =          "ftp://netlib.att.com/netlib/att/cs/doc/91/4-10.ps.Z",
  acknowledgement = ack-nhfb,
  ajournal =     "Acta Numer.",
  document-size = "187.8 kbytes",
  fjournal =     "Acta Numerica",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANU",
  onlinedate =   "07 November 2008",
  scope =        "opt",
}

@Article{Wright:1993:CPW,
  author =       "Stephen J. Wright",
  title =        "A Collection of Problems for Which {Gaussian}
                 Elimination with Partial Pivoting is Unstable",
  journal =      j-SISSC,
  volume =       "14",
  number =       "1",
  pages =        "231--238",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@InProceedings{Wright:1996:DSM,
  author =       "Margaret H. Wright",
  editor =       "D. F. Griffiths and G. A. Watson",
  booktitle =    "Numerical Analysis \textup{1995}, Proceedings of the
                 \textup{16}th Dundee Conference",
  title =        "Direct Search Methods: {Once} Scorned, Now
                 Respectable",
  volume =       "344",
  publisher =    pub-AWLongman # ", " # pub-AWLongman:adr,
  pages =        "191--208",
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Pitman Research Notes in Mathematics",
}

@Book{Wright:1997:PDI,
  author =       "Stephen J. Wright",
  title =        "Primal-Dual Interior-Point Methods",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xx + 289",
  year =         "1997",
  ISBN =         "0-89871-382-X",
  ISBN-13 =      "978-0-89871-382-4",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Wallis:1972:CRS,
  author =       "W. D. Wallis and Anne Penfold Street and Jennifer
                 Seberry Wallis",
  title =        "Combinatorics: {Room} Squares, Sum-Free Sets,
                 {Hadamard} Matrices",
  volume =       "292",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "508",
  year =         "1972",
  ISBN =         "3-540-06035-9",
  ISBN-13 =      "978-3-540-06035-2",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  series =       "Lecture Notes in Mathematics",
}

@Article{Weiss:1986:ACN,
  author =       "N. Weiss and G. W. Wasilkowski and H. Wo{\'z}niakowski
                 and M. Shub",
  title =        "Average Condition Number for Solving Linear
                 Equations",
  journal =      j-LAA,
  volume =       "83",
  pages =        "79--102",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Yalamov:2000:ASS,
  author =       "Plamen Y. Yalamov",
  title =        "On the Almost Strong Stability of the Circular
                 Deconvolution Algorithm",
  journal =      j-SIMAX,
  volume =       "22",
  number =       "2",
  pages =        "358--363",
  year =         "2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@TechReport{Yalamov:1995:GSA,
  author =       "P. Y. Yalamov",
  title =        "Graphs and Stability of Algorithms",
  type =         "Preprint",
  number =       "N27",
  institution =  "University of Rousse",
  address =      "Bulgaria",
  pages =        "17",
  month =        feb,
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Yeung:1997:PAG,
  author =       "Man-Chung Yeung and Tony. F. Chan",
  title =        "Probabilistic Analysis of {Gaussian} Elimination
                 Without Pivoting",
  journal =      j-SIMAX,
  volume =       "18",
  number =       "2",
  pages =        "499--517",
  year =         "1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Yip:1986:NSS,
  author =       "E. L. Yip",
  title =        "A Note on the Stability of Solving a Rank-{$p$}
                 Modification of a Linear System by the
                 {Sherman--Morrison--Woodbury} Formula",
  journal =      j-SISSC,
  volume =       "7",
  number =       "3",
  pages =        "507--513",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Young:1972:SNM,
  author =       "David M. Young and Robert T. Gregory",
  title =        "A Survey of Numerical Mathematics",
  volume =       "1",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "x + 492 + appendices",
  year =         "1972",
  ISBN =         "0-486-65691-8",
  ISBN-13 =      "978-0-486-65691-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted by Dover, New York, 1988",
}

@Article{Yohe:1979:SIA,
  author =       "J. M. Yohe",
  title =        "Software for Interval Arithmetic: {A} Reasonably
                 Portable Package",
  journal =      j-TOMS,
  volume =       "5",
  number =       "1",
  pages =        "50--63",
  year =         "1979",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Yohe:1979:INA,
  author =       "J. M. Yohe",
  title =        "Implementing Nonstandard Arithmetics",
  journal =      j-SIREV,
  volume =       "21",
  number =       "1",
  pages =        "34--56",
  year =         "1979",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Yohe:1980:PSI,
  author =       "J. M. Yohe",
  title =        "Portable Software for Interval Arithmetic",
  journal =      j-COMPUTING,
  volume =       "Suppl. 2",
  pages =        "211--229",
  year =         "1980",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Book{Young:1971:ISL,
  author =       "David M. Young",
  title =        "Iterative Solution of Large Linear Systems",
  publisher =    "Academic Press",
  address =      "New York",
  pages =        "xxiv + 570",
  year =         "1971",
  ISBN =         "0-12-773050-8",
  ISBN-13 =      "978-0-12-773050-9",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Young:1989:HOI,
  author =       "David M. Young",
  title =        "A Historical Overview of Iterative Methods",
  journal =      j-COMP-PHYS-COMM,
  volume =       "53",
  number =       "1--3",
  pages =        "1--17",
  month =        may,
  year =         "1989",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(89)90145-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  MRclass =      "65F10 (65-03)",
  MRnumber =     "90e:65047",
  bibdate =      "Mon Feb 13 10:28:26 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465589901458",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  reviewer =     "H. R. Schwarz",
}

@Article{Ypma:1983:ERE,
  author =       "Tjalling J. Ypma",
  title =        "The Effect of Rounding Errors on {Newton}-like
                 Methods",
  journal =      j-IMAJNA,
  volume =       "3",
  pages =        "109--118",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ypma:1983:FMZ,
  author =       "Tjalling J. Ypma",
  title =        "Finding a Multiple Zero by Transformations and
                 {Newton}-like Methods",
  journal =      j-SIREV,
  volume =       "25",
  number =       "3",
  pages =        "365--378",
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ypma:1995:HDN,
  author =       "Tjalling J. Ypma",
  title =        "Historical Development of the {Newton--Raphson}
                 Method",
  journal =      j-SIREV,
  volume =       "37",
  number =       "4",
  pages =        "531--551",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Yuval:1978:SPS,
  author =       "Gideon Yuval",
  title =        "A Simple Proof of {Strassen's} Result",
  journal =      j-INFPL,
  volume =       "7",
  number =       "6",
  pages =        "285--286",
  year =         "1978",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Zawilski:1991:NSC,
  author =       "Adam T. Zawilski",
  title =        "Numerical Stability of the Cyclic {Richardson}
                 Iteration",
  journal =      j-NUM-MATH,
  volume =       "60",
  pages =        "251--290",
  year =         "1991",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Zha:1993:CPA,
  author =       "Hongyuan Zha",
  title =        "A Componentwise Perturbation Analysis of the {$QR$}
                 Decomposition",
  journal =      j-SIMAX,
  volume =       "14",
  number =       "4",
  pages =        "1124--1131",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Zha:1993:P,
  author =       "Hongyuan Zha",
  title =        "Problem 10312",
  journal =      j-AMM,
  volume =       "100",
  number =       "5",
  pages =        "499",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Zha:1995:NCS,
  author =       "Hongyuan Zha and Zhenyue Zhang",
  title =        "A Note on Constructing a Symmetric Matrix with
                 Specified Diagonal Entries and Eigenvalues",
  journal =      j-BIT,
  volume =       "35",
  pages =        "448--452",
  year =         "1995",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Zielke:1986:RTM,
  author =       "G. Zielke",
  title =        "Report on Test Matrices for Generalized Inverses",
  journal =      j-COMPUTING,
  volume =       "36",
  pages =        "105--162",
  year =         "1986",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Zielke:1988:SRM,
  author =       "Gerhard Zielke",
  title =        "Some Remarks on Matrix Norms, Condition Numbers, and
                 Error Estimates for Linear Equations",
  journal =      j-LAA,
  volume =       "110",
  pages =        "29--41",
  year =         "1988",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Zietak:1985:PCI,
  author =       "K. Zi{\c{e}}tak",
  title =        "On a Particular Case of the Inconsistent Linear Matrix
                 Equation {$AX+YB=C$}",
  journal =      j-LAA,
  volume =       "66",
  pages =        "249--258",
  year =         "1985",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ziv:1982:RDE,
  author =       "Abraham Ziv",
  title =        "Relative Distance---{An} Error Measure in Round-Off
                 Error Analysis",
  journal =      j-MATH-COMP,
  volume =       "39",
  number =       "160",
  pages =        "563--569",
  year =         "1982",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Ziv:1991:FEE,
  author =       "Abraham Ziv",
  title =        "Fast Evaluation of Elementary Mathematical Functions
                 with Correctly Rounded Last Bit",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "410--423",
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Ziv:1995:CAE,
  author =       "Abraham Ziv",
  title =        "Converting Approximate Error Bounds into Exact Ones",
  journal =      j-MATH-COMP,
  volume =       "64",
  number =       "209",
  pages =        "265--277",
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Article{Zlatev:1986:CNE,
  author =       "Zahari Zlatev and Jerzy Wasniewski and Kjeld
                 Schaumburg",
  title =        "Condition Number Estimators in a Sparse Matrix
                 Software",
  journal =      j-SISSC,
  volume =       "7",
  number =       "4",
  pages =        "1175--1189",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Cox:1990:RNC,
  editor =       "M. G. Cox and S. J. Hammarling",
  title =        "Reliable Numerical Computation",
  publisher =    pub-OUP,
  pages =        "xvi + 339",
  year =         "1990",
  ISBN =         "0-19-853564-3",
  ISBN-13 =      "978-0-19-853564-5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

%%% ====================================================================
%%% Cross-referenced entries must come last:

@Proceedings{harv46,
  key =          "Harvard",
  title =        "A Manual of Operation for the Automatic Sequence
                 Controlled Calculator",
  publisher =    pub-Harvard,
  address =      pub-Harvard:adr,
  year =         "1946",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted, with new foreword and introduction, Volume
                 8 in the Charles Babbage Institute Reprint Series for
                 the History of Computing, MIT Press, Cambridge, MA,
                 USA, 1985",
}

@Proceedings{harv48,
  key =          "Harvard",
  title =        "Proceedings of a Symposium on Large-Scale Digital
                 Calculating Machinery",
  volume =       "16",
  publisher =    pub-Harvard,
  address =      pub-Harvard:adr,
  year =         "1948",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  note =         "Reprinted, with a new introduction by William Aspray,
                 Volume 7 in the Charles Babbage Institute Reprint
                 Series for the History of Computing, MIT Press,
                 Cambridge, MA, USA, 1985",
  series =       "The Annals of the Computation Laboratory of Harvard
                 University",
}

@Proceedings{Kulisch:1983:NAS,
  editor =       "Ulrich W. Kulisch and Willard L. Miranker",
  title =        "A New Approach to Scientific Computation",
  publisher =    pub-AP # ", " # pub-AP:adr-NY,
  pages =        "xv + 384",
  year =         "1983",
  ISBN =         "0-12-428660-7",
  ISBN-13 =      "978-0-12-428660-3",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}

@Book{Wilkinson:1971:LA,
  editor =       "James H. Wilkinson and Christian Reinsch",
  booktitle =    "Linear Algebra",
  title =        "Linear Algebra",
  volume =       "II",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 439",
  year =         "1971",
  ISBN =         "0-387-05414-6, 3-540-05414-6",
  ISBN-13 =      "978-0-387-05414-8, 978-3-540-05414-6",
  LCCN =         "QA251 .W67",
  bibdate =      "Wed Dec 15 18:44:50 1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  series =       "Handbook for Automatic Computation, Editors: {F. L.
                 Bauer, A. S. Householder, F. W. J. Olver, H.
                 Rutishauser, K. Samelson and E. Stiefel}",
  acknowledgement = ack-nhfb,
  tableofcontents = "Part I: Linear systems, least squares and linear
                 programming \\
                 J. H. Wilkinson / Introduction to Part I / 1--8 \\
                 1. Introduction \\
                 2. List of procedures \\
                 3. Positive definite symmetric matrices \\
                 4. Non-positive definite symmetric matrices \\
                 5. Non-Hermitian matrices \\
                 6. Least squares and related problems \\
                 7. The linear programming problem \\
                 R. S. Martin, G. Peters and J. H. Wilkinson / Symmetric
                 decomposition of a positive definite matrix / 9--30 \\
                 Martin, Peters and Wilkinson / Iterative refinement of
                 the solution of a positive definite system of equations
                 / 31--44 \\
                 F. L. Bauer and C. Reinsch / Inversion of positive
                 definite matrices by the Gauss-Jordan method / 45--49
                 \\
                 Martin and Wilkinson / Symmetric decomposition of
                 positive definite band matrices / 50--56 \\
                 T. Ginsburg / The conjugate gradient method / 57--69
                 \\
                 Martin and Wilkinson / Solution of symmetric and
                 unsymmetric band equations and the calculation of
                 eigenvectors of band matrices / 70--92 \\
                 H. J. Bowdler, Martin, Peters and Wilkinson / Solution
                 of real and complex systems of linear equations /
                 93--110 \\
                 P. Businger and G. H. Golub / Linear least squares
                 solutions by Householder transformations / 111--118 \\
                 Bauer / Elimination with weighted row combinations for
                 solving linear equations and least squares problems /
                 119--133 \\
                 Golub and Reinsch / Singular value decomposition and
                 least squares solutions / 134--151 \\
                 R. H. Bartels, J. Stoer and Ch. Zenger / A realization
                 of the simplex method based on triangular
                 decompositions / 152--190 \\
                 Part II: The algebraic eigenvalue problem \\
                 Wilkinson / Introduction to Part II / 191--201 \\
                 1. Introduction \\
                 2. List of procedures \\
                 3. Real, dense, symmetric matrices \\
                 4. Symmetric band matrices \\
                 5. Simultaneous determination of dominant eigenvalues
                 and eigenvectors of a symmetric sparse matrix \\
                 6. The generalized symmetric eigenvalue problems $A x =
                 \lambda B x$ and $A B x = \lambda x$ \\
                 7. Hermitian matrices \\
                 8. Real dense unsymmetric matrices \\
                 9. Unsymmetric band matrices \\
                 10. Dense unsymmetric matrices with complex elements,
                 H. Rutishauser / The Jacobi method for real symmetric
                 matrices / 202--211 \\
                 Martin, Reinsch and Wilkinson / Householder's
                 tridiagonalization of a symmetric matrix / 212--226 \\
                 H. Bowdler, Martin, Reinsch and Wilkinson / The $QR$
                 and $QL$ algorithms for symmetric matrices / 227--240
                 \\
                 A. Dubrulle, Martin and Wilkinson / The implicit $QL$
                 algorithm / 241--248 \\
                 W. Barth, Martin, and Wilkinson / Calculation of the
                 eigenvalues of a symmetric tridiagonal matrix by the
                 method of bisection / 249--256 \\
                 Reinsch and Bauer / Rational $QR$ transformation with
                 Newton shift for symmetric tridiagonal matrices /
                 257--265 \\
                 Martin, Reinsch and Wilkinson / The $QR$ algorithm for
                 band symmetric matrices / 266--272 \\
                 H. R. Schwarz / Tridiagonalization of a symmetric band
                 matrix / 273--283 \\
                 Rutishauser / Simultaneous iteration method for
                 symmetric matrices / 284--302 \\
                 Martin and Wilkinson / Reduction of the symmetric
                 eigenproblem $A x = \lambda B x$ and related problems
                 to standard form / 303--314 \\
                 B. N. Parlett and Reinsch / Balancing a matrix for
                 calculation of eigenvalues and eigenvectors / 315--326
                 \\
                 P. J. Eberlein and J. Boothroyd / Solution to the
                 eigenproblem by a norm reducing Jacobi type method /
                 327--338 \\
                 Martin and Wilkinson / Similarity reduction of a
                 general matrix to Hessenberg form / 339--358 \\
                 Martin, Peters and Wilkinson / The $QR$ algorithm for
                 real Hessenberg matrices / 359--371 \\
                 Peters and Wilkinson / Eigenvectors of real and complex
                 matrices by $LR$ and $QR$ triangularizations / 372--395
                 \\
                 Martin and Wilkinson / The modified $LR$ algorithm for
                 complex Hessenberg matrices / 396--403 \\
                 Eberlein / Solution to the complex eigenproblem by a
                 norm reducing Jacobi type method / 404--417 \\
                 Peters and Wilkinson / The calculation of specified
                 eigenvectors by inverse iteration / 418--439",
}

.