%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author-1 = "Nelson H. F. Beebe", %%% author-2 = "Stefano Foresti", %%% version = "1.103", %%% date = "07 November 2025", %%% time = "15:27:26 MDT", %%% filename = "golub-gene-h.bib", %%% address-1 = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% address-2 = "Center for High-Performance Computing %%% University of Utah %%% Salt Lake City, UT 84112 %%% USA", %%% telephone-1 = "+1 801 581 5254", %%% telephone-2 = "+1 801 581 3173", %%% FAX-2 = "+1 801 585 5366", %%% URL-1 = "https://www.math.utah.edu/~beebe", %%% checksum = "64875 17946 84135 835135", %%% email-1 = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% email-2 = "stefano at chpc.utah.edu (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography, linear algebra, numerical %%% analysis, singular value decomposition, SVD", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a fairly complete bibliography of %%% publications of the late Gene Howard Golub %%% (February 29, 1932--November 16, 2007). %%% %%% Part 1 covers his publications, and Part 2 %%% covers publications about him by others. %%% %%% At version 1.103, the year coverage looked %%% like this: %%% %%% 1959 ( 1) 1982 ( 8) 2005 ( 14) %%% 1960 ( 0) 1983 ( 8) 2006 ( 14) %%% 1961 ( 2) 1984 ( 7) 2007 ( 17) %%% 1962 ( 2) 1985 ( 5) 2008 ( 11) %%% 1963 ( 3) 1986 ( 4) 2009 ( 7) %%% 1964 ( 2) 1987 ( 14) 2010 ( 2) %%% 1965 ( 8) 1988 ( 9) 2011 ( 2) %%% 1966 ( 1) 1989 ( 14) 2012 ( 0) %%% 1967 ( 6) 1990 ( 17) 2013 ( 2) %%% 1968 ( 4) 1991 ( 21) 2014 ( 0) %%% 1969 ( 13) 1992 ( 16) 2015 ( 0) %%% 1970 ( 12) 1993 ( 13) 2016 ( 3) %%% 1971 ( 10) 1994 ( 18) 2017 ( 0) %%% 1972 ( 8) 1995 ( 8) 2018 ( 1) %%% 1973 ( 18) 1996 ( 13) 2019 ( 4) %%% 1974 ( 9) 1997 ( 19) 2020 ( 1) %%% 1975 ( 7) 1998 ( 10) 2021 ( 1) %%% 1976 ( 15) 1999 ( 16) 2022 ( 1) %%% 1977 ( 14) 2000 ( 7) 2023 ( 3) %%% 1978 ( 14) 2001 ( 9) 2024 ( 1) %%% 1979 ( 21) 2002 ( 8) 2025 ( 2) %%% 1980 ( 8) 2003 ( 10) %%% 1981 ( 4) 2004 ( 12) %%% %%% Article: 287 %%% Book: 29 %%% InBook: 1 %%% InCollection: 21 %%% InProceedings: 63 %%% Misc: 3 %%% PhdThesis: 1 %%% Proceedings: 62 %%% TechReport: 67 %%% %%% Total entries: 534 %%% %%% This bibliography was collected from %%% multiple sources: %%% %%% * the authors' own files; %%% * the TeX User Group bibliography %%% collection on ftp.math.utah.edu in %%% /pub/tex/bib; %%% * the very large Computer Science %%% bibliography collection on ftp.ira.uka.de %%% in /pub/bibliography, to which many people %%% have contributed; %%% * the ACM Computing Archive CD ROM, %%% covering literature of the 1980s; %%% * the IEEE Inspec CD ROMs for 1989--1996; %%% * Internet library catalogs, including %%% University of California MELVYL, Stanford %%% University RLIN, Library of Congress, %%% OCLC; %%% * the OCLC Contents1st and Article1st %%% databases; %%% * the AMS MathSciNet database; %%% * Gene Golub's personal curriculum vita %%% file. %%% %%% BibTeX citation tags are uniformly chosen %%% as name:year:abbrev, where name is the %%% family name of the first author or editor, %%% year is a 4-digit number, and abbrev is a %%% 3-letter condensation of important title %%% words. Citation tags were automatically %%% generated by software developed for the %%% BibNet Project. %%% %%% In this bibliography, entries are sorted %%% first by ascending year, and within each %%% year, alphabetically by author or editor, %%% and then, if necessary, by the 3-letter %%% abbreviation at the end of the BibTeX %%% citation tag, using the bibsort -byyear %%% utility. %%% %%% 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.", %%% } %%% ==================================================================== @Preamble{"\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi"} %%% ==================================================================== %%% Acknowledgement abbreviations: @String{ack-do = "Dianne O'Leary, Department of Computer Science, University of Maryland, College Park, MD, USA, email: \path|oleary@cs.umd.edu|"} @String{ack-gg = "Grant Gustafson, Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA, Tel: +1 801 581 6879, e-mail: Internet: \path|gustafso@math.utah.edu|"} @String{ack-nhfb = "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|https://www.math.utah.edu/~beebe/|"} @String{ack-nj = "Norbert Juffa, 2445 Mission College Blvd. Santa Clara, CA 95054 USA email: \path=norbert@iit.com="} @String{ack-sf = "Stefano Foresti, Center for High-Performance Computing, University of Utah, Salt Lake City, UT 84112, USA, Tel: +1 801 581 3173, FAX: +1 801 585 5366, e-mail: \path|stefano@chpc.utah.edu|"} %%% ==================================================================== %%% Institutional abbreviations: @String{inst-ANL = "Argonne National Laboratory"} @String{inst-ANL:adr = "9700 South Cass Avenue, Argonne, IL 60439-4801, USA"} @String{inst-CORNELL = "Cornell University"} @String{inst-CORNELL:adr = "Ithaca, NY, 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-CSRD = "Center for Supercomputing Research and Development"} @String{inst-CSRD:adr = "University of Illinois at Urbana-Champaign, Urbana, IL, USA"} @String{inst-STAN-CS = "Stanford University, Department of Computer Science"} @String{inst-STAN-CS:adr = "Stanford, CA, USA"} @String{inst-U-MARYLAND = "University of Maryland"} @String{inst-U-MARYLAND:adr = "College Park, MD, USA"} @String{inst-U-MARYLAND-CS = "Department of Computer Science, University of Maryland"} @String{inst-U-MARYLAND-CS:adr = "College Park, MD, USA"} %%% ==================================================================== %%% Journal abbreviations: @String{j-ACTA-NUMERICA = "Acta Numerica"} @String{j-ALMAGEST = "Almagest: International Journal for the History of Scientific Ideas"} @String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"} @String{j-AMER-STAT = "The American Statistician"} @String{j-ANN-HIST-COMPUT = 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Circuits and Systems for Video Technology"} @String{j-IEEE-TRANS-COMPUT = "IEEE Transactions on Computers"} @String{j-IEEE-TRANS-IMAGE-PROCESS = "IEEE Transactions on Image Processing"} @String{j-IEEE-TRANS-MED-IMAG = "IEEE Transactions on Medical Imaging"} @String{j-IEEE-TRANS-SIG-PROC = "IEEE Transactions on Signal Processing"} @String{j-IMA-J-NUMER-ANAL = "IMA Journal of Numerical Analysis"} @String{j-IMA-VOL-MATH-APPL = "The IMA volumes in mathematics and its applications"} @String{j-INT-J-NUMER-METHODS-ENG = "International Journal for Numerical Methods in Engineering"} @String{j-INT-J-NUMER-METHODS-FLUIDS = "International Journal for Numerical Methods in Fluids"} @String{j-INTERNET-MATH = "Internet Mathematics"} @String{j-INVERSE-PROBLEMS = "Inverse Problems"} @String{j-J-AM-STAT-ASSOC = "Journal of the American Statistical Association"} @String{j-J-COMPUT-APPL-MATH = "Journal of Computational and Applied Mathematics"} @String{j-J-COMPUT-GRAPH-STAT = "Journal of Computational and Graphical Statistics"} @String{j-J-COMPUT-PHYS = "Journal of Computational Physics"} @String{j-J-ECONOMETRICS = "Journal of Econometrics"} @String{j-J-FLUID-MECH = "Journal of Fluid Mechanics"} @String{j-J-MATH-ANAL-APPL = "Journal of Mathematical Analysis and Applications"} @String{j-J-STAT-COMPUT-SIMUL = "Journal of Statistical Computation and Simulation"} @String{j-LECT-NOTES-COMP-SCI = "Lecture Notes in Computer Science"} @String{j-LECT-NOTES-MATH = "Lecture Notes in Mathematics"} @String{j-LINEAR-ALGEBRA-APPL = "Linear Algebra and its Applications"} @String{j-MAA-STUD-MATH = "MAA studies in mathematics"} @String{j-MATH-COMPUT = "Mathematics of Computation"} @String{j-MATH-PROG = "Mathematical Programming"} @String{j-MITT-MATH-GES-HAMBURG = "Mitteilungen der Mathematischen Gessellschaft in Hamburg"} @String{j-NAMS = "Notices of the American Mathematical Society"} @String{j-NORDISK-TIDSKR-INFORM-BEHAND = "Nordisk tidskrift for informationsbehandling"} @String{j-NUM-LIN-ALG-APPL = "Numerical Linear Algebra with Applications"} @String{j-NUM-MATH = "Numerische Mathematik"} @String{j-NUMER-ALGORITHMS = "Numerical Algorithms"} @String{j-PAMM = "Proceedings in Applied Mathematics and Mechanics"} @String{j-PROC-IEEE = "Proceedings of the IEEE"} @String{j-PROC-NATL-ACAD-SCI-USA = "Proceedings of the National Academy of Sciences of the United States of America"} @String{j-PROC-SPIE = "Proceedings of the SPIE --- The International Society for Optical Engineering"} @String{j-ROCKY-MOUNTAIN-J-MATH = "Rocky Mountain Journal of Mathematics"} @String{j-SIAM = "Journal of the Society for Industrial and Applied Mathematics"} @String{j-SIAM-J-ALG-DISC-METH = "SIAM Journal of Algebraic Discrete Methods"} @String{j-SIAM-J-APPL-MATH = "SIAM Journal on Applied Mathematics"} @String{j-SIAM-J-MAT-ANA-APPL = "SIAM Journal on Matrix Analysis and Applications"} @String{j-SIAM-J-NUMER-ANAL = "SIAM Journal on Numerical Analysis"} @String{j-SIAM-J-NUM-ANALYSIS-B = "Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis"} @String{j-SIAM-J-SCI-COMP = "SIAM Journal on Scientific Computing"} @String{j-SIAM-J-SCI-STAT-COMP = "SIAM Journal on Scientific and Statistical Computing"} @String{j-SIAM-NEWS = "SIAM News"} @String{j-SIAM-REVIEW = "SIAM Review"} @String{j-SIGNUM = "ACM SIGNUM Newsletter"} @String{j-SIGPLAN = "ACM SIGPLAN Notices"} @String{j-SYST-CONTROL = "Systems and Control"} @String{j-SYST-CONTROL-LETT = "Systems and Control Letters"} @String{j-TECHNOMETRICS = "Technometrics"} @String{j-TOMS = "ACM Transactions on Mathematical Software"} @String{j-Z-ANGE-MATH-MECH = "{Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik}"} @String{j-Z-ANGE-MATH-PHYS = "Z. Angew. Math. Phys"} %%% ==================================================================== %%% Miscellaneous abbreviations: @String{prep-latex = "Prepared with {\LaTeX}."} %%% ==================================================================== %%% 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, NY 10036, USA"} @String{pub-AMS = "American Mathematical Society"} @String{pub-AMS:adr = "Providence, RI, USA"} @String{pub-BIRKHAUSER = "Birkh{\"a}user Verlag"} @String{pub-BIRKHAUSER:adr = "Basel, Switzerland"} @String{pub-CUP = "Cambridge University Press"} @String{pub-CUP:adr = "Cambridge, UK"} @String{pub-ELS = "Elsevier"} @String{pub-ELS:adr = "Amsterdam, The Netherlands"} @String{pub-ENH = "Elsevier North-Holland, Inc."} @String{pub-ENH:adr = "New York, NY, USA"} @String{pub-ESP = "Elsevier Science Publishers"} @String{pub-ESP:adr = "Amsterdam, The Netherlands"} @String{pub-EYROLLES = "Editions Eyrolles"} @String{pub-EYROLLES:adr = "Paris, France"} @String{pub-IEEE = "IEEE Computer Society Press"} @String{pub-IEEE:adr = "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-JOHNS-HOPKINS = "The Johns Hopkins University Press"} @String{pub-JOHNS-HOPKINS:adr = "Baltimore, MD, USA"} @String{pub-KLUWER = "Kluwer Academic Publishers Group"} @String{pub-KLUWER:adr = "Norwell, MA, USA, and Dordrecht, The Netherlands"} @String{pub-LONGMAN = "Longman Scientific and Technical"} @String{pub-LONGMAN:adr = "Essex, UK"} @String{pub-MATH-ASSOC-AMER = "Mathematical Association of America"} @String{pub-MATH-ASSOC-AMER:adr = "Washington, DC, USA"} @String{pub-NH = "North-Holland Publishing Co."} @String{pub-NH:adr = "Amsterdam, The Netherlands"} @String{pub-NORTH-OXFORD = "North Oxford Academic"} @String{pub-NORTH-OXFORD:adr = "Oxford, England"} @String{pub-OXFORD = "Oxford University Press"} @String{pub-OXFORD:adr = "Walton Street, Oxford OX2 6DP, UK"} @String{pub-PHYSICA = "Physica-Verlag"} @String{pub-PHYSICA:adr = "Wien, Austria"} @String{pub-PRINCETON = "Princeton University Press"} @String{pub-PRINCETON:adr = "Princeton, NJ, USA"} @String{pub-ROCQUENCOURT = "Rocquencourt"} @String{pub-ROCQUENCOURT:adr = "Centre de Rocquencourt, France"} @String{pub-SIAM = "Society for Industrial and Applied Mathematics"} @String{pub-SIAM:adr = "Philadelphia, PA, USA"} @String{pub-SPARTAN = "Spartan Books"} @String{pub-SPARTAN:adr = "London, England"} @String{pub-SV = "Spring{\-}er-Ver{\-}lag"} @String{pub-SV:adr = "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-TEUBNER = "Teubner"} @String{pub-TEUBNER:adr = "Stuttgart, Germany; Leipzig, Germany"} @String{pub-U-ILLINOIS-PRESS = "University of Illinois Press"} @String{pub-U-ILLINOIS-PRESS:adr = "Urbana, IL, USA"} @String{pub-US-ARO = "U.S. Army Research Office"} @String{pub-US-ARO:adr = "Research Triangle Park, NC, USA"} @String{pub-WATERLOO = "University of Waterloo"} @String{pub-WATERLOO:adr = "Waterloo, Ontario, Canada"} @String{pub-WESTERN-PERIODICALS = "Western Periodicals Co.,"} @String{pub-WESTERN-PERIODICALS:adr = "North Hollywood, CA"} @String{pub-WORLD-SCI = "World Scientific Publishing Co. Pte. Ltd."} @String{pub-WORLD-SCI:adr = "P. O. Box 128, Farrer Road, Singapore 9128, and River Edge, NJ, USA"} %%% ==================================================================== %%% Series abbreviations: @String{ser-LECT-NOTES-MATH = "Lecture Notes in Mathematics"} %%% ==================================================================== %%% %%% Part 1 (of 2): publications by Gene H. Golub %%% %%% Bibliography entries, sorted by year, and then by citation label %%% (with ``bibsort -byyear''): @PhdThesis{Golub:1959:UCM, author = "Gene Howard Golub", title = "The Use of {Chebyshev} Matrix Polynomials in the Iterative Solution of Linear Equations Compared to the Method of Successive Overrelaxation", type = "Ph.D. Thesis in Mathematics", school = "Department of Computer Science, University of Illinois at Urbana-Champaign", address = "Urbana, IL, USA", pages = "vi + 134", month = mar, year = "1959", bibdate = "Mon Oct 24 11:58:32 MDT 1994", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/university-of-illinois-urbana-champagne.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Also published as Technical Report UIUC-DCS-R-59-85. Abstracted in Dissertation Abstracts, v. 20 (1959), no. 5.", acknowledgement = ack-nhfb, advisor = "Abraham Haskel Taub", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "numerical analysis; numerical calculations; relaxation methods (mathematics)", remark = "Gene Golub received a Master's degree with coursework, but no thesis, in 1954 at UIUC \cite[page 13]{Haigh:2005:IGG}. In that interview, Golub expresses hard feelings about his thesis advisor.", } @Article{Golub:1961:CSIa, author = "Gene H. Golub and Richard S. Varga", title = "{Chebyshev} Semi-Iterative Methods, Successive Overrelaxation Iterative Methods, and Second Order {Richardson} Iterative Methods. {I}", journal = j-NUM-MATH, volume = "3", number = "1", pages = "147--156", month = dec, year = "1961", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65.35", MRnumber = "26\#3207", MRreviewer = "J. R. Cannon", bibdate = "Sun Jan 14 10:09:19 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "nla, relaxation, iter, semi-iterative method, Richardson's method", } @Article{Golub:1961:CSIb, author = "Gene H. Golub and Richard S. Varga", title = "{Chebyshev} Semi-Iterative Methods, Successive Overrelaxation Iterative Methods, and Second Order {Richardson} Iterative Methods. {II}", journal = j-NUM-MATH, volume = "3", number = "1", pages = "157--168", month = dec, year = "1961", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65.35", MRnumber = "26\#3208", MRreviewer = "J. R. Cannon", bibdate = "Sun Jan 14 10:09:24 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "nla, relaxation, iter, semi-iterative method, Richardson's method", } @Article{Golub:1962:BET, author = "Gene H. Golub", title = "Bounds for Eigenvalues of Tridiagonal Symmetric Matrices Computed by the {LR} Method", journal = j-MATH-COMPUT, volume = "16", number = "80", pages = "438--445", month = oct, year = "1962", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65.40", MRnumber = "29 \#732", MRreviewer = "P. Henrici", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database", URL = "http://www.jstor.org/stable/2003134", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Golub:1962:BRE, author = "Gene H. Golub", title = "Bounds for the Round-Off Errors in the {Richardson} Second Order Method", journal = j-NORDISK-TIDSKR-INFORM-BEHAND, volume = "2", number = "4", pages = "212--223", month = dec, year = "1962", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/BF01940168", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", MRclass = "65.35", MRnumber = "29\#2958", MRreviewer = "A. S. Householder", bibdate = "Wed Jan 4 18:52:07 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=212", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", journal-URL = "http://link.springer.com/journal/10543", keywords = "floating-point arithmetic; rounding errors", } @Article{Golub:1963:CVM, author = "Gene H. Golub", title = "Comparison of the Variance of Minimum Variance and Weighted Least Squares Regression Coefficients", journal = j-ANN-MATH-STAT, volume = "34", number = "3", pages = "984--991", month = sep, year = "1963", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177704021", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", MRclass = "62.55", MRnumber = "27\#5336", MRreviewer = "A. C. Cohen", bibdate = "Sat May 31 09:11:02 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/annmathstat.bib", URL = "http://projecteuclid.org/euclid.aoms/1177704021", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Golub:1963:LBR, author = "Gene H. Golub", title = "On a Lower Bound for the Rank of a Partitioned Square Matrix", journal = j-MATH-COMPUT, volume = "17", number = "82", pages = "186--188", month = apr, year = "1963", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "15.05", MRnumber = "28\#1209", MRreviewer = "Ky Fan", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database", URL = "http://www.jstor.org/stable/2003639", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Golub:1963:RBG, author = "Gene H. Golub", title = "Review: {{\booktitle{A Guide to ALGOL Programming}}, by Daniel D. McCracken}", journal = j-J-AM-STAT-ASSOC, volume = "58", number = "304", pages = "1202--1202", month = dec, year = "1963", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:37 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314185; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1960.bib", URL = "http://www.jstor.org/stable/2283384", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @TechReport{Golub:1964:NMS, author = "Gene H. Golub and Peter A. Businger", title = "Numerical methods for solving linear least squares problems (by {G. Golub}); An {Algol} procedure for finding linear least squares solutions (by {Peter Businger})", type = "Technical Report", number = "CS-TR-64-12", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = aug, year = "1964", bibdate = "Thu Nov 06 17:05:25 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-64-12.html", abstract = "A common problem in a Computer Laboratory is that of finding linear least squares solutions. These problems arise in a variety of areas and in a variety of contexts. Linear least squares problems are particularly difficult to solve because they frequently involve large quantities of data, and they are ill-conditioned by their very nature. In this paper, we shall consider stable numerical methods for handling these problems. Our basic tool is a matrix decomposition based on orthogonal Householder transformations.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1964:RPP, author = "G. H. Golub", title = "Recent Publications and Presentations: {{\em An Introduction to Computational Methods}}, by {K. A. Redish}", journal = j-AMER-MATH-MONTHLY, volume = "71", number = "10", pages = "1145--1145", month = dec, year = "1964", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:42 MDT 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Businger:1965:LLS, author = "Peter A. Businger and Gene H. Golub", title = "Linear Least Squares Solutions by {Householder} Transformations", journal = j-NUM-MATH, volume = "7", number = "3", pages = "269--276", month = jun, year = "1965", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65.20", MRnumber = "31\#862", bibdate = "Sun Jan 14 10:04:47 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "Also in \cite[pp. 111--118]{Wilkinson:1971:LA}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "Householder transformation; lsq; nla; qrd; software", } @TechReport{Forsythe:1965:MSD, author = "George E. Forsythe and Gene H. Golub", title = "Maximizing a second-degree polynomial on the unit sphere", type = "Technical Report", number = "CS-TR-65-16", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "iv + 31", day = "5", month = feb, year = "1965", bibdate = "Thu Nov 06 14:11:10 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-65-16.html", abstract = "Let $A$ be a Hermitian matrix of order $n$, and $b$ a known vector in $ C^n$. The problem is to determine which vectors make $ \Phi (x) = {(x - b)}^H A(x - b)$ a maximum or minimum on the unit sphere {$ U = \{ x \colon x^H x = 1 \} $}. The problem is reduced to the determination of a finite point set, the spectrum of $ (A, b)$. The theory reduces to the usual theory of Hermitian forms when $ b = 0$.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007); George Elmer Forsythe (8 January 1917--9 April 1972)", } @Article{Forsythe:1965:SVS, author = "George E. Forsythe and Gene H. Golub", title = "On the Stationary Values of a Second-Degree Polynomial on the Unit Sphere", journal = j-SIAM, volume = "13", number = "4", pages = "1050--1068", month = dec, year = "1965", CODEN = "JSIMAV", ISSN = "0368-4245 (print), 1095-712X (electronic)", MRclass = "65.30", MRnumber = "MR0195250 (33 \#3453)", MRreviewer = "A. V. Balakrishnan", bibdate = "Sun Jan 14 10:01:11 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/siam.bib; JSTOR database", note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least squares, which is available by anonymous ftp from {\tt math.liu.se} in {\tt pub/references}.", URL = "http://www.jstor.org/stable/2946425", ZMnumber = "0168.03005", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "forms; linear algebra; nla; updating", } @Article{Golub:1965:CSV, author = "G. H. Golub and W. Kahan", title = "Calculating the Singular Values and Pseudo-Inverse of a Matrix", journal = j-SIAM-J-NUM-ANALYSIS-B, volume = "2", number = "2", pages = "205--224", month = "????", year = "1965", ISSN = "0887-459X (print), 1095-7170 (electronic)", ISSN-L = "0887-459X", MRclass = "65.35", MRnumber = "32 \#587", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR database", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis", journal-URL = "http://epubs.siam.org/loi/sjnaam.1", keywords = "nla, svd, ginv", } @InProceedings{Golub:1965:IRL, author = "G. H. Golub and J. H. Wilkinson", title = "Iterative Refinement of Least Square Solution", crossref = "Kalenich:1965:IPP", pages = "606--607", year = "1965", bibdate = "Wed Apr 13 09:33:42 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "nla, lsq, iterative refinement", } @Article{Golub:1965:NMSa, author = "Gene H. Golub", title = "Numerical methods for solving linear least squares problems", journal = j-APL-MAT, volume = "10", number = "??", pages = "213--216", month = "????", year = "1965", CODEN = "APMTAK", ISSN = "0373-6725", MRclass = "65.20", MRnumber = "31\#5324", MRreviewer = "W. J. Kotz{\'e}", bibdate = "Sun Jan 14 10:03:53 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Aplikace Matematiky", } @Article{Golub:1965:NMSb, author = "G. H. Golub", title = "Numerical Methods for Solving Linear Least Squares Problems", journal = j-NUM-MATH, volume = "7", number = "3", pages = "206--216", month = jun, year = "1965", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65.20", MRnumber = "31\#5323", MRreviewer = "W. J. Kotz{\'e}", bibdate = "Sun Jan 14 10:03:43 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "Householder transformation; lsq; nla; qrd; updating", } @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", number = "2", pages = "139--148", month = dec, year = "1966", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65.20", MRnumber = "35 \#3849", MRreviewer = "W. J. Kotz{\'e}", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "condition; iterative refinement; la; lsq; nla; pert", } @TechReport{Bartels:1967:CCR, author = "Richard H. Bartels and Gene H. Golub", title = "Computational considerations regarding the calculation of {Chebyshev} solutions for overdetermined linear equation systems by the exchange method", type = "Technical Report", number = "CS-TR-67-67", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = jun, year = "1967", bibdate = "Thu Nov 06 17:15:53 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-67-67.html", abstract = "An implementation, using Gaussian $ L U $ decomposition with row interchanges, of Stiefel's exchange algorithm for determining a Chebyshev solution to an overdetermined system of linear equations is presented. The implementation is computationally more stable than those usually given in the literature. A generalization of Stiefel's algorithm is developed which permits the occasional exchange of two equations simultaneously. Finally, some experimental comparisons are offered", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Bjorck:1967:API, author = "{\AA}ke Bj{\"o}rck and Gene H. Golub", title = "{Algol} programming: Iterative Refinement of Linear Least Squares Solutions by {Householder} Transformation", journal = j-BIT, volume = "7", number = "4", pages = "322--337", month = dec, year = "1967", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/BF01939326", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", bibdate = "Wed Jan 4 18:52:10 MST 2006", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/gvl.bib; http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=7&issue=4; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=7&issue=4&spage=322", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "BIT (Nordisk tidskrift for informationsbehandling)", journal-URL = "http://link.springer.com/journal/10543", keywords = "nla, lsq, iterative refinement, Householder transformation", } @TechReport{Golub:1967:CAC, author = "Gene H. Golub and Lyle B. Smith", title = "{Chebyshev} approximation of continuous functions by a {Chebyshev} system of functions", type = "Technical Report", number = "CS-TR-67-72", institution = inst-STAN-CS, address = inst-STAN-CS:adr, year = "1967", bibdate = "Thu Nov 06 17:18:45 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-67-72.html", abstract = "The second algorithm of Remez can be used to compute the minimax approximation to a function, $ f(x) $, by a linear combination of functions, $ {\{ Q_i (x) \} }^N_O $, which form a Chebyshev system. The only restriction on the function to be approximated is that it be continuous on a finite interval $ [a, b] $. An Algol 60 procedure is given which will accomplish the approximation. This implementation of the second algorithm of Remez is quite general in that the continuity of $ f(x) $ is all that is required whereas previous implementations have required differentiability, that the end points of the interval be ``critical points,'' and that the number of ``critical points'' be exactly $ N + 2 $. Discussion of the method used and its numerical properties is given as well as some computational examples of the use of the algorithm. The use of orthogonal polynomials (which change at each iteration) as the Chebyshev system is also discussed.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Golub:1967:CGQ, author = "Gene H. Golub and John H. Welsch", title = "Calculation of {Gauss} quadrature rules", type = "Technical Report", number = "CS-TR-67-81", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = nov, year = "1967", bibdate = "Thu Nov 06 17:21:41 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-67-81.html", abstract = "Most numerical integration techniques consist of approximating the integrand by a polynomial in a region or regions and then integrating the polynomial exactly. Often a complicated integrand can be factored into a non-negative 'weight' function and another function better approximated by a polynomial, thus $ \int_a^b g(t)d t = \int_a^b \omega (t)f(t)d t \approx \sum_{i = 1}^N w_i f(t_i) $. Hopefully, the quadrature rule $ {\{ w_j, t_j \} }_{j = 1}^N $ corresponding to the weight function $ \omega (t) $ is available in tabulated form, but more likely it is not. We present here two algorithms for generating the Gaussian quadrature rule defined by the weight function when: (a) the three term recurrence relation is known for the orthogonal polynomials generated by $ \omega (t) $, and (b) the moments of the weight function are known or can be calculated.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Golub:1967:GBAa, author = "Gene H. Golub and Thomas N. Robertson", title = "A generalized {Bairstow} algorithm", type = "Technical Report", number = "CS-TR-67-54", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = jan, year = "1967", bibdate = "Thu Nov 06 17:13:36 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-67-54.html", abstract = "This report discusses convergence and applications for the generalized Bairstow algorithm.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1967:GBAb, author = "G. H. Golub and T. N. Robertson", title = "A generalized {Bairstow} algorithm", journal = j-CACM, volume = "10", number = "6", pages = "371--373", month = jun, year = "1967", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", MRclass = "65.50", MRnumber = "39 \#2315", bibdate = "Sat Nov 26 10:31:36 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @Article{Bartels:1968:ACS, author = "Richard H. Bartels and Gene H. Golub", title = "{Algorithm 328}: {Chebyshev} Solution to An Overdetermined Linear System [{F4}]", journal = j-CACM, volume = "11", number = "6", pages = "428--430", month = jun, year = "1968", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:20 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib", note = "See certification \cite{Schryer:1969:CA}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", editorsnote = "The following algorithm by Barrels and Golub relates to the paper by the same authors in the Numerical Analysis department of this issue on pages 401--406 \cite{Bartels:1968:NAS}. This is the first instance of this type of concurrent publication in Communications under the policy announced by the Editors of the two departments, J. G. Herriot and J. F. Traub, in the March 1967 issue.", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @Article{Bartels:1968:NAS, author = "Richard H. Bartels and Gene H. Golub", title = "Numerical Analysis: Stable numerical methods for obtaining the {Chebyshev} solution to an overdetermined system of equations", journal = j-CACM, volume = "11", number = "6", pages = "401--406", month = jun, year = "1968", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", MRclass = "65.35", MRnumber = "39\#2302", bibdate = "Thu Dec 08 06:16:41 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib", note = "See algorithm \cite{Bartels:1968:ACS}.", abstract = "An implementation of Stiefel's exchange algorithm for determining a Chebyshev solution to an overdetermined system of linear equations is presented, that uses Gaussian LU decomposition with row interchanges. The implementation is computationally more stable than those usually given in the literature. A generalization of Stiefel's algorithm is developed which permits the occasional exchange of two equations simultaneously.", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "Chebyshev solutions; exchange algorithm; linear equations; overdetermined linear systems", } @TechReport{Bjorck:1968:IRL, author = "{\AA}ke Bj{\"o}rck and Gene H. Golub", title = "Iterative refinements of linear least squares solutions by {Householder} transformations", type = "Technical Report", number = "CS-TR-68-83", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "i + 28", day = "19", month = jan, year = "1968", bibdate = "Thu Nov 06 17:24:15 2025", 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", URL = "http://i.stanford.edu/TR/CS-TR-68-83.html", abstract = "An algorithm is presented in ALGOL for iteratively refining the solution to a linear least squares problem with linear constraints. Numerical results presented show that a high degree of accuracy is obtained.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1968:LSS, author = "G. H. Golub", title = "Least Squares, Singular Values, and Matrix Approximations", journal = j-APL-MAT, volume = "13", number = "??", pages = "44--51", month = "????", year = "1968", CODEN = "APMTAK", ISSN = "0373-6725", MRclass = "65.35", MRnumber = "37 \#4944", MRreviewer = "L. W. Ehrlich", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Aplikace Matematiky", keywords = "nla, lsq, regr, svd, Schmidt-Mirsky theorem", } @Article{Bartels:1969:ASM, author = "Richard H. Bartels and Gene H. Golub", title = "{Algorithm 350}: simplex method procedure employing {LU} decomposition [{H}]", journal = j-CACM, volume = "12", number = "5", pages = "275--278", month = may, year = "1969", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/362946.362982", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Sat Nov 26 10:31:36 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/cacm.bib", note = "ACM Algorithm 350.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @Article{Bartels:1969:SML, author = "Richard H. Bartels and Gene H. Golub", title = "The Simplex Method of Linear Programming Using {LU} Decomposition", journal = j-CACM, volume = "12", number = "5", pages = "266--268", month = may, year = "1969", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/362946.362974", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Sat Nov 26 10:31:36 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/cacm.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "nla, nlop, lud, linear programming, updating", } @Article{Businger:1969:AAS, author = "Peter A. Businger and Gene H. Golub", title = "{Algorithm 358}: singular value decomposition of a complex matrix [{F1}, 4, 5]", journal = j-CACM, volume = "12", number = "10", pages = "564--565", month = oct, year = "1969", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Sat Nov 26 10:31:36 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/cacm.bib", note = "ACM Algorithm 358.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @TechReport{Buzbee:1969:MOE, author = "B. L. Buzbee and Gene H. Golub and C. W. Nielson", title = "The method of odd\slash even reduction and factorization with application to {Poisson}'s equation", type = "Technical Report", number = "CS-TR-69-128", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = apr, year = "1969", bibdate = "Thu Nov 06 17:28:54 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-69-128.html", abstract = "Several algorithms are presented for solving block tridiagonal systems of linear algebraic equations when the matrices on the diagonal are equal to each other and the matrices on the subdiagonals are all equal to each other. It is shown that these matrices arise from the finite difference approximation to certain elliptic partial differential equations on rectangular regions. Generalizations are derived for higher order equations and non-rectangular regions.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Dahlquist:1969:BEL, author = "Germund Dahlquist and Stanley C. Eisenstat and Gene H. Golub", title = "Bounds for the error of linear systems of equations using the theory of moments", type = "Technical Report", number = "CS-TR-69-141", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = oct, year = "1969", bibdate = "Thu Nov 06 17:33:07 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-69-141.html", abstract = "Consider the system of linear equations $ A \underset ~ \to x = \underset ~ \to b $ where A is an n$ \times $ n real symmetric, positive definite matrix and $ \underset \to b $ is a known vector. Suppose we are given an approximation to $ \underset ~ \to x $, $ \underset ~ \to \xi $, and we wish to determine upper and lower bounds for $ \Vert \underset ~ \to x \ - \underset ~ \to \xi \Vert $ where $ \Vert ... \Vert $ indicates the Euclidean norm. Given the sequence of vectors $ {\{ {\underset \to r}_i \} }^k_{i = 0} $ where $ {\underset ~ \to r}_i \ = A{\underset ~ \to r}_{i - 1} $ and $ {\underset ~ \to r}_o \ = \underset ~ \to b - A \underset ~ \to \xi $, it is shown how to construct a sequence of upper and lower bounds for $ \Vert \underset ~ \to x \ - \underset ~ \to \xi \Vert $ using the theory of moments. In addition, consider the Jacobi algorithm for solving the system $ \underset ~ \to x \ = M \underset ~ \to x + \underset ~ \to b \underline {viz.} {\underset ~ \to x}_{i + 1} = M{\underset \to x}_i + \underset ~ \to b $. It is shown that by examining $ {\underset ~ \to \delta }_i \ = {\underset ~ \to x}_{i + 1} - {\underset ~ \to x}_i $, it is possible to construct upper and lower bounds for $ \Vert {\underset \to x}_i - \underset ~ \to x \Vert $.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1969:CGQ, author = "Gene H. Golub and John H. Welsch", title = "Calculation of {Gauss} Quadrature Rules", journal = j-MATH-COMPUT, volume = "23", number = "106", pages = "221--230 + s1--s10", month = apr, year = "1969", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR database; Theory/Matrix.bib", note = "Loose microfiche suppl A1--A10. Reprinted in \cite{Chan:2007:MMC}.", URL = "http://www.jstor.org/stable/2004418", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "na, Gaussian quadrature", } @TechReport{Golub:1969:LLS, author = "Gene H. Golub and Michael A. Saunders", title = "Linear least squares and quadratic programming", type = "Technical Report", number = "CS-TR-69-134", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = may, year = "1969", bibdate = "Thu Nov 06 17:31:24 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-69-134.html", abstract = "Several algorithms are presented for solving linear least squares problems; the basic tool is orthogonalization techniques. A highly accurate algorithm is presented for solving least squares problems with linear inequality constraints. A method is also given for finding the least squares solution when there is a quadratic constraint on the solution.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Golub:1969:MDS, author = "Gene H. Golub", title = "Matrix decompositions and statistical calculations", type = "Technical Report", number = "CS-TR-69-124", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = mar, year = "1969", bibdate = "Thu Nov 06 17:26:56 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-69-124.html", abstract = "Several matrix decompositions which are of some interest in statistical calculations are presented. An accurate method for calculating the canonical correlation is given.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Golub:1969:MDSa, author = "G. H. Golub", title = "Matrix Decompositions and Statistical Calculations", type = "Technical Report", number = "124", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = "????", year = "1969", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "stat, nla, lsq, qrd, svd", } @InCollection{Golub:1969:MDSb, author = "G. H. Golub", title = "Matrix Decompositions and Statistical Computation", crossref = "Milton:1969:CSC", pages = "365--397", year = "1969", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Golub:1969:SVR, author = "Gene H. Golub and Richard R. Underwood", title = "Stationary Values of the Ratio of Quadratic Forms Subject to Linear Constraints", type = "Technical Report", number = "CS-TR-69-142", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = nov, year = "1969", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least squares, which is available by anonymous ftp from {\tt math.liu.se} in {\tt pub/references}.", URL = "http://i.stanford.edu/TR/CS-TR-69-142.html", abstract = "Let $A$ be a real symmetric matrix of order $n$, $B$ a real symmetric positive definite matrix of order $n$, and $C$ an $ n \times p$ matrix of rank $r$ with $ r \leq p < n$. We wish to determine vectors $ \underset ~ \to x $ for which $ {\underset ~ \to x}^T \ A \underset ~ \to x \ / {\underset \to x}^T \ B \underset ~ \to x $ is stationary and $ C^T \underset ~ \to x \ = \underset ~ \to \Theta $, the null vector. An algorithm is given for generating a symmetric eigensystem whose eigenvalues are the stationary values and for determining the vectors $ \underset ~ \to x $. Several Algol procedures are included.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "nla, geig, regularization", } @TechReport{Bartels:1970:NTMa, author = "Richard H. Bartels and Gene H. Golub and Michael A. Saunders", title = "Numerical techniques in mathematical programming", type = "Technical Report", number = "CS-TR-70-162", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = may, year = "1970", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-70-162.html", abstract = "The application of numerically stable matrix decompositions to minimization problems involving linear constraints is discussed and shown to be feasible without undue loss of efficiency. Part A describes computation and updating of the product-form of the LU decomposition of a matrix and shows it can be applied to solving linear systems at least as efficiently as standard techniques using the product-form of the inverse. Part B discusses orthogonalization via Householder transformations, with applications to least squares and quadratic programming algorithms based on the principal pivoting method of Cottle and Dantzig. Part C applies the singular value decomposition to the nonlinear least squares problem and discusses related eigenvalue problems.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InCollection{Bartels:1970:NTMb, author = "R. H. Bartels and G. H. Golub and M. A. Saunders", title = "Numerical Techniques in Mathematical Programming", crossref = "Rosen:1970:SNP", pages = "123--176", year = "1970", MRclass = "90.58 (65.00)", MRnumber = "42 \#7277", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least squares, which is available by anonymous ftp from {\tt math.liu.se} in {\tt pub/references}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "nla, qrd, rank determination", } @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-SIAM-J-NUMER-ANAL, volume = "7", number = "4", pages = "627--656", month = dec, year = "1970", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65.66", MRnumber = "44 \#4920", MRreviewer = "G. T. McAllister", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR database", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", keywords = "nla, pde, direct Poisson solver, sparse", } @TechReport{Buzbee:1970:DSD, author = "B. L. Buzbee and Fred W. Dorr and John Alan George and Gene H. Golub", title = "The direct solution of the discrete {Poisson} equation on irregular regions", type = "Technical Report", number = "CS-TR-71-195", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = dec, year = "1970", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-71-195.html", abstract = "There are several very fast direct methods which can be used to solve the discrete Poisson equation on rectangular domains. We show that these methods can also be used to treat problems on irregular regions.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Buzbee:1970:MOE, author = "B. L. Buzbee and Gene H. Golub and C. W. Nielson", title = "The method of odd\slash even reduction and factorization with application to {Poisson}'s equation, part {II}", type = "Technical Report", number = "CS-TR-70-155", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = mar, year = "1970", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-70-155.html", abstract = "In this paper, we derive and generalize the methods of Buneman for solving elliptic partial difference equations in a rectangular region. We show why the Buneman methods lead to numerically accurate solutions whereas the CORF algorithm may be numerically unstable. Several numerical examples are given and discussed.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Golub:1970:LAS, author = "G. H. Golub and R. Underwood and J. H. Wilkinson", title = "The {Lanczos} Algorithm for the Symmetric {$ A x = \lambda B x $} problem", type = "Technical report", number = "142", institution = "Computer Science Department, Stanford University", address = "Stanford, CA, USA", year = "1970", bibdate = "Fri Nov 10 07:11:31 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007); James H. Wilkinson (27 September 1919--5 October 1986)", } @InProceedings{Golub:1970:LLS, author = "G. H. Golub and M. A. Saunders", title = "Linear Least Squares and Quadratic Programming", crossref = "Abadie:1970:INP", pages = "229--256", year = "1970", MRclass = "90C20", MRnumber = "55 \#9983", bibdate = "Fri Dec 20 16:55:01 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least squares, which is available by anonymous ftp from {\tt math.liu.se} in {\tt pub/references}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "nlop, qrd, lsq, quadratic programming", } @TechReport{Golub:1970:SUL, author = "G. H. Golub", title = "Some uses of the {Lanczos} algorithm in numerical linear algebra", type = "Report", number = "STAN-CS-72-302", institution = "Computer Science Department, Stanford University", address = "Stanford, CA, USA", year = "1970", bibdate = "Fri Nov 10 07:15:29 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", remark = "Republished in \cite{Golub:1973:SUL}", } @Article{Golub:1970:SVD, author = "G. H. Golub and C. Reinsch", title = "Singular Value Decomposition and Least Squares Solutions", journal = j-NUM-MATH, volume = "14", number = "5", pages = "403--420", month = apr, year = "1970", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "Also in \cite[pp. 134--151]{Wilkinson:1971:LA}. Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022); Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "lsq; nla; rank determination; regularization; software; svd", } @Article{Golub:1970:SVR, author = "Gene H. Golub and Richard Underwood", title = "Stationary Values of the Ratio of Quadratic Forms Subject to Linear Constraints", journal = j-Z-ANGE-MATH-PHYS, volume = "21", number = "??", pages = "319--326 (or 318--326??)", month = "????", year = "1970", CODEN = "ZAMPDB", ISSN = "0044-2275 (print), 1420-9039 (electronic)", ISSN-L = "0044-2275", MRclass = "65.40", MRnumber = "42\#7056", MRreviewer = "J. D. P. Donnelly", bibdate = "Sun Jan 14 09:57:25 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und Physik = Journal of Applied Mathematics and Physics}", journal-URL = "http://link.springer.com/journal/33", } @TechReport{Bjorck:1971:NMC, author = "{\AA}ke Bj{\"o}rck and Gene H. Golub", title = "Numerical methods for computing angles between linear subspaces", type = "Technical Report", number = "CS-TR-71-225", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = jul, year = "1971", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/stanford-cstr.bib", URL = "http://i.stanford.edu/TR/CS-TR-71-225.html", abstract = "Assume that two subspaces $F$ and $G$ of unitary space are defined as the ranges (or nullspaces) of given rectangular matrices $A$ and $B$. Accurate numerical methods are developed for computing the principal angles $ \theta_k (F, G) $ and orthogonal sets of principal vectors $ u_k \ \epsilon F $ and $ v_k \epsilon G $, $ k = 1, 2, \ldots {}, q = \dim (G) \leq \dim (F)$. An important application in statistics is computing the canonical correlations $ \sigma_k = \cos \theta_k $ between two sets of variates. A perturbation analysis shows that the condition number for $ \theta_k $ essentially is $ \max (\kappa (A), \kappa (B)) $, where $ \kappa $ denotes the condition number of a matrix. The algorithms are based on a preliminary $ Q R$-factorization of $A$ and $B$ (or $ A^H$ and $ B^H$), for which either the method of Householder transformations (HT) or the modified Gram--Schmidt method (MGS) is used. Then $ \cos \theta_k$ and $ \sin \theta_k$ are computed as the singular values of certain related matrices. Experimental results are given, which indicates that MGS gives $ \theta_k $ with equal precision and fewer arithmetic operations than HT. However, HT gives principal vectors, which are orthogonal to working accuracy, which is not in general true for MGS. Finally the case when $A$ and\slash or $B$ are rank deficient is discussed.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Buzbee:1971:DSD, author = "B. L. Buzbee and F. W. Dorr and J. A. George and G. H. Golub", title = "The Direct Solution of the Discrete {Poisson} Equation on Irregular Regions", journal = j-SIAM-J-NUMER-ANAL, volume = "8", number = "4", pages = "722--736", month = dec, year = "1971", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65Q05", MRnumber = "45 \#1403", MRreviewer = "J. R. Kuttler", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR database", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", keywords = "nla, pde, direct Poisson solver, sparse", } @Article{Golub:1971:AAC, author = "G. H. Golub and L. B. Smith", title = "{ACM} Algorithm 414: {Chebyshev} Approximation of Continuous Functions by a {Chebyshev} System of Functions", journal = j-CACM, volume = "14", number = "11", pages = "737--746", month = nov, year = "1971", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Tue Sep 20 19:46:04 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/cacm.bib", note = "ACM Algorithm 414.", acknowledgement = ack-nj, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @InCollection{Golub:1971:DMS, author = "G. H. Golub", title = "Direct methods for solving elliptic difference equations", crossref = "Morris:1971:STN", pages = "1--19", year = "1971", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1971:MMM, author = "Gene Golub", title = "Matrix methods in mathematical programming", journal = j-LECT-NOTES-MATH, volume = "193", pages = "21--39", year = "1971", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/BFb0060342", ISBN = "3-540-05422-7 (print), 3-540-36538-9 (e-book)", ISBN-13 = "978-3-540-05422-1 (print), 978-3-540-36538-9 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", bibdate = "Fri May 9 19:07:44 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/lnm1970.bib", URL = "http://link.springer.com/chapter/10.1007/BFb0060342/", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", book-DOI = "https://doi.org/10.1007/BFb0060340", book-URL = "http://www.springerlink.com/content/978-3-540-36538-9", fjournal = "Lecture Notes in Mathematics", journal-URL = "http://link.springer.com/bookseries/304", } @TechReport{Golub:1971:NCU, author = "Gene H. Golub and George P. H. Styan", title = "Numerical computations for univariate linear models", type = "Technical Report", number = "CS-TR-71-236", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = sep, year = "1971", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-71-236.html", abstract = "We consider the usual univariate linear model E($ \underset ~ \to y$) = $ \underset ~ \to X \underset ~ \to \gamma $ , V ($ \underset ~ \to y$) = $ \sigma^2 \underset ~ \to I$. In Part One of this paper $ \underset ~ \to X$ has full column rank. Numerically stable and efficient computational procedures are developed for the least squares estimation of $ \underset ~ \to \gamma $ and the error sum of squares. We employ an orthogonal triangular decomposition of $ \underset ~ \to X$ using Householder transformations. A lower bound for the condition number of $ \underset ~ \to X$ is immediately obtained from this decomposition. Similar computational procedures are presented for the usual F-test of the general linear hypothesis $ \underset ~ \to L \ ' \underset ~ \to \gamma $ = $ \underset ~ \to 0$ ; $ \underset ~ \to L \ ' \underset ~ \to \gamma $ = $ \underset ~ \to m$ is also considered for $ \underset ~ \to m \ \neq \ 0$. Updating techniques are given for adding to or removing from ($ \underset ~ \to X, \underset ~ \to y$) a row, a set of rows or a column . In Part Two, $ \underset ~ \to X$ has less than full rank. Least squares estimates are obtained using generalized inverses. The function $ \underset ~ \to L ' \underset ~ \to \gamma $ is estimable whenever it admits an unbiased estimator linear in $ \underset ~ \to y$. We show how to computationally verify estimability of $ \underset ~ \to L ' \underset ~ \to \gamma $ and the equivalent testability of $ \underset ~ \to L ' \underset ~ \to \gamma \ = \underset ~ \to 0$.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Golub:1971:SMEa, author = "Gene H. Golub", title = "Some modified eigenvalue problems", type = "Technical Report", number = "CS-TR-71-234", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = aug, year = "1971", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-71-234.html", abstract = "We consider the numerical calculation of several eigenvalue problems which require some manipulation before the standard algorithms may be used. This includes finding the stationary values of a quadratic form subject to linear constraints and determining the eigenvalues of a matrix which is modified by a matrix of rank one. We also consider several inverse eigenvalue problems. This includes the problem of computing the Gauss-Radau and Gauss-Lobatto quadrature rules. In addition, we study several eigenvalue problems which arise in least squares.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1971:SMEb, author = "G. H. Golub", title = "Some modified eigenvalue problems", journal = j-LECT-NOTES-MATH, volume = "228", pages = "56--56", year = "1971", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/BFb0069447", ISBN = "3-540-05656-4 (print), 3-540-36976-7 (e-book)", ISBN-13 = "978-3-540-05656-0 (print), 978-3-540-36976-9 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", bibdate = "Fri May 9 19:07:43 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/lnm1970.bib", URL = "http://link.springer.com/chapter/10.1007/BFb0069447", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", book-DOI = "https://doi.org/10.1007/BFb0069442", book-URL = "http://www.springerlink.com/content/978-3-540-36976-9", fjournal = "Lecture Notes in Mathematics", journal-URL = "http://link.springer.com/bookseries/304", } @TechReport{Anderssen:1972:RNS, author = "Robert S. Anderssen and Gene H. Golub", title = "{Richardson}'s non-stationary matrix iterative procedure", type = "Technical Report", number = "CS-TR-72-304", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = aug, year = "1972", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-72-304.html", abstract = "Because of its simplicity, Richardson's non-stationary iterative scheme is a potentially powerful method for the solution of (linear) operator equations. However, its general application has more or less been blocked by (a) the problem of constructing polynomials, which deviate least from zero on the spectrum of the given operator, and which are required for the determination of the iteration parameters of the non-stationary method, and (b) the instability of this scheme with respect to rounding error effects. Recently, these difficulties were examined in two Russian papers. In the first, Lebedev [1969] constructed polynomials which deviate least from zero on a set of subintervals of the real axis which contains the spectrum of the given operator. In the second, Lebedev and Finogenov [1971] gave an ordering for the iteration parameters of the non-stationary Richardson scheme which makes it a stable numerical process. Translation of these two papers appear as Appendices 1 and 2, respectively, in this report. The body of the report represents an examination of the properties of Richardson's non-stationary scheme and the pertinence of the two mentioned papers along with the results of numerical experimentation testing the actual implementation of the procedures given in them.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Concus:1972:UFD, author = "Paul Concus and Gene H. Golub", title = "Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations", type = "Technical Report", number = "CS-TR-72-278", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = apr, year = "1972", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-72-278.html", abstract = "We study an iterative technique for the numerical solution of strongly elliptic equations of divergence form in two dimensions with Dirichlet boundary conditions on a rectangle. The technique is based on the repeated solution by a fast direct method of a discrete Helmholtz equation on a uniform rectangular mesh. The problem is suitably scaled before iteration, and Chebyshev acceleration is applied to improve convergence. We show that convergence can be exceedingly rapid and independent of mesh size for smooth coefficients. Extensions to other boundary conditions, other equations, and irregular mesh spacings are discussed, and the performance of the technique is illustrated with numerical examples.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Dahlquist:1972:BEL, author = "Germund Dahlquist and Stanley C. Eisenstat and Gene H. Golub", title = "Bounds for the error of linear systems of equations using the theory of moments", journal = j-J-MATH-ANAL-APPL, volume = "37", number = "1", pages = "151--166", month = jan, year = "1972", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(72)90264-8", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "65F99", MRnumber = "45 1368", MRreviewer = "J. G. Herriot", bibdate = "Sun Jan 14 09:56:10 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", } @TechReport{Gill:1972:MMM, author = "Phillip E. Gill and Gene H. Golub and Walter A. Murray and Michael A. Saunders", title = "Methods for modifying matrix factorizations", type = "Technical Report", number = "CS-TR-72-322", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = nov, year = "1972", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-72-322.html", abstract = "In recent years several algorithms have appeared for modifying the factors of a matrix following a rank-one change. These methods have always been given in the context of specific applications and this has probably inhibited their use over a wider field. In this report several methods are described for modifying Cholesky factors. Some of these have been published previously while others appear for the first time. In addition, a new algorithm is presented for modifying the complete orthogonal factorization of a general matrix, from which the conventional QR factors are obtained as a special case. A uniform notation has been used and emphasis has been placed on illustrating the similarity between different methods.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Golub:1972:CBS, author = "Gene H. Golub and James M. Varah", title = "On a characterization of the best $ \ell_2 $ scaling of a matrix", type = "Technical Report", number = "CS-TR-72-319", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = oct, year = "1972", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-72-319.html", abstract = "This paper is concerned with best two-sided scaling of a general square matrix, and in particular with a certain characterization of that best scaling: namely that the first and last singular vectors (on left and right) of the scaled matrix have components of equal modulus. Necessity, sufficiency, and its relation with other characterizations are discussed. Then the problem of best scaling for rectangular matrices is introduced and a conjecture made regarding a possible best scaling. The conjecture is verified for some special cases.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Golub:1972:DPN, author = "Gene H. Golub and Victor Pereyra", title = "The differentiation of pseudoinverses and nonlinear least squares problems whose variables separate", type = "Technical Report", number = "CS-TR-72-261", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = feb, year = "1972", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-72-261.html", abstract = "For given data ($ t_i \, y_i), i = 1, \ldots, m $ , we consider the least squares fit of nonlinear models of the form F($ \underset ~ \to a \, \underset ~ \to \alpha \; t) = \sum_{j = 1}^n \ g_j (\underset ~ \to a) \varphi_j (\underset ~ \to \alpha \; t), \underset ~ \to a \ \epsilon R^s \, \underset ~ \to \alpha \ \epsilon R^k \ $. For this purpose we study the minimization of the nonlinear functional r($ \underset ~ \to a \, \underset ~ \to \alpha) = \sum_{i = 1}^m {(y_i - F(\underset ~ \to a, \underset ~ \to \alpha, t_i))}^2 $. It is shown that by defining the matrix $ { \{ \Phi (\underset ~ \to \alpha \} }_{i, j} = \varphi_j (\underset ~ \to \alpha; t_i) $ , and the modified functional $ r_2 (\underset ~ \to \alpha) = {\l } \ \underset ~ \to y \ - \Phi (\underset ~ \to \alpha) \Phi^+(\underset ~ \to \alpha) \underset ~ \to y {\l }_2^2 $, it is possible to optimize first with respect to the parameters $ \underset ~ \to \alpha $ , and then to obtain, a posteriori, the optimal parameters $ \overset^\to {\underset ~ \to a} $. The matrix $ \Phi^+(\underset ~ \to \alpha $) is the Moore-Penrose generalized inverse of $ \Phi (\underset ~ \to \alpha $), and we develop formulas for its Frechet derivative under the hypothesis that $ \Phi (\underset ~ \to \alpha $) is of constant (though not necessarily full) rank. From these formulas we readily obtain the derivatives of the orthogonal projectors associated with $ \Phi (\underset ~ \to \alpha $), and also that of the functional $ r_2 (\underset ~ \to \alpha $). Detailed algorithms are presented which make extensive use of well-known reliable linear least squares techniques, and numerical results and comparisons are given. These results are generalizations of those of H. D. Scolnik [1971].", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Golub:1972:LAS, author = "Gene H. Golub and Richard R. Underwood and James H. Wilkinson", title = "The {Lanczos} Algorithm for the Symmetric {$ A x = \lambda B x $} Problem", type = "Technical Report", number = "CS-TR-72-270", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "24", month = mar, year = "1972", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", URL = "http://i.stanford.edu/TR/CS-TR-72-270.html", abstract = "The problem of computing the eigensystem of Ax = $ \lambda $Bx when A and B are symmetric and B is positive definite is considered. A generalization of the Lanczos algorithm for reducing the problem to a symmetric tridiagonal eigenproblem is given. A numerically stable variant of the algorithm is described. The new algorithm depends heavily upon the computation of elementary Hermitian matrices. An ALGOL W procedure and a numerical example are also given.", acknowledgement = ack-nhfb, author-dates = "Cornelius Lanczos (2 February 1893--25 June 1974); Gene Howard Golub (February 29, 1932--November 16, 2007); James H. Wilkinson (27 September 1919--5 October 1986)", keywords = "nla, geig, Lanczos algorithm", } @Article{Bjorck:1973:NMC, author = "{\AA}ke Bj{\"o}rck and Gene H. Golub", title = "Numerical Methods for Computing Angles between Linear Subspaces", journal = j-MATH-COMPUT, volume = "27", number = "123", pages = "579--594", month = jul, year = "1973", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F30", MRnumber = "50 1485", MRreviewer = "J. Legras", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database; Parallel/par.lin.alg.bib; Theory/Matrix.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", URL = "http://www.jstor.org/stable/2005662", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classcodes = "B0240 (Probability and statistics); B0290H (Linear algebra); C1140 (Probability and statistics); C4140 (Linear algebra)", corpsource = "Link{\"o}ping Univ., Sweden", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "angles between linear; canonical; computing; correlations; matrix algebra; numerical methods; rectangular matrices; statistics; subspaces", kwds = "math, nla, gsvd, canonical angles, subspace metric", treatment = "T Theoretical or Mathematical", } @Article{Concus:1973:UFD, author = "Paul Concus and Gene H. Golub", title = "Use of Fast Direct Methods for the Efficient Numerical Solution of Nonseparable Elliptic Equations", journal = j-SIAM-J-NUMER-ANAL, volume = "10", number = "6", pages = "1103--1120", month = dec, year = "1973", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65N05", MRnumber = "49", MRreviewer = "P. Laasonen", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/gvl.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database", URL = "http://www.jstor.org/stable/2156207", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", keywords = "nla, fast algorithm, elliptic pde, direct Poisson solver", } @InCollection{Dantzig:1973:NSO, author = "G. B. Dantzig and R. W. Cottle and B. C. Eaves and G. H. Golub and F. S. Hillier and A. S. Manne and D. J. Wilde and R. B. Wilson", title = "On the need for a {Systems Optimization Laboratory}", crossref = "Hu:1973:MPP", pages = "1--32", year = "1973", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", xxnote = "Is the cross-reference correct?? The original title Mathematical Programming matches a great many library catalog entries.", } @TechReport{Dent:1973:CLI, author = "Warren T. Dent and Gene H. Golub", title = "Computation of the limited information maximum likelihood estimator", type = "Technical Report", number = "CS-TR-73-339", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = feb, year = "1973", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-73-339.html", abstract = "Computation of the Limited Information Maximum Likelihood Estimator (LIMLE) of the set of coefficients in a single equation of a system of interdependent relations is sufficiently complicated to detract from other potentially interesting properties. Although for finite samples the LIMLE has no moments, asymptotically it remains normally distributed and retains other properties associated with maximum likelihood. The most extensive application of the estimator has been made in the Brookings studies. We believe that current methods of estimation are clumsy, and present a numerically stable estimation schema based on Householder transformations and the singular value decomposition. The analysis permits a convenient demonstration of equivalence with the Two Stage Least Squares Estimator (TSLSE) in the instance of just identification.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InProceedings{Golub:1973:CLI, author = "G. H. Golub and W. Dent", title = "Computation of the limited information maximum likelihood estimator", crossref = "Tarter:1973:PCS", pages = "60--65", year = "1973", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Golub:1973:CSDa, author = "Gene H. Golub and Eugene Seneta", title = "Computation of the stationary distribution of an infinite {Markov} matrix", type = "Technical Report", number = "CS-TR-73-335", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = jan, year = "1973", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-73-335.html", abstract = "An algorithm is presented for computing the unique stationary distribution of an infinite stochastic matrix possessing at least one column whose elements are bounded away from zero. Elementwise convergence rate is discussed by means of two examples.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1973:CSDb, author = "G. H. Golub and E. Seneta", title = "Computation of the stationary distribution of an infinite {Markov} matrix", journal = j-BULL-AUSTRAL-MATH-SOC, volume = "8", number = "??", pages = "333--341", month = "????", year = "1973", CODEN = "ALNBAB", ISSN = "0004-9727 (print), 1755-1633 (electronic)", ISSN-L = "0004-9727", MRclass = "60J10 (68A10)", MRnumber = "50 \#8710", MRreviewer = "I. Vaduva", bibdate = "Fri Dec 20 17:00:44 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Bulletin of the Australian Mathematical Society", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ", } @Article{Golub:1973:DPI, author = "G. H. Golub and V. Pereyra", title = "The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate", journal = j-SIAM-J-NUMER-ANAL, volume = "10", number = "2", pages = "413--432", month = apr, year = "1973", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65F15", MRnumber = "49 \#1753", MRreviewer = "R. P. Tewarson", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR database", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", } @InProceedings{Golub:1973:EPR, author = "Gene H. Golub and Irwin Guttman and Rudolf Dutter", title = "Examination of pseudo-residuals of outliers for detecting spurosity in the general univariate linear model", crossref = "Kabe:1973:MSI", pages = "63--108", year = "1973", MRclass = "62J05", MRnumber = "51 9380", MRreviewer = "Colin L. Mallows", bibdate = "Sun Jan 14 09:51:59 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1973:NCU, author = "Gene H. Golub and George P. H. Styan", title = "Numerical computations for univariate linear models", journal = j-J-STAT-COMPUT-SIMUL, volume = "2", number = "3", pages = "253--274", year = "1973", CODEN = "JSCSAJ", DOI = "https://doi.org/10.1080/00949657308810051", ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163", ISSN-L = "0094-9655", MRclass = "62J05 (65F05)", MRnumber = "51 11840", MRreviewer = "Valery Fedorov", bibdate = "Tue Apr 22 09:10:34 MDT 2014", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Journal of Statistical Computation and Simulation", journal-URL = "http://www.tandfonline.com/loi/gscs20", keywords = "stat, nla, regr, lsq, qrd", } @InProceedings{Golub:1973:SAN, author = "G. H. Golub and George P. H. Styan", title = "Some aspects of numerical computations for linear models", crossref = "Kennedy:1973:PCS", pages = "189--192", year = "1973", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1973:SMM, author = "Gene H. Golub", title = "Some Modified Matrix Eigenvalue Problems", journal = j-SIAM-REVIEW, volume = "15", number = "2", pages = "318--334", month = apr, year = "1973", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1015032", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "65F15", MRnumber = "48 7569", MRreviewer = "J. F. Traub", bibdate = "Thu Mar 27 09:06:49 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/15/2; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least squares, which is available at \verb=ftp://math.liu.se/pub/references=. Reprinted in \cite{Chan:2007:MMC}.", URL = "http://www.jstor.org/stable/2028604", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", error = "conflicting pages with your cv: 318-335", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", keywords = "nla, eig, updating", onlinedate = "April 1973", xxpages = "318--344", } @InCollection{Golub:1973:SUL, author = "G. H. Golub", title = "Some uses of the {Lanczos} algorithm in numerical algebra", crossref = "Miller:1973:TNA", pages = "173--184", year = "1973", MRclass = "65F15", MRnumber = "50 \#11743", MRreviewer = "F. Szidarovszky", bibdate = "Fri Dec 20 17:46:23 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Cottle:1974:SLS, author = "Richard W. Cottle and Gene H. Golub and Richard S. Sacher", title = "On the solution of large, structured linear complementarity problems: {III}", type = "Technical Report", number = "CS-TR-74-439", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = aug, year = "1974", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-74-439.html", abstract = "This paper addresses the problem of solving a class of specially-structured linear complementarity problems of potentially very large size. An efficient method which couples a modification of the block successive overrelaxation technique and several techniques discussed by the authors in previous papers is proposed. Problems of the type considered arise, for example, in solving approximations to both the free boundary problem for finite-length journal bearings and percolation problems in porous dams by numerical methods. These applications and our computational experience with the method are presented here.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Fischer:1974:FTM, author = "D. Fischer and G. Golub and O. Hald and C. Leiva and O. Widlund", title = "On {Fourier--Toeplitz} Methods for Separable Elliptic Problems", journal = j-MATH-COMPUT, volume = "28", number = "126", pages = "349--368", month = apr, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F05 (65N20)", MRnumber = "54 \#4072", MRreviewer = "R. H. Bartels", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classcodes = "B0290P (Differential equations); B0220 (Mathematical analysis); C4170 (Differential equations)", corpsource = "New York Univ., NY, USA", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "differential equations; elliptic; fast; fast Fourier transforms; Fourier Toeplitz method; Fourier transform; numerical methods; separable elliptic problems; Toeplitz factorizations", treatment = "T Theoretical or Mathematical", } @Article{Gill:1974:MMM, author = "P. E. Gill and G. H. Golub and W. Murray and M. A. Saunders", title = "Methods for Modifying Matrix Factorizations", journal = j-MATH-COMPUT, volume = "28", number = "126", pages = "505--535", month = apr, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F05", MRnumber = "49 \#8299", MRreviewer = "L. W. Ehrlich", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database; Theory/Matrix.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)", corpsource = "Nat. Phys. Lab., Teddington, UK", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "Cholesky factors; complete orthogonal factorisation; matrix algebra; matrix factorizations; rank one change", kwds = "math, nla, qrd, lud, updating", treatment = "T Theoretical or Mathematical", } @Article{Golub:1974:BMM, author = "G. H. Golub", title = "Bounds for matrix moments", journal = j-ROCKY-MOUNTAIN-J-MATH, volume = "4", number = "2", pages = "207--211", month = "????", year = "1974", CODEN = "RMJMAE", DOI = "https://doi.org/10.1216/RMJ-1974-4-2-207", ISSN = "0035-7596 (print), 1945-3795 (electronic)", ISSN-L = "0035-7596", MRclass = "65F30", MRnumber = "48 12803", MRreviewer = "Walter Gautschi", bibdate = "Sun Jan 14 09:54:42 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Proceedings of the International Conference on Pad{\'e} Approximants, Continued Fractions and Related Topics (Univ. Colorado, Boulder, Colo., 1972; dedicated to the memory of H. S. Wall)", URL = "http://projecteuclid.org/euclid.rmjm/1250130962", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Rocky Mountain Journal of Mathematics", journal-URL = "http://projecteuclid.org/euclid.rmjm", } @Article{Golub:1974:CBS, author = "G. H. Golub and J. M. Varah", title = "On a Characterization of the Best $ l_2 $-Scaling of a Matrix", journal = j-SIAM-J-NUMER-ANAL, volume = "11", number = "3", pages = "472--479", month = jun, year = "1974", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65F35 (15A12)", MRnumber = "55 \#9510", MRreviewer = "H. Schwerdtfeger", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR database", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", keywords = "nla, condition, scaling", } @Article{Golub:1974:CSD, author = "G. H. Golub and E. Seneta", title = "Computation of the stationary distribution of an infinite stochastic matrix of special form", journal = j-BULL-AUSTRAL-MATH-SOC, volume = "10", number = "??", pages = "255--261", month = "????", year = "1974", CODEN = "ALNBAB", ISSN = "0004-9727 (print), 1755-1633 (electronic)", ISSN-L = "0004-9727", MRclass = "60J10", MRnumber = "51 \#9212", MRreviewer = "Dean Isaacson", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Bulletin of the Australian Mathematical Society", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ", } @InProceedings{Golub:1974:MCE, author = "G. H. Golub", title = "Methods for computing eigenvalues of sparse matrix equations", crossref = "Pereyra:1974:ADS", pages = "127--148", year = "1974", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Book{Miller:1974:TNA, editor = "John J. H. Miller", title = "Topics in Numerical Analysis {II}: Proceedings of the Royal Irish Academy Conference on Numerical Analysis, 1974", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "xiv + 266", year = "1974", ISBN = "0-12-496952-6", ISBN-13 = "978-0-12-496952-0", LCCN = "QA297.R69 1974", bibdate = "Sat Oct 22 18:09:20 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Bjorck:1975:EMA, author = "{\AA}ke Bj{\"o}rck and Gene H. Golub", title = "Eigenproblems for matrices associated with periodic boundary conditions", type = "Technical Report", number = "CS-TR-75-486", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = mar, year = "1975", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-75-486.html", abstract = "A survey of algorithms for solving the eigenproblem for a class of matrices of nearly tridiagonal form is given. These matrices arise from eigenvalue problems for differential equations where the solution is subject to periodic boundary conditions. Algorithms both for computing selected eigenvalues and eigenvectors and for solving the complete eigenvalue problem are discussed.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InProceedings{Concus:1975:GCG, author = "Paul Concus and Gene H. Golub", title = "A generalized conjugate gradient method for non-symmetric systems of linear equations", crossref = "Glowinski:1975:CMA", pages = "56--65", year = "1975", MRclass = "65F10", MRnumber = "57 7968", MRreviewer = "David R. Kincaid", bibdate = "Sun Jan 14 09:49:28 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Golub:1975:ICE, author = "Gene H. Golub and James H. Wilkinson", title = "Ill-Conditioned Eigensystems and the Computation of the {Jordan} Canonical Form", type = "Technical Report", number = "CS-TR-75-478", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = feb, year = "1975", bibdate = "Wed Aug 24 16:47:40 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib", note = "Published as \cite{Golub:1976:ICE}.", URL = "http://i.stanford.edu/TR/CS-TR-75-478.html", abstract = "The solution of the complete eigenvalue problem for a non-normal matrix A presents severe practical difficulties when A is defective or close to a defective matrix. However in the presence of rounding errors one cannot even determine whether or not a matrix is defective. Several of the more stable methods for computing the Jordan canonical form are discussed together with the alternative approach of computing well-defined bases (usually orthogonal) of the relevant invariant subspaces.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InCollection{Golub:1975:SMC, author = "G. H. Golub", title = "Sparse matrix computations: Eigenvalues and linear equations", crossref = "Anonymous:1975:SI", pages = "117--140", year = "1975", bibdate = "Fri Dec 20 18:47:30 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1975:WPS, author = "G. H. Golub and L. Jenning and W. H. Yang", title = "Waves in periodically structured media", journal = j-J-COMPUT-PHYS, volume = "17", number = "4", pages = "349--357", month = apr, year = "1975", CODEN = "JCTPAH", DOI = "https://doi.org/10.1016/0021-9991(75)90039-X", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", bibdate = "Sun Jan 1 09:15:17 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib", URL = "http://www.sciencedirect.com/science/article/pii/002199917590039X", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991/", } @InProceedings{Cline:1976:CNM, author = "A. K. Cline and G. H. Golub and G. W. Platzman", title = "Calculation of Normal Modes of Oceans Using a {Lanczos} Method", crossref = "Bunch:1976:SMC", pages = "409--426", year = "1976", bibdate = "Sat Oct 22 18:13:05 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "nla, eig, Lanczos algorithm", } @TechReport{Concus:1976:GCGa, author = "Paul Concus and Gene H. Golub and Dianne Prost O'Leary", title = "A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations", type = "Technical Report", number = "CS-TR-76-533", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = jan, year = "1976", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-76-533.html", abstract = "We consider a generalized conjugate gradient method for solving sparse, symmetric, positive-definite systems of linear equations, principally those arising from the discretization of boundary value problems for elliptic partial differential equations. The method is based on splitting off from the original coefficient matrix a symmetric, positive-definite one that corresponds to a more easily solvable system of equations, and then accelerating the associated iteration using conjugate gradients. Optimality and convergence properties are presented, and the relation to other methods is discussed. Several splittings for which the method seems particularly effective are also discussed, and for some, numerical examples are given.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Concus:1976:GCGb, author = "Paul Concus and Gene H. Golub", title = "A Generalized {Conjugate Gradient} Method for Nonsymmetric Systems of Linear Equations", type = "Technical Report", number = "CS-TR-76-535", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = jan, year = "1976", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/par.lin.alg.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-76-535.html", abstract = "We consider a generalized conjugate gradient method for solving systems of linear equations having nonsymmetric coefficient matrices with positive-definite symmetric part. The method is based on splitting the matrix into its symmetric and skew-symmetric parts, and then accelerating the associated iteration using conjugate gradients, which simplifies in this case, as only one of the two usual parameters is required. The method is most effective for cases in which the symmetric part of the matrix corresponds to an easily solvable system of equations. Convergence properties are discussed, as well as an application to the numerical solution of elliptic partial differential equations.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InProceedings{Concus:1976:GCGc, author = "Paul Concus and Gene H. Golub and Dianne P. O'Leary", title = "A Generalized Conjugate Gradient Method for the Numerical Solution of Elliptic Partial Differential Equations", crossref = "Bunch:1976:SMC", pages = "309--332", year = "1976", MRclass = "65F10 (65P05)", MRnumber = "58", MRreviewer = "M. R. Hestenes", bibdate = "Sun Jan 14 09:48:20 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "nla, conjugate gradients, elliptic pde", } @TechReport{Concus:1976:NSN, author = "Paul Concus and Gene H. Golub and Dianne Prost O'Leary", title = "Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method", type = "Technical Report", number = "CS-TR-76-585", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "43", month = dec, year = "1976", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-76-585.html", abstract = "We have studied previously a generallized conjugate gradient method for solving sparse positive-definite systems of linear equations arising from the discretization of elliptic partial-differential boundary-value problems. Here, extensions to the nonlinear case are considered. We split the original discretized operator into the sum of two operators, one of which corresponds to a more easily solvable system of equations, and accelerate the associated iteration based on this splitting by (nonlinear) conjugate gradients. The behavior of the method is illustrated for the minimal surface equation with splittings corresponding to nonlinear SSOR, to approximate factorization of the Jacobian matrix, and to elliptic operators suitable for use with fast direct methods. The results of numerical experiments are given as well for a mildly nonlinear example, for which, in the corresponding linear case, the finite termination property of the conjugate gradient algorithm is crucial.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "differential equations, elliptic --- numerical solutions", } @Article{Golub:1976:CVO, author = "G. H. Golub and M. Heath and G. Wahba", title = "Cross-Validation and Optimum Ridge Regression", journal = j-SIAM-REVIEW, volume = "18", number = "4", pages = "806--806", month = "????", year = "1976", CODEN = "SIREAD", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Thu Jun 6 10:13:11 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @InCollection{Golub:1976:DPI, author = "G. H. Golub and V. Pereyra", title = "Differentiation of Pseudo-Inverses, Separable Nonlinear Least Squares Problems and Other Tales", crossref = "Nashed:1976:GIA", pages = "303--324", year = "1976", MRclass = "65F20 (15A09 65J05)", MRnumber = "58 \#8200", MRreviewer = "B. Levinger", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @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-SIAM-REVIEW, volume = "18", number = "4", pages = "578--619", month = "????", year = "1976", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1018113", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "65F15 (15A21)", MRnumber = "54 \#1570", MRreviewer = "Robert Todd Gregory", bibdate = "Fri Dec 20 17:05:12 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", keywords = "nla, eig, Jordan form, condition, pert, ill-conditioned problem", } @TechReport{Golub:1976:RDL, author = "Gene H. Golub and Virginia C. Klema and Gilbert W. Stewart", title = "Rank degeneracy and least squares problems", type = "Technical Report", number = "CS-TR-76-559", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = aug, year = "1976", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-76-559.html", abstract = "This paper is concerned with least squares problems when the least squares matrix A is near a matrix that is not of full rank. A definition of numerical rank is given. It is shown that under certain conditions when A has numerical rank r there is a distinguished r dimensional subspace of the column space of A that is insensitive to how it is approximated by r independent columns of A. The consequences of this fact for the least squares problem are examined. Algorithms are described for approximating the stable part of the column space of A.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Golub:1976:RDLa, author = "Gene H. Golub and Virginia Klema and G. W. Stewart", title = "Rank Degeneracy and Least Squares Problems", type = "Technical Report", number = "TR-456", institution = inst-U-MARYLAND, address = inst-U-MARYLAND:adr, pages = "????", month = jun, year = "1976", bibdate = "Wed May 28 17:40:15 2014", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/university-of-maryland.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; 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.bib", note = "Also published as Stanford University Computer Science Department Technical Report STAN-CS-76-559.", abstract = "This paper is concerned with least squares problems when the least squares matrix \$A\$ is near a matrix that is not of full rank. A definition of numerical rank is given. It is shown that under certain conditions when \$A\$ has numerical rank \$r\$ there is a distinguished \$r\$ dimensional subspace of the column space of \$A\$ that is insensitive to how it is approximated by \$r\$ independent columns of \$A\$. The consequences of this fact for the least squares problem are examined. Algorithms are described for approximating the stable part of the column space of \$A\$.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "nla, svd, qrd, condition estimation, rank determination, pert, variable selection", xxnote = "Check: is this the same as Golub:1976:RDLb? If so, which report number is correct??", } @TechReport{Golub:1976:RDLb, author = "G. H. Golub and Virginia Klema and G. W. {Stewart III}", title = "Rank Degeneracy and Least Squares Problems", type = "Report", number = "TR-751", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, pages = "????", month = "????", year = "1976", bibdate = "Thu May 29 16:12:45 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", GWS-number = "N6", xxnote = "Check: is this the same as Golub:1976:RDLa? If so, which report number is correct??", } @InProceedings{Golub:1976:SVD, author = "G. H. Golub and F. Luk", title = "Singular value decomposition: applications and computations", crossref = "ARO:1976:PAN", pages = "??--??", year = "1976", bibdate = "Sat Oct 29 16:12:16 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Bjorck:1977:EMA, author = "{\AA}ke Bj{\"o}rck and Gene H. Golub", title = "Eigenproblems for Matrices Associated with Periodic Boundary Conditions", journal = j-SIAM-REVIEW, volume = "19", number = "1", pages = "5--16", month = jan, year = "1977", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1019002", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "65F15", MRnumber = "55 1716", MRreviewer = "B. Levinger", bibdate = "Sat Mar 29 09:52:39 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/19/1; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "http://www.jstor.org/stable/2029322", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "January 1977", } @TechReport{Boley:1977:IEPa, author = "D. Boley and Gene H. Golub", title = "Inverse eigenvalue problems for band matrices", type = "Technical Report", number = "STAN-CS-77-623", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "9", month = "????", year = "1977", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "eigenvalues; matrices", } @InCollection{Boley:1977:IEPb, author = "D. Boley and G. H. Golub", title = "Inverse eigenvalue problems for band matrices", crossref = "Watson:1978:NAP", pages = "??--??", month = jun, year = "1977", bibdate = "Sat Oct 29 18:52:59 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InCollection{Buzbee:1977:VCS, author = "B. Buzbee and G. Golub and J. Howell", title = "Vectorizations for the {CRAY-1} of Some Methods for Solving Elliptic Difference Equations", crossref = "Kuck:1977:HSC", pages = "255--271", year = "1977", bibdate = "Thu Sep 12 14:08:54 2002", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/ovr.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{deBoor:1977:NSR, author = "Carl de Boor and Gene H. Golub", title = "The numerically stable reconstruction of a {Jacobi} matrix from spectral data", type = "Technical Report", number = "CS-TR-77-602", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "18", month = mar, year = "1977", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-77-602.html", abstract = "We show how to construct, from certain spectral data, a discrete inner product for which the associated sequence of monic orthogonal polynomials coincides with the sequence of appropriately normalized characteristic polynomials of the left principal submatrices of the Jacobi matrix. The generation of these orthogonal polynomials via their three term recurrence relation, as popularized by Forsythe, then provides a stable means of computing the entries of the Jacobi matrix. The resulting algorithm might be of help in the approximate solution of inverse eigenvalue problems for Sturm-Liouville equations. Our construction provides, incidentally, very simple proofs of known results concerning existence and uniqueness of a Jacobi matrix satisfying given spectral data and its continuous dependence on that data.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "jacobi varieties; matrices", } @TechReport{Golub:1977:BLMa, author = "Gene H. Golub and Franklin T. Luk and Michael L. Overton", title = "A block {Lanczos} method to compute the singular values and corresponding singular vectors of a matrix", type = "Technical Report", number = "CS-TR-77-635", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = oct, year = "1977", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/stanford-cstr.bib", URL = "http://i.stanford.edu/TR/CS-TR-77-635.html", abstract = "We present a block Lanczos method to compute the largest singular values and corresponding left and right singular vectors of a large sparse matrix. Our algorithm does not transform the matrix $A$ but accesses it only through a user-supplied routine which computes $ A X $ or $ A^t X $ for a given matrix $X$. This paper also includes a thorough discussion of the various ways to compute the singular value decomposition of a banded upper triangular matrix; this problem arises as a subproblem to be solved during the block Lanczos procedure.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InCollection{Golub:1977:BLMb, author = "G. H. Golub and R. Underwood", title = "The Block {Lanczos} Method for Computing Eigenvalues", crossref = "Rice:1977:MSI", pages = "364--377 (or 361--377??)", year = "1977", MRclass = "65F15", MRnumber = "57 \#14376", MRreviewer = "Colette Lebaud", bibdate = "Fri Dec 20 17:48:35 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "nla, block algorithm, Lanczos algorithm, eig", } @TechReport{Golub:1977:GCV, author = "Gene H. Golub and Michael Heath and Grace Wahba", title = "Generalized cross-validation as a method for choosing a good ridge parameter", type = "Technical Report", number = "STAN-CS-77-622", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "24", month = "????", year = "1977", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Also issued as Dept. of Statistics Technical Report no. 491, University of Wisconsin, Madison, WI.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "graphic methods; regression analysis", } @InProceedings{Golub:1977:TTC, author = "Gene H. Golub and Franklin T. Luk", title = "Singular value decomposition: applications and computations", crossref = "Army:1977:TTC", pages = "577--605", year = "1977", MRclass = "65F30", MRnumber = "58 31784", bibdate = "Sun Jan 14 09:45:27 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InProceedings{Golub:1977:TTS, author = "Gene H. Golub and Franklin T. Luk", title = "Singular value decomposition: applications and computations", crossref = "Army:1977:TTC", pages = "577--605", year = "1977", MRclass = "65F30", MRnumber = "58 \#31784", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InProceedings{Boley:1978:IEP, author = "D. Boley and G. H. Golub", title = "Inverse eigenvalue problems for band matrices", crossref = "Watson:1978:NAP", pages = "23--31", year = "1978", MRclass = "65F15", MRnumber = "57 \#14375", MRreviewer = "H. Hochstadt", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Boley:1978:MIE, author = "Daniel L. Boley and Gene H. Golub", title = "The matrix inverse eigenvalue problem for periodic {Jacobi} matrices", type = "Technical Report", number = "CS-TR-78-684", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = dec, year = "1978", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-78-684.html", abstract = "A stable numerical algorithm is presented for generating a periodic Jacobi matrix from two sets of eigenvalues and the product of the off-diagonal elements of the matrix. The algorithm requires a simple generalization of the Lanczos algorithm. It is shown that the matrix is not unique, but the algorithm will generate all possible solutions.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Boley:1978:MIEa, author = "D. Boley and Gene H. Golub", title = "The Matrix Inverse Eigenvalue Problem for Periodic {Jacobi} Matrices", type = "Technical Report", number = "STAN-CS-78-684", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "[5] + 14", month = "????", year = "1978", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "eigenvalues; matrices", } @InProceedings{Boley:1978:MIEb, author = "D. L. Boley and G. H. Golub", title = "The Matrix Inverse Eigenvalue Problem for Periodic {Jacobi} Matrices", crossref = "Marek:1978:PFS", pages = "63--76", year = "1978", MRclass = "15A21 (58F07 65F15 65F30)", MRnumber = "81e:15005", MRreviewer = "J. S. Joel", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Concus:1978:NSN, author = "P. Concus and G. H. Golub and D. P. O'Leary", title = "Numerical Solution of Nonlinear Elliptic Partial Differential Equations by a Generalized Conjugate Gradient Method", journal = j-COMPUTING, volume = "19", number = "4", pages = "321--339", month = "????", year = "1978", CODEN = "CMPTA2", DOI = "https://doi.org/10.1007/BF02252030", ISSN = "0010-485X (print), 1436-5057 (electronic)", ISSN-L = "0010-485X", MRclass = "65H10 (65N99)", MRnumber = "58 \#31799", MRreviewer = "L. Hageman", bibdate = "Fri Dec 20 17:41:37 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Computing: Archiv f{\"u}r informatik und numerik", journal-URL = "http://link.springer.com/journal/607", keywords = "nla, conjugate gradients", } @Article{Cottle:1978:SLS, author = "Richard W. Cottle and Gene H. Golub and Richard S. Sacher", title = "On the solution of large structured linear complementarity problems: the block partitioned case", journal = j-APPL-MATH-OPTIM, volume = "4", number = "4", pages = "347--363", month = "????", year = "1978", CODEN = "AMOMBN", ISSN = "0095-4616 (print), 1432-0606 (electronic)", ISSN-L = "0095-4616", MRclass = "90C30 (90C05)", MRnumber = "80a:90120", bibdate = "Mon Jan 15 09:15:16 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Applied Mathematics and Optimization", journal-URL = "http://link.springer.com/journal/245", } @Article{deBoor:1978:NSR, author = "C. de Boor and G. H. Golub", title = "The numerically stable reconstruction of a {Jacobi} matrix from spectral data", journal = j-LINEAR-ALGEBRA-APPL, volume = "21", number = "3", pages = "245--260", month = sep, year = "1978", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A18 (15A57)", MRnumber = "80i:15007", MRreviewer = "O. Pokorn{\'a}", bibdate = "Tue Feb 16 18:50:27 MST 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/linala1970.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", URL = "http://www.sciencedirect.com/science/article/pii/0024379578900861", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @TechReport{Golub:1978:SHM, author = "G. H. Golub and S. Nash and C. {Van Loan}", title = "A {Schur-Hessenberg} Method for the Problem {$ {Ax + xB = C} $}", type = "Technical Report", number = "TR 78-354", institution = inst-CORNELL, address = inst-CORNELL:adr, month = oct, year = "1978", bibdate = "Sat Oct 22 18:23:16 1994", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/cornell-university.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "mailto::lmc@cs.cornell.edu", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Golub:1978:UPD, author = "G. H. Golub and C. {Van Loan}", title = "Unsymmetric Positive Definite Linear Systems", type = "Technical Report", number = "TR 78-352", institution = inst-CORNELL, address = inst-CORNELL:adr, month = sep, year = "1978", bibdate = "Sat Oct 22 18:23:16 1994", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/cornell-university.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "mailto::lmc@cs.cornell.edu", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{VanLoan:1978:SUP, author = "C. {Van Loan} and G. H. Golub", title = "Solving Unsymmetric Positive Definite Linear Systems", journal = j-SIAM-REVIEW, volume = "20", number = "3", pages = "636--636", month = "????", year = "1978", CODEN = "SIREAD", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Fri Jun 21 11:25:02 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @Article{Bauer:1979:ES, author = "F. L. Bauer and G. H. Golub and A. S. Householder and K. Samelson", title = "{Eduard L. Stiefel}: 4/21/1909--11/27/1978", journal = j-NUM-MATH, volume = "32", number = "4", pages = "480--481", month = dec, year = "1979", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "01A70", MRnumber = "82e:01083", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "With a German translation.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", } @TechReport{Chan:1979:UFP, author = "Tony F. Chan and Gene H. Golub and Randall J. LeVeque", title = "Updating formulae and a pairwise algorithm for computing sample variances", type = "Technical Report", number = "CS-TR-79-773", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = nov, year = "1979", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-79-773.html", abstract = "A general formula is presented for computing the simple variance for a sample of size m + n given the means and variances for two subsamples of sizes m and n. This formula is used in the construction of a pairwise algorithm for computing the variance. Other applications are discussed as well, including the use of updating formulae in a parallel computing environment. We present numerical results and rounding error analyses for several numerical schemes.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InProceedings{Dahlquist:1979:BEL, author = "Germund Dahlquist and Gene H. Golub and Stephen G. Nash", title = "Bounds for the error in linear systems", crossref = "Hettich:1979:SIP", pages = "154--172", year = "1979", MRclass = "65F10 (90C05)", MRnumber = "154--172", MRreviewer = "Jacques Dubois", bibdate = "Sun Jan 14 09:41:57 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InProceedings{Dahlquist:1979:SIP, author = "Germund Dahlquist and Gene H. Golub and Stephen G. Nash", title = "Bounds for the error in linear systems", crossref = "Hettich:1979:SIP", pages = "154--172", year = "1979", MRclass = "65F10 (90C05)", MRnumber = "81b:65028", MRreviewer = "Jacques Dubois", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InProceedings{Golub:1979:CMA, author = "Gene H. Golub and Robert J. Plemmons", title = "Sparse least squares problems", crossref = "Glowinski:1979:CMA", pages = "489--496", year = "1979", MRclass = "65F05", MRnumber = "82a:65025", MRreviewer = "D. S. Henderson", bibdate = "Sun Jan 14 08:25:42 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1979:DSE, author = "G. H. Golub and W. Langlois", title = "Direct solution of the equation for the {Stokes} stream function", journal = j-COMPUT-METH-APPL-MECH-ENG, volume = "19", number = "3", pages = "391--399", month = sep, year = "1979", CODEN = "CMMECC", DOI = "https://doi.org/10.1016/0045-7825(79)90066-5", ISSN = "0045-7825 (print), 1879-2138 (electronic)", ISSN-L = "0045-7825", MRclass = "76D05 (65P05)", MRnumber = "82c:76029", MRreviewer = "C. Taylor", bibdate = "Fri Dec 20 17:07:23 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, ajournal = "Comp. Methods in Appl. Mech. and Engrg.", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Computer Methods in Applied Mechanics and Engineering", journal-URL = "http://www.sciencedirect.com/science/journal/00457825", } @InProceedings{Golub:1979:EUV, author = "Gene H. Golub and Randall J. LeVeque", title = "Extensions and Uses of the Variable Projection Algorithm for Solving Nonlinear Least Squares Problems", crossref = "ARO:1979:PAN", pages = "1--12", year = "1979", MRclass = "65F20", MRnumber = "81b:65036", bibdate = "Sun Jan 14 09:40:39 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "nlop, nllsq", } @Article{Golub:1979:GCV, author = "Gene H. Golub and Michael T. Heath and Grace Wahba", title = "Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter", journal = j-TECHNOMETRICS, volume = "21", number = "2", pages = "215--223", month = may, year = "1979", CODEN = "TCMTA2", DOI = "https://doi.org/10.1080/00401706.1979.10489751", ISSN = "0040-1706 (print), 1537-2723 (electronic)", ISSN-L = "0040-1706", MRclass = "62J07", MRnumber = "81e:62079", MRreviewer = "Colin L. Mallows", bibdate = "Sun Jan 14 09:39:58 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least squares, which is available at \verb=ftp://math.liu.se/pub/references=. Reprinted in \cite{Chan:2007:MMC}.", URL = "http://www.jstor.org/stable/1268518", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Technometrics", journal-URL = "http://www.jstor.org/journals/00401706.html; http://www.tandfonline.com/loi/utch20", keywords = "nla, stat, ridge regression, cross validation, regularization", } @TechReport{Golub:1979:HSMa, author = "Gene H. Golub and Stephen Nash and Charles F. {Van Loan}", title = "A {Hessenberg--Schur} method for the problem {$ {AX + XB = C} $}", type = "Technical Report", number = "STAN-CS-79-713", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "50", month = "????", year = "1979", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "matrix mechanics; numerical analysis", } @Article{Golub:1979:HSMb, author = "G. H. Golub and S. Nash and C. {Van Loan}", title = "A {Hessenberg--Schur} Method for the Matrix Problem {$ A X + X B = C $}", journal = j-IEEE-TRANS-AUTOMAT-CONTR, volume = "24", number = "6", pages = "909--913", month = "????", year = "1979", CODEN = "IETAA9", DOI = "https://doi.org/10.1109/TAC.1979.1102170", ISSN = "0018-9286 (print), 1558-2523 (electronic)", ISSN-L = "0018-9286", MRclass = "65F30 (93C05)", MRnumber = "81a:65046", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "IEEE Transactions on Automatic Control", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9", keywords = "nla, Sylvester equation, Hessenberg matrix, Schur form, Lyapunov equation, matrix equation", } @TechReport{Golub:1979:LSG, author = "Gene H. Golub and Robert J. Plemmons", title = "Large scale geodetic least squares adjustment by dissection and orthogonal decomposition", type = "Technical Report", number = "CS-TR-79-774", institution = inst-STAN-CS, address = inst-STAN-CS:adr, month = nov, year = "1979", bibdate = "Fri Nov 7 07:00:05 MST 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://i.stanford.edu/TR/CS-TR-79-774.html", abstract = "Very large scale matrix problems currently arise in the context of accurately computing the coordinates of points on the surface of the earth. Here geodesists adjust the approximate values of these coordinates by computing least squares solutions to large sparse systems of equations which result from relating the coordinates to certain observations such as distances or angles between points. The purpose of this paper is to suggest an alternative to the formation and solution of the normal equations for these least squares adjustment problems. In particular, it is shown how a block-orthogonal decomposition method can be used in conjunction with a nested dissection scheme to produce an algorithm for solving such problems which combines efficient data management with numerical stability. As an indication of the magnitude that these least squares adjustment problems can sometimes attain, the forthcoming readjustment of the North American Datum in 1983 by the National Geodetic Survey is discussed. Here it becomes necessary to linearize and solve an overdetermined system of approximately 6,000,000 equations in 400,000 unknowns - a truly large-scale matrix problem.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InProceedings{Golub:1979:LSL, author = "G. H. Golub and F. Luk and M. Pagano", title = "A large sparse least squares problem in photogrammetry", crossref = "Gentleman:1979:PCS", pages = "??--??", year = "1979", bibdate = "Sat Oct 29 15:12:07 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InProceedings{Golub:1979:SLS, author = "G. H. Golub and R. Plemmons", title = "Sparse least squares problems", crossref = "ISCMASE:1979:PIF", pages = "??--??", year = "1979", bibdate = "Mon Jan 15 08:31:40 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InProceedings{Golub:1979:TLS, author = "Gene H. Golub and Charles F. {Van Loan}", title = "Total least squares", crossref = "Gasser:1979:STC", pages = "69--76", year = "1979", MRclass = "65D10 (65U05)", MRnumber = "82a:65013", MRreviewer = "Valery Fedorov", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least squares, which is available by anonymous ftp from {\tt math.liu.se} in {\tt pub/references}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "nla, svd, total least squares", } @Article{Golub:1979:UPD, author = "Gene H. Golub and Charles F. {Van Loan}", title = "Unsymmetric Positive Definite Linear Systems", journal = j-LINEAR-ALGEBRA-APPL, volume = "28", number = "??", pages = "85--97", month = dec, year = "1979", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(79)90122-8", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A23 (65F05)", MRnumber = "80k:15016", MRreviewer = "Colette Lebaud", bibdate = "Tue Feb 16 18:50:44 MST 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/linala1970.bib", URL = "http://www.sciencedirect.com/science/article/pii/0024379579901228", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "nla, linear system, positive definite matrix, nonsymmetric matrix", } @TechReport{Golub:1980:ATLa, author = "G. H. Golub and C. F. {Van Loan}", title = "An Analysis of the Total Least Squares Problem", type = "Technical Report", number = "80-411", institution = inst-CORNELL, address = inst-CORNELL:adr, month = feb, year = "1980", bibdate = "Sat Oct 22 18:23:16 1994", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/cornell-university.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "mailto::lmc@cs.cornell.edu", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1980:ATLb, author = "Gene H. Golub and Charles F. {Van Loan}", title = "An Analysis of the Total Least Squares Problem", journal = j-SIAM-J-NUMER-ANAL, volume = "17", number = "6", pages = "883--893", month = dec, year = "1980", CODEN = "SJNAAM", DOI = "https://doi.org/10.1137/0717073", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65D10", MRnumber = "83g:65020", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR database", note = "Reprinted in \cite{Chan:2007:MMC}.", URL = "http://www.jstor.org/stable/2156807", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", keywords = "statistics, least squares, math, nla, lsq, svd, deriv, total least squares", } @Article{Golub:1980:LSG, author = "Gene H. Golub and Robert J. Plemmons", title = "Large-Scale Geodetic Least-Squares Adjustment by Dissection and Orthogonal Decomposition", journal = j-LINEAR-ALGEBRA-APPL, volume = "34", pages = "3--28", month = dec, year = "1980", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(80)90156-1", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "86A30 (15A23 65F10)", MRnumber = "81k:86010", MRreviewer = "K. R. Koch", bibdate = "Sun Jan 14 09:38:35 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "nla, lsq, sparse, geodesy, qrd", } @Article{Golub:1980:RSD, author = "G. Golub and V. Klema and S. C. Peters", title = "Rules and Software for Detecting Rank Degeneracy", journal = j-J-ECONOMETRICS, volume = "12", number = "1", pages = "41--48", month = "????", year = "1980", CODEN = "JECMB6", DOI = "https://doi.org/10.1016/0304-4076(80)90051-2", ISSN = "0304-4076 (print), 1872-6895 (electronic)", ISSN-L = "0304-4076", bibdate = "Thu Jun 6 10:13:11 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Journal of Econometrics", journal-URL = "http://www.sciencedirect.com/science/journal/03044076", } @InProceedings{Golub:1980:SLS, author = "Gene H. Golub and Robert J. Plemmons", title = "Sparse least squares problems", crossref = "Glowinski:1980:CMA", pages = "489--496", year = "1980", MRclass = "65F05", MRnumber = "82a:65025", MRreviewer = "D. S. Henderson", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Ward:1980:NLA, author = "Robert C. Ward and Gene H. Golub", title = "Numerical linear algebra", journal = j-SIGNUM, volume = "15", number = "3", pages = "9--26", month = sep, year = "1980", CODEN = "SNEWD6", ISSN = "0163-5778 (print), 1558-0237 (electronic)", ISSN-L = "0163-5778", bibdate = "Tue Apr 12 07:50:09 MDT 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "ACM SIGNUM Newsletter", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690", } @Article{Bjorck:1981:EMA, author = "{\AA}ke Bj{\"o}rck and Gene H. Golub", title = "Eigenproblems for matrices associated with periodic boundary conditions. ({Chinese})", journal = "Yingyong Shuxue yu Jisuan Shuxue", volume = "1", number = "??", pages = "10--18", month = "????", year = "1981", MRclass = "65F15", MRnumber = "83d:65110", bibdate = "Sun Jan 14 09:34:26 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Translated from the English by Cheng Ming Huang", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1981:BDV, author = "G. H. Golub and W. P. Tang", title = "The Block Decomposition of a {Vandermonde} Matrix and Its Applications", journal = j-BIT, volume = "21", number = "??", pages = "505--517", year = "1981", CODEN = "BITTEL", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "BIT (Nordisk tidskrift for informationsbehandling)", journal-URL = "http://link.springer.com/journal/10543", keywords = "nla, block algorithm, Vandermonde matrix", } @Article{Golub:1981:BLM, author = "Gene H. Golub and Franklin T. Luk and Michael L. Overton", title = "A Block {Lanczos} Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix", journal = j-TOMS, volume = "7", number = "2", pages = "149--169", month = jun, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355945.355946", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50 (65F15)", MRnumber = "84h:65045", bibdate = "Sun Jan 14 09:28:55 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least squares, which is available by anonymous ftp from {\tt math.liu.se} in {\tt pub/references}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", keywords = "nla, svd, Lanczos algorithm, block Lanczos method, singular values, singular vectors, large sparse matrix, singular-value decomposition, upper-triangular band matrix, nla, svd, Lanczos algorithm", } @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", number = "4", pages = "505--517", month = dec, year = "1981", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/BF01932847", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", MRclass = "65F30 (15A06)", MRnumber = "83e:65077", MRreviewer = "V. Syamala Devi", bibdate = "Wed Jan 4 18:52:17 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=21&issue=4; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=21&issue=4&spage=505", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "BIT (Nordisk tidskrift for informationsbehandling)", journal-URL = "http://link.springer.com/journal/10543", keywords = "nla, block algorithm, Vandermonde matrix", } @TechReport{Chan:1982:ACS, author = "T. F. Chan and G. H. Golub and R. J. {Le Veque}", title = "Algorithms for Computing the Sample Variance: Analysis and Recommendations", type = "??", number = "222", institution = "Department of Computer Science, Yale University", address = "??", month = "????", year = "1982", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "stat, na, variance, standard deviation", } @InProceedings{Chan:1982:UFP, author = "T. F. Chan and G. H. Golub and R. J. LeVeque", title = "Updating formulae and a pairwise algorithm for computing sample variances", crossref = "Caussinus:1982:CSH", pages = "30--41", year = "1982", bibdate = "Sat Oct 22 18:37:14 1994", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", descriptors = "Simulation; statistics; numeric calculation", } @InProceedings{Golub:1982:CTS, author = "Gene H. Golub and Michael L. Overton", title = "Convergence of a two-stage {Richardson} iterative procedure for solving systems of linear equations", crossref = "Watson:1982:NAP", pages = "125--139", year = "1982", DOI = "https://doi.org/10.1007/BFb0093153", MRclass = "65F10", MRnumber = "83f:65045", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1982:NAV, author = "Gene H. Golub and Stephen G. Nash", title = "Nonorthogonal Analysis of Variance using a Generalized Conjugate-Gradient Algorithm", journal = j-J-AM-STAT-ASSOC, volume = "77", number = "377", pages = "109--116", month = mar, year = "1982", CODEN = "JSTNAL", DOI = "https://doi.org/10.2307/2287776", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", MRclass = "62J10 (65U05)", MRnumber = "83i:62135", MRreviewer = "Walter Schlee", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least squares, which is available by anonymous ftp from {\tt math.liu.se} in {\tt pub/references}.", URL = "http://www.jstor.org/stable/2287776", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", error = "in Gene's cv is Statistical Computing, but we found this reference: The American Statistician", fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", keywords = "stat, anova, conjugate gradients", } @Article{Paige:1982:LAS, author = "C. C. Paige and M. A. Saunders", title = "{LSQR}: an algorithm for sparse linear equations and sparse least squares", journal = j-TOMS, volume = "8", number = "1", pages = "43--71", month = mar, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 22 16:35:44 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", keywords = "algorithms; measurement", review = "ACM CR 39252", subject = "G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems \\ G.1.6 Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods G Mathematics of Computing, MATHEMATICAL SOFTWARE", } @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", month = aug, year = "1983", CODEN = "ASTAAJ", DOI = "https://doi.org/10.2307/2683386", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", MRclass = "62-04", MRnumber = "84k:62003", bibdate = "Mon May 5 09:19:29 MDT 1997", bibsource = "Distributed/QLD.bib; Distributed/QLD/1983.bib; ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.jstor.org/stable/2683386", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", country = "USA", date = "13/05/93", descriptors = "Simulation; statistics; numeric calculation", enum = "7109", fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", location = "SEL: Wi", references = "0", revision = "16/01/94", } @Article{Golub:1983:CGQ, author = "G. H. Golub and J. Kautsk{\'y}", title = "Calculation of {Gauss} quadratures with multiple free and fixed knots", journal = j-NUM-MATH, volume = "41", number = "2", pages = "147--163", month = jun, year = "1983", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/BF01390210", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65D32 (65F15)", MRnumber = "84i:65030", bibdate = "Sat Oct 22 16:35:44 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "B0290M (Numerical integration and differentiation); C4160 (Numerical integration and differentiation)", corpsource = "Dept. of Computer Sci., Stanford Univ., Stanford, CA, USA", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "algorithms; fixed knots; Gauss knots; Gauss quadratures; integration; Jacobi matrix; quadratic convergence; theory", subject = "G.1.4 Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Gaussian quadrature", treatment = "T Theoretical or Mathematical", } @Book{Golub:1983:MC, author = "Gene H. Golub and Charles F. {Van Loan}", title = "Matrix Computations", publisher = pub-JOHNS-HOPKINS # " and " # pub-NORTH-OXFORD, address = pub-JOHNS-HOPKINS:adr # " and " # pub-NORTH-OXFORD:adr, pages = "xvi + 476", year = "1983", ISBN = "0-8018-3010-9 (hardcover), 0-8018-3011-7 (paperback), 0-946536-00-7, 0-946536-05-8 (paperback)", ISBN-13 = "978-0-8018-3010-5 (hardcover), 978-0-8018-3011-2 (paperback), 978-0-946536-00-9, 978-0-946536-05-4 (paperback)", LCCN = "QA188 .G65 1983", MRclass = "65Fxx (65-02)", MRnumber = "85h:65063", MRreviewer = "C. Ilioi", bibdate = "Sun Jan 14 09:27:53 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/master.bib", series = "Johns Hopkins Series in the Mathematical Sciences", URL = "http://www.jstor.org/stable/2008107; http://www.jstor.org/stable/2030489; http://www.jstor.org/stable/3616959", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "algebra --- matrices --- computation by digital computer systems; matrices --- data processing", remark = "See review by James W. Demmel in SIAM Review, Vol. 28, No. 2 (Jul., 1986), pp. 252-255, review by David F. Mayers, Mathematics of Computation, Vol. 47, No. 175 (Jul., 1986), pp. 376-377, and review by T. J. Randall, The Mathematical Gazette, Vol. 69, No. 448 (Jun., 1985), p. 152.", tableofcontents = "Preface to the Third Edition \\ Software \\ Selected References \\ Matrix Multiplication Problems / 1 \\ Matrix Analysis / 48 \\ General Linear Systems / 87 \\ Special Linear Systems / 133 \\ Orthogonalization and Least Squares / 206 \\ Parallel Matrix Computations / 275 \\ The Unsymmetric Eigenvalue Problem / 308 \\ The Symmetric Eigenvalue Problem / 391 \\ Lanczos Methods / 470 \\ Iterative Methods for Linear Systems / 508 \\ Functions of Matrices / 555 \\ Special Topics / 579 \\ Bibliography / 637 \\ Index / 687", } @Book{Golub:1983:RNG, author = "Gene H. Golub and G{\'e}rard A. Meurant", title = "{R}{\'e}solution Num{\'e}rique des Grands Syst{\`e}mes Lin{\'e}aires (English: Numerical solution of large linear systems)", volume = "49", publisher = pub-EYROLLES, address = pub-EYROLLES:adr, pages = "x + 329", year = "1983", ISBN = "??", ISBN-13 = "??", LCCN = "??", MRclass = "65-01 (65F10 65F20 65N20)", MRnumber = "86b:65002", MRreviewer = "G. Maess", bibdate = "Sun Jan 14 09:26:25 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", series = "Collection de la Direction des Etudes et Recherches de l'Electricit\'e de France", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "book, nla, linear system, sparse", } @InProceedings{Golub:1983:UPI, author = "G. Golub and D. Mayers", title = "The Use of Preconditioning Over Irregular Regions", crossref = "Blackburn:1983:SIC", pages = "??--??", year = "1983", bibdate = "Fri Dec 20 18:59:15 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/ovr.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Kautsky:1983:CJM, author = "J. Kautsk{\'y} and G. H. Golub", title = "On the Calculation of {Jacobi} Matrices", journal = j-LINEAR-ALGEBRA-APPL, volume = "52/53", pages = "439--456", year = "1983", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(83)90028-9", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F30 (15A99 33A65)", MRnumber = "84g:65050", MRreviewer = "Walter Gautschi", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "nla, Jacobi matrix", } @Article{Boley:1984:LAA, author = "D. L. Boley and G. H. Golub", title = "The {Lanczos--Arnoldi} Algorithm and controllability", journal = j-SYST-CONTROL-LETT, volume = "4", number = "6", pages = "317--324", month = sep, year = "1984", CODEN = "SCLEDC", DOI = "https://doi.org/10.1016/S0167-6911(84)80072-9", ISSN = "0167-6911 (print), 1872-7956 (electronic)", ISSN-L = "0167-6911", MRclass = "93B40 (93B05)", MRnumber = "86a:93044", bibdate = "Fri Dec 20 17:12:57 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Systems and Control Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01676911", keywords = "nla, controllability, Lanczos algorithm, Arnoldi's method, algorithms", subject = "G.1 Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous", } @Article{Boley:1984:MMR, author = "Daniel Boley and Gene H. Golub", title = "A modified method for reconstructing periodic {Jacobi} matrices", journal = j-MATH-COMPUT, volume = "42", number = "165", pages = "143--150", month = jan, year = "1984", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2007564", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F15 (15A18)", MRnumber = "85h:65078", MRreviewer = "Alan L. Andrew", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database", URL = "http://www.jstor.org/stable/2007564", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classcodes = "B0210 (Algebra); C1110 (Algebra)", corpsource = "Computer Sci. Dept., Univ. of Minnesota, Minneapolis, MN, USA", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "algorithm; initial data items; matrix algebra; numerically stable; periodic Jacobi matrices; spectral data", treatment = "T Theoretical or Mathematical", } @Article{Concus:1984:GCG, author = "Paul Concus and Gene H. Golub and Dianne P. O'Leary", title = "A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations", journal = j-MAA-STUD-MATH, volume = "24", number = "??", pages = "178--198", month = "????", year = "1984", CODEN = "MSTMBI", ISSN = "0081-8208", MRclass = "65N20 (65F10 65F15)", MRnumber = "925 214", bibdate = "Sun Jan 14 08:25:42 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "MAA studies in mathematics", } @Article{Gallant:1984:ICR, author = "A. Ronald Gallant and Gene H. Golub", title = "Imposing curvature restrictions on flexible functional forms", journal = j-J-ECONOMETRICS, volume = "26", number = "3", pages = "295--321", month = dec, year = "1984", CODEN = "JECMB6", DOI = "https://doi.org/10.1016/0304-4076(84)90024-1", ISSN = "0304-4076 (print), 1872-6895 (electronic)", ISSN-L = "0304-4076", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Journal of Econometrics", journal-URL = "http://www.sciencedirect.com/science/journal/03044076", } @InCollection{Golub:1984:UPI, author = "Gene H. Golub and David Mayers", title = "The use of preconditioning over irregular regions", crossref = "Glowinski:1983:CMA", pages = "3--14", year = "1984", MRclass = "65F10 (65F35)", MRnumber = "87h:65059", bibdate = "Sun Jan 14 09:23:24 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.grid.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Concus:1985:BPC, author = "P. Concus and G. H. Golub and G. A. Meurant", title = "Block Preconditioning for the Conjugate Gradient Method", journal = j-SIAM-J-SCI-STAT-COMP, volume = "6", number = "??", pages = "220--252", month = "????", year = "1985", CODEN = "SIJCD4", DOI = "https://doi.org/10.1137/0906018", ISSN = "0196-5204", MRclass = "65F10 (65N20)", MRnumber = "87c:65035a", MRreviewer = "Ian Gladwell", bibdate = "Thu Apr 09 15:41:33 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "See corrigendum \cite{Concus:1985:CBP}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Scientific and Statistical Computing", journal-URL = "http://epubs.siam.org/loi/sijcd4", keywords = "nla, block algorithm, preconditioning, conjugate gradients", } @Article{Concus:1985:CBP, author = "P. Concus and G. H. Golub and G. Meurant", title = "Corrigendum: {``Block preconditioning for the conjugate gradient method''}", journal = j-SIAM-J-SCI-STAT-COMP, volume = "6", number = "3", pages = "791--791", month = "????", year = "1985", CODEN = "SIJCD4", ISSN = "0196-5204", MRclass = "65F10 (65N20)", MRnumber = "87c:65035b", MRreviewer = "Ian Gladwell", bibdate = "Thu Apr 09 15:41:30 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "See \cite{Concus:1985:BPC}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Scientific and Statistical Computing", journal-URL = "http://epubs.siam.org/loi/sijcd4", } @Article{Golub:1985:SLS, author = "G. H. Golub", title = "Solution of Large Sparse Structured Least-Squares Problem", journal = j-BIOMETRICS, volume = "41", number = "3", pages = "799--799", month = "????", year = "1985", CODEN = "BIOMB6", ISSN = "0006-341X (print), 1541-0420 (electronic)", ISSN-L = "0006-341X", bibdate = "Thu Jun 6 10:13:11 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/biometrics1980.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Biometrics", journal-URL = "http://www.jstor.org/journal/biometrics", } @Article{Golub:1986:CBS, author = "G. H. Golub and P. Manneback and Ph. L. Toint", title = "A Comparison Between some Direct and Iterative Methods for Large Scale Geodetic Least Squares Problems", journal = j-SIAM-J-SCI-STAT-COMP, volume = "7", number = "3", pages = "799--816", month = jul, year = "1986", CODEN = "SIJCD4", DOI = "https://doi.org/10.1137/0907053", ISSN = "0196-5204", MRclass = "65F50 (65U05)", MRnumber = "87g:65063", bibdate = "Sat Oct 22 16:35:44 MDT 1994", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least squares, which is available by anonymous ftp from {\tt math.liu.se} in {\tt pub/references}.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Scientific and Statistical Computing", journal-URL = "http://epubs.siam.org/loi/sijcd4", keywords = "algorithms; conjugate gradients; geodesy; iter; lsq; nested dissection; nla; sparse; theory; verification", subject = "G.1.6 Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods \\ J.2 Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Physics", } @Article{Golub:1986:CTS, author = "Gene H. Golub and R. Kannan", title = "Convergence of a two-stage {Richardson} process for nonlinear equations", journal = j-BIT, volume = "26", number = "2", pages = "209--216", month = jun, year = "1986", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/BF01933747", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", MRclass = "65H10 (47H17 65F10)", MRnumber = "87f:65064", MRreviewer = "V. Pereyra", bibdate = "Wed Jan 4 18:52:19 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=2; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=2&spage=209", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "BIT (Nordisk tidskrift for informationsbehandling)", journal-URL = "http://link.springer.com/journal/10543", } @TechReport{Golub:1986:PBS, author = "Gene H. Golub and Robert J. Plemmons and Ahmed Sameh", title = "Parallel Block Schemes for Large Scale Least Squares Computations", type = "Technical Report", number = "574", institution = inst-CSRD, address = inst-CSRD:adr, pages = "20", month = apr, year = "1986", bibdate = "Wed Jan 4 18:52:19 MST 2006", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/ovr.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "matrices; parallel processing (electronic computers)", } @Article{Golub:1986:UFG, author = "Gene H. Golub and Carl D. {Meyer, Jr.}", title = "Using the {$ {QR} $} Factorization and Group Inversion to Compute, Differentiate, and estimate the Sensitivity of Stationary Probabilities for {Markov} Chains", journal = j-SIAM-J-ALG-DISC-METH, volume = "7", number = "2", pages = "273--281", month = apr, year = "1986", CODEN = "SJAMDU", DOI = "https://doi.org/10.1137/0607031", ISSN = "0196-5212 (print), 2168-345X (electronic)", ISSN-L = "0196-5212", MRclass = "60J10 (65F05)", MRnumber = "87i:60073", MRreviewer = "M. F. Neuts", bibdate = "Sun Jan 14 09:22:16 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Algebraic and Discrete Methods", journal-URL = "http://epubs.siam.org/loi/sjamdu", keywords = "eig; ginv; Markov chain; nla; qrd; theory; verification", subject = "F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices \\ G.2.1 Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics", } @TechReport{Arbenz:1987:SDH, author = "P. Arbenz and G. H. Golub", title = "On the Spectral Decomposition of {Hermitian} Matrices Subject to Indefinite Low Rank Perturbations with Applications", type = "??", number = "NA 87-07", institution = "Computer Science, Stanford University", address = "Stanford, CA", month = "????", year = "1987", bibdate = "Sun Jan 14 09:22:16 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Boley:1987:SMI, author = "Daniel Boley and Gene H. Golub", title = "A survey of matrix inverse eigenvalue problems", journal = j-INVERSE-PROBLEMS, volume = "3", number = "4", pages = "595--622", month = "????", year = "1987", CODEN = "INPEEY", DOI = "https://doi.org/10.1088/0266-5611/3/4/010", ISSN = "0266-5611 (print), 1361-6420 (electronic)", ISSN-L = "0266-5611", MRclass = "65F15", MRnumber = "89m:65036", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Inverse Problems", journal-URL = "http://iopscience.iop.org/0266-5611/", } @InProceedings{Ferziger:1987:BSA, author = "J. H. Ferziger and G. H. Golub and M. C. Thompson", title = "Block {SOR} applied to the cyclically-reduced equations as an efficient solution technique for convection-diffusion equations", crossref = "Noye:1987:CTA", pages = "??--??", year = "1987", bibdate = "Sat Oct 29 15:20:30 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1987:D, author = "Gene H. Golub and Iain Duff and Cleve Moler", title = "Dedication", journal = j-LINEAR-ALGEBRA-APPL, volume = "88/89", pages = "1--12", year = "1987", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "01A70", MRnumber = "88e:01060", bibdate = "Mon Jan 15 17:54:33 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @Article{Golub:1987:GEY, author = "G. H. Golub and Alan Hoffman and G. W. Stewart", title = "A generalization of the {Eckart--Young--Mirsky} matrix approximation theorem", journal = j-LINEAR-ALGEBRA-APPL, volume = "88/89", pages = "317--327", year = "1987", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(87)90114-5", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "41A45 (15A60 62J05 65F99)", MRnumber = "88f:41039", MRreviewer = "R. A. Lorentz", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @Article{Golub:1987:JW, author = "Gene H. Golub and Miki Neumann and James W. Demmel and Paul Saylor and James M. Boyle and Iain Duff and Jack Dongarra", title = "{James Wilkinson} (1919--1986)", journal = j-ANN-HIST-COMPUT, volume = "9", number = "2", pages = "205--210", month = apr # "\slash " # jun, year = "1987", CODEN = "AHCOE5", ISSN = "0164-1239", bibdate = "Sat Jul 14 18:11:40 2001", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.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''.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Annals of the History of Computing", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650", keywords = "obituary", } @Article{Golub:1987:LAA, author = "G. H. Golub and C. Moler", title = "Linear Algebra and its Applications --- in Memory of {James H. Wilkinson}", journal = j-LINEAR-ALGEBRA-APPL, volume = "88--89", pages = "1--3", month = apr, year = "1987", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(87)90098-X", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Thu Jun 6 10:13:11 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @InProceedings{Golub:1987:LSL, author = "G. H. Golub", title = "Large scale least squares problems", crossref = "Heiberger:1987:CSS", pages = "3", month = "????", year = "1987", bibdate = "Mon Sep 9 12:13:04 MDT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", abstract = "Summary form only given as follows. With the advent of satellites, it is possible to collect large sets of data which are frequently analysed through least squares methods. These problems can have over a million observations and several hundred thousand unknowns. Fortunately, the data is highly structured so that one can combine direct and iterative methods for solving the associated least squares problem. Furthermore, it is possible to decompose the problem in such a way that the computation can be performed in parallel. The author discusses this computation and points out its connection to other large scale least squares problems.", acknowledgement = ack-nhfb, affiliation = "Stanford Univ., CA, USA", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "C4130 (Interpolation and function approximation); C7310 (Mathematics)", keywords = "Associated least squares problem; Highly structured; Iterative methods; Large scale least squares problems; Least squares methods; Observations; Parallel; Satellites; Unknowns", thesaurus = "Least squares approximations; Mathematics computing", } @TechReport{Golub:1987:SHC, author = "Gene H. Golub and Dianne P. O'Leary", title = "Some history of the conjugate gradient and {Lanczos} algorithms: 1948--1976", type = "Technical Report", number = "TR-1859, UMIACS-TR-87-20", institution = inst-U-MARYLAND-CS, address = inst-U-MARYLAND-CS:adr, pages = "51", month = "????", year = "1987", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "Algorithms --- Bibliography", } @Article{Arbenz:1988:RRM, author = "Peter Arbenz and Walter Gander and Gene H. Golub", title = "Restricted Rank Modification of the Symmetric Eigenvalue Problem: Theoretical Considerations", journal = j-LINEAR-ALGEBRA-APPL, volume = "104", pages = "75--95", year = "1988", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(88)90309-6", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F15 (15A18)", MRnumber = "89h:65052", MRreviewer = "V. S. Zaja{\v{c}}kovski", bibdate = "Sun Jan 14 09:18:09 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "nla, eig, symmetric matrix, updating", } @Article{Arbenz:1988:SDH, author = "Peter Arbenz and Gene H. Golub", title = "On the Spectral Decomposition of {Hermitian} Matrices Modified by Low Rank Perturbations with Applications", journal = j-SIAM-J-MAT-ANA-APPL, volume = "9", number = "1", pages = "40--58", month = "????", year = "1988", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/0609004", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A57 (15A18 65F15)", MRnumber = "89c:15028", MRreviewer = "Moody T. Chu", bibdate = "Tue Jan 21 07:54:58 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", keywords = "algorithms; eig; indefinite matrix; nla; symmetric matrix; theory; updating", subject = "F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices \\ I.1.1 Computing Methodologies, ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions \\ G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Stability (and instability) \\ G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Error analysis", } @InProceedings{Gander:1988:CEP, author = "Walter Gander and Gene H. Golub and Urs {von Matt}", title = "A constrained eigenvalue problem", crossref = "Golub:1991:NLA", pages = "677--686", year = "1988", MRclass = "65F15", MRnumber = "92k:65067", bibdate = "Sun Jan 14 08:57:55 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", abstract = "Variants of this problem occur in many applications. The authors show how to eliminate the linear constraint. Three different methods are presented for the solution of the resulting Lagrange equations.", acknowledgement = ack-nhfb, affiliation = "Inst. fur Inf., ETH, Zurich, Switzerland", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "B0210 (Algebra); C1110 (Algebra)", keywords = "Constrained eigenvalue problem; Lagrange equations; Linear constraint", thesaurus = "Eigenvalues and eigenfunctions; Matrix algebra", } @Article{Golub:1988:CIC, author = "Gene H. Golub and Michael L. Overton", title = "The Convergence of Inexact {Chebyshev} and {Richardson} Iterative Methods for Solving Linear Systems", journal = j-NUM-MATH, volume = "53", number = "5", pages = "571--593", month = aug, year = "1988", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/BF01397553", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65F10", MRnumber = "90b:65054", bibdate = "Sat Oct 22 16:35:44 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "B0290H (Linear algebra); C4140 (Linear algebra)", corpsource = "Dept. of Comput. Sci., Stanford Univ., CA, USA", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "Chebyshev approximation; convergence; convergence of numerical methods; error analysis; error bound; experimentation; inexactness; iter; iterative methods; linear algebra; linear system; linear systems; measurement; nla; nonsymmetric inexact Chebyshev iteration; numerical experiments; performance; preconditioned iteration; Richardson iterative methods; skew-symmetric iteration; spectral radius; theory; verification", subject = "G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods)", treatment = "T Theoretical or Mathematical", xxtitle = "The Convergence of Inexact {Tschebyscheff} and {Richardson} Iterative Methods for Solving Linear-Systems", } @Article{Golub:1988:GEY, author = "G. H. Golub and A. Hoffman and G. W. Stewart", title = "A Generalization of the {Eckart--Young--Mirsky} Approximation Theorem", journal = j-LINEAR-ALGEBRA-APPL, volume = "88/89", pages = "317--328", year = "1988", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Sat Oct 22 16:35:44 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @Article{Golub:1988:OPH, author = "Gene H. Golub and Richard S. Varga", title = "Obituary to {Peter Henrici (13. September 1923--13. March 1987)}", journal = j-NUM-MATH, volume = "52", number = "5", pages = "481--482", month = may, year = "1988", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/BF01400886", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "01A70", MRnumber = "89i:01077", bibdate = "Sun Jan 14 09:17:43 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", subject-dates = "Peter Karl Henrici (13 September 1923--13 March 1987)", } @InCollection{Golub:1988:PBS, author = "Gene H. Golub and Robert J. Plemmons and Ahmed Sameh", title = "Parallel Block Schemes for Large-Scale Least-Squares Computations", crossref = "Wilhelmson:1988:HSC", pages = "171--179", year = "1988", bibdate = "Sat Oct 22 16:35:44 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", price = "US\$29.95", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "algorithms; design; theory", subject = "J.2 Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Engineering \\ F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices \\ G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms \\ G.1.6 Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods", } @TechReport{DeMoor:1989:GSV, author = "Bart L. R. {De Moor} and Gene H. Golub", title = "Generalized singular value decompositions: a proposal for a standardized nomenclature", type = "Technical Report", number = "STAN-CS-TR-2002", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "12", month = "????", year = "1989", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "decomposition (mathematics)", } @TechReport{DeMoor:1989:RSV, author = "Bart L. R. {De Moor} and Gene H. Golub", title = "The restricted singular value decomposition: properties and applications", type = "Technical Report", number = "STAN-CS-TR-2001", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "69", month = "????", year = "1989", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "decomposition (mathematics)", } @TechReport{Elhay:1989:UDO, author = "Sylvan Elhay and Gene H. Golub and Jaroslav Kautsk{\'y}", title = "Updating and downdating of orthogonal polynomials with data fitting applications", type = "Technical Report", number = "STAN-CS-89-04, NA-89-04", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "32", month = "????", year = "1989", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "least squares; orthogonal polynomials", } @TechReport{Elman:1989:IMC, author = "Howard C. Elman and Gene H. Golub", title = "Iterative methods for cyclically reduced non-self-adjoint linear systems {II}", type = "Technical Report", number = "STAN CS-TR-2238, UMIACS-TR-89-45", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "26", month = "????", year = "1989", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "iterative methods (mathematics); linear systems", } @InProceedings{Elman:1989:LIM, author = "Howard C. Elman and Gene H. Golub", title = "Line iterative methods for cyclically reduced non-self-adjoint elliptic problems", crossref = "ARO:1990:TSA", pages = "457--466", year = "1989", MRclass = "65F10 (65N20)", MRnumber = "057 847", bibdate = "Sun Jan 14 10:11:05 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Gander:1989:CEP, author = "Walter Gander and Gene H. Golub and Urs {von Matt}", title = "A constrained eigenvalue problem", journal = j-LINEAR-ALGEBRA-APPL, volume = "114/115", pages = "815--839", year = "1989", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(89)90494-1", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A18 (15A23)", MRnumber = "90e:15008", MRreviewer = "Lajos L{\'a}szl{\'o}", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @Article{Gander:1989:DLS, author = "Walter Gander and Gene H. Golub", title = "Discussion: Linear Smoothers and Additive Models", journal = j-ANN-STAT, volume = "17", number = "2", pages = "529--532", month = jun, year = "1989", CODEN = "ASTSC7", DOI = "https://doi.org/10.1214/aos/1176347120", ISSN = "0090-5364 (print), 2168-8966 (electronic)", ISSN-L = "0090-5364", bibdate = "Tue May 18 17:06:23 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://projecteuclid.org/euclid.aos/1176347120; http://www.jstor.org/stable/2241565", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Annals of Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aos/", } @InCollection{Gander:1989:SLE, author = "Walter Gander and Gene H. Golub and Dominik Gruntz", title = "Solving linear equations by extrapolation", crossref = "Kowalik:1989:S", pages = "279--293", year = "1989", MRclass = "65F10", MRnumber = "91j:65060", MRreviewer = "R. P. Tewarson", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1989:CEP, author = "Walter Gander and Gene H. Golub and Urs {von Matt}", title = "A Constrained Eigenvalue Problem", journal = j-LINEAR-ALGEBRA-APPL, volume = "114/115", pages = "815--839", year = "1989", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A18 (15A23)", MRnumber = "90e:15008", MRreviewer = "Lajos L{\'a}szl{\'o}", bibdate = "Sun Jan 14 09:13:37 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "nla, eig, constrained eigenvalue problem", } @Article{Golub:1989:EEI, author = "Gene H. Golub and Mark D. Kent", title = "Estimates of Eigenvalues for Iterative Methods", journal = j-MATH-COMPUT, volume = "53", number = "188", pages = "619--626", month = oct, year = "1989", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2008724", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F10 (65F15)", MRnumber = "90e:65043", MRreviewer = "Vasile I. Ionescu", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database", URL = "http://www.jstor.org/stable/2008724", abstract = "Describes a procedure for determining estimates of the eigenvalues of operators used in various iterative methods for the solution of linear systems of equations. The authors show how to determine upper and lower bounds for the error in the approximate solution of linear equations, using essentially the same information as that needed for the eigenvalue calculations. The methods described depend strongly upon the theory of moments and Gauss quadrature.", acknowledgement = ack-nhfb # " and " # ack-sf, affiliation = "Dept. of Comp. Sci., Stanford Univ., CA, USA", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classcodes = "C4140 (Linear algebra); C4130 (Interpolation and function approximation); C4160 (Numerical integration and differentiation)", corpsource = "Dept. of Comp. Sci., Stanford Univ., CA, USA", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "approximate solution; approximation theory; eigenvalues; eigenvalues and eigenfunctions; error; estimates; Gauss quadrature; integration; iterative methods; linear equations; linear systems; lower bounds; theory of moments; upper bounds", thesaurus = "Approximation theory; Eigenvalues and eigenfunctions; Integration; Iterative methods", treatment = "T Theoretical or Mathematical", } @Book{Golub:1989:MC, author = "Gene H. Golub and Charles F. {Van Loan}", title = "Matrix Computations", volume = "3", publisher = pub-JOHNS-HOPKINS, address = pub-JOHNS-HOPKINS:adr, edition = "Second", pages = "xix + 642", year = "1989", ISBN = "0-8018-3772-3 (hardcover), 0-8018-3739-1 (paperback)", ISBN-13 = "978-0-8018-3772-2 (hardcover), 978-0-8018-3739-5 (paperback)", LCCN = "QA188 .G65 1989", MRclass = "65Fxx (65-02)", MRnumber = "90d:65055", MRreviewer = "Perry Smith", bibdate = "Mon Oct 26 07:31:01 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/bibnet/subjects/domain-decomp.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/texbook2.bib", price = "US\$14.50", series = "Johns Hopkins Series in the Mathematical Sciences", ZMnumber = "0733.65016", abstract = "Thoroughly revised, updated, and expanded by more than one third, this new edition of Golub and Van Loan's landmark book in scientific computing provides the vital mathematical background and algorithmic skills required for the production of numerical software. New chapters on high performance computing use matrix multiplication to show how to organize a calculation for vector processors as well as for computers with shared or distributed memories. Also new are discussions of parallel vector methods for linear equations, least squares, and eigenvalue problems.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "book; math; matrices --- data processing; matrices --- informatique; na; nla", libnote = "Not yet in my library.", remark = "See review by G. W. Steward in Mathematics of Computation, Vol. 56, No. 193 (Jan., 1991), pp. 380--381.", shorttableofcontents = "Preface to the Third Edition \\ Software \\ Selected References \\ Matrix Multiplication Problems / 1 \\ Matrix Analysis / 48 \\ General Linear Systems / 87 \\ Special Linear Systems / 133 \\ Orthogonalization and Least Squares / 206 \\ Parallel Matrix Computations / 275 \\ The Unsymmetric Eigenvalue Problem / 308 \\ The Symmetric Eigenvalue Problem / 391 \\ Lanczos Methods / 470 \\ Iterative Methods for Linear Systems / 508 \\ Functions of Matrices / 555 \\ Special Topics / 579 \\ Bibliography / 637 \\ Index / 687", tableofcontents = "Preface to the First Edition / xi \\ Preface to the Second Edition / xv \\ Using the Book / xvii \\ 1: Matrix Multiplication Problems / 1 \\ 1.1 Basic Algorithms and Notations / 2 \\ 1.2 Exploiting Structure / 16 \\ 1.3 Block Matrices and Algorithms / 25 \\ 1.4 Aspects of Vector Pipeline Computing / 35 \\ 2: Matrix Analysis / 49 \\ 2.1 Basic Ideas from Linear Algebra / 49 \\ 2.2 Vector Norms / 53 \\ 2.3 Matrix Norms / 55 \\ 2.4 Finite Precision Matrix Computations / 60 \\ 2.5 Orthogonality and the SVD / 70 \\ 2.6 Projections and the CS Decomposition / 75 \\ 2.7 The Sensitivity of Square Linear Systems / 79 \\ 3: General Linear Systems / 86 \\ 3.1 Triangular Systems / 86 \\ 3.2 Computing the LU Factorization / 92 \\ 3.3 Roundoff Analysis of Gaussian Elimination / 104 \\ 3.4 Pivoting / 108 \\ 3.5 Improving and Estimating Accuracy / 123 \\ 4: Special Linear Systems / 133 \\ 4.1 The $LDM^T$ and $LDL^T$ Factorizations / 134 \\ 4.2 Positive Definite Systems / 139 \\ 4.3 Banded Systems / 149 \\ 4.4 Symmetric Indefinite Systems / 159 \\ 4.5 Block Tridiagonal Systems / 170 \\ 4.6 Vandermonde Systems / 178 \\ 4.7 Toeplitz Systems / 183 \\ 5: Orthogonalization and Least Squares / 193 \\ 5.1 Householder and Givens Transformations / 194 \\ 5.2 The $Q R$ Factorization / 211 \\ 5.3 The Full Rank Least Squares Problem / 221 \\ 5.4 Other Orthogonal Factorizations / 233 \\ 5.5 The Rank Deficient Least Squares Problem / 241 \\ 5.6 Weighting and Iterative Improvement / 250 \\ 5.7 A Note on Square and Underdetermined Systems / 256 \\ 6: Parallel Matrix Computations / 260 \\ 6.1 Distributed Memory Gaxpy / 261 \\ 6.2 Shared Memory Gaxpy / 276 \\ 6.3 Parallel Matrix Multiplication / 288 \\ 6.4 Ring Factorization Procedures / 301 \\ 6.5 Mesh Factorization Procedures / 310 \\ 6.6 Shared Memory Factorization Methods / 321 \\ 7: The Unsymmetric Eigenvalue Problem / 331 \\ 7.1 Properties and Decompositions / 332 \\ 7.2 Perturbation Theory / 341 \\ 7.3 Power Iterations / 351 \\ 7.4 Hessenberg and Real Schur Forms / 361 \\ 7.5 The Practical $Q R$ Algorithm / 373 \\ 7.6 Invariant Subspace Computations / 382 \\ 7.7 The $QZ$ Method for $A x = \lambda B x$ / 394 \\ 8: The Symmetric Eigenvalue Problem / 409 \\ 8.1 Properties, Decompositions, Perturbation Theory / 410 \\ 8.2 The Symmetric $Q R$ Algorithm / 418 \\ 8.3 Computing the SVD / 427 \\ 8.4 Some Special Methods / 437 \\ 8.5 Jacobi Methods / 444 \\ 8.6 A Divide and Conquer Method / 459 \\ 8.7 More Generalized Eigenvalue Problems / 466 \\ 9: Lanczos Methods / 475 \\ 9.1 Derivation and Convergence Properties / 476 \\ 9.2 Practical Lanczos Procedures / 484 \\ 9.3 Applications and Extensions / 494 \\ 10: Iterative Methods for Linear Systems / 505 \\ 10.1 The Standard Iterations / 506 \\ 10.2 The Conjugate Gradient Method / 516 \\ 10.3 Preconditioned Conjugate Gradient Methods / 527 \\ 11: Functions of Matrices / 539 \\ 11.1 Eigenvalue Methods / 540 \\ 11.2 Approximation Methods / 546 \\ 11.3 The Matrix Exponential / 555 \\ 12: Special Topics / 561 \\ 12.1 Some Constrained Least Squares Problems / 561 \\ 12.2 Subset Selection Using the SVD / 571 \\ 12.3 Total Least Squares / 576 \\ 12.4 Comparing Subspaces Using the SVD / 581 \\ 12.5 Some Modified Eigenvalue Problems / 587 \\ 12.6 Updating the $Q R$ Factorization / 592 \\ Bibliography / 601 \\ Index / 635", } @TechReport{Golub:1989:MMI, author = "Gene H. Golub and Martin H. Gutknecht", title = "Modified moments for indefinite weight functions", type = "Technical Report", number = "STAN-CS-89-08, NA-89-08", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "19", month = "????", year = "1989", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "orthogonal polynomials", } @Article{Golub:1989:SHC, author = "Gene H. Golub and Dianne P. O'Leary", title = "Some History of the Conjugate Gradient and {Lanczos} Algorithms: 1948--1976", journal = j-SIAM-REVIEW, volume = "31", number = "1", pages = "50--102", month = mar, year = "1989", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1031003", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "65-03 (00A15 01A60 65-00 65Fxx 90-03)", MRnumber = "90b:65003", bibdate = "Mon Jan 20 10:31:25 MST 1997", bibsource = "Compendex database; ftp://ftp.ira.uka.de/pub/bibliography/Parallel/par.lin.alg.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib", URL = "http://www.jstor.org/stable/2030847", abstract = "The conjugate gradient and Lanczos algorithms for solving linear systems of equations and eigenproblems represent very important computational innovations of the early 1950s. These methods came into wide use only in the mid-1970s. Shortly thereafter, vector computers and massive computer memories made it possible to use these methods to solve problems which could not be solved in any other way. Since that time, the algorithms have been further refined and have become a basic tool for solving a wide variety of problems on a wide variety of computer architectures. The conjugate gradient algorithm has also been extended to solve nonlinear systems of equations and optimization problems, and this has had tremendous impact on the computation of unconstrained and constrained optimization problems. This paper gives some of the history of the conjugate gradient and Lanczos algorithms and an annotated bibliography for the period 1948--1976.", acknowledgement = ack-nhfb, affiliation = "Stanford Univ", affiliationaddress = "Stanford, CA, USA", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "723; 921", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", journalabr = "SIAM Rev", keywords = "Algorithms; Computer Programming--Algorithms; Conjugate Gradient Algorithm; Lanczos Algorithm; Mathematical Techniques; Optimization--Theory; Variable Metric Algorithms", mynote = "June 1987 Maryland TR-1859", subject = "G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods) \\ G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues \\ G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion", subject-dates = "Eduard Stiefel (21 April 1909--25 November 1978); Magnus Rudolph Hestenes (13 February 1906--31 May 1991)", } @Article{Comon:1990:TFE, author = "Pierre Comon and Gene H. Golub", title = "Tracking a Few Extreme Singular Values and Vectors in Signal Processing", journal = j-PROC-IEEE, volume = "78", number = "8", pages = "1327--1343", month = aug, year = "1990", CODEN = "IEEPAD", DOI = "https://doi.org/10.1109/5.58320", ISSN = "0018-9219 (print), 1558-2256 (electronic)", ISSN-L = "0018-9219", bibdate = "Mon Sep 9 11:37:15 MDT 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=58320", abstract = "In various applications it is necessary to keep track of a low-rank approximation of a covariance matrix, R(t), slowly varying with time. It is convenient to track the left singular vectors associated with the largest singular values of the triangular factor, L(t), of its Cholesky factorization. These algorithms are referred to as square-root. The drawback of the eigenvalue decomposition (EVD) or the singular value decompositions (SVD) is usually the volume of the computations. Various numerical methods for carrying out this task are surveyed, and it is shown why this heavy computational burden is questionable in numerous situations and should be revised. Indeed, the complexity per eigenpair is generally a quadratic function of the problem size, but there exist faster algorithms with linear complexity. Finally, in order to make a choice among the large and fuzzy set of available techniques, comparisons based on computer simulations in a relevant signal processing context are made.", acknowledgement = ack-nhfb, affiliation = "Thomson-Sintra, Cagnes-sur-Mer, France", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "B0290 (Numerical analysis); B6140 (Signal processing and detection); C1260 (Information theory); C4100 (Numerical analysis)", fjournal = "Proceedings of the IEEE", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5", keywords = "Adaptive algorithms; Cholesky factorization; Computer simulations; Covariance matrix; Eigenvalue decomposition; Extreme singular values; Extreme singular vectors; Linear complexity; Low-rank approximation; nla, signal processing, Lanczos algorithm, rank determination; Numerical methods; Signal processing; Singular value decompositions; Square root algorithms; Tracking; Triangular factor", thesaurus = "Computational complexity; Eigenvalues and eigenfunctions; Matrix algebra; Numerical methods; Signal processing", } @Article{Elman:1990:IMC, author = "Howard C. Elman and Gene H. Golub", title = "Iterative methods for cyclically reduced non-self-adjoint linear systems", journal = j-MATH-COMPUT, volume = "54", number = "190", pages = "671--700", month = apr, year = "1990", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2008506", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F10 (65N22)", MRnumber = "91b:65036", MRreviewer = "Harry Yserentant", bibdate = "Mon Sep 09 12:10:35 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://www.jstor.org/stable/2008506", abstract = "The authors study iterative methods for solving linear systems of the type arising from two-cyclic discretizations of non-self-adjoint two-dimensional elliptic partial differential equations. A prototype is the convection-diffusion equation. The methods consist of applying one step of cyclic reduction, resulting in a `reduced system' of half the order of the original discrete problem, combined with a reordering and a block iterative technique for solving the reduced system. For constant-coefficient problems, they present analytic bounds on the spectral radii of the iteration matrices in terms of cell Reynolds numbers that show the methods to be rapidly-convergent. In addition, they describe numerical experiments that supplement the analysis and that indicate that the methods compare favourably with methods for solving the `unreduced' system.", acknowledgement = ack-nhfb # " and " # ack-sf, affiliation = "Dept. of Comput. Sci., Maryland Univ., College Park, MD, USA", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "B0290P (Differential equations); C4170 (Differential equations)", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "Analytic bounds; Block iterative technique; Cell Reynolds numbers; Convection-diffusion equation; Cyclically reduced non-self-adjoint linear systems; Elliptic partial differential equations; Iterative methods; Linear systems; Numerical experiments; Rapidly-convergent; Reordering; Spectral radii", thesaurus = "Convergence of numerical methods; Iterative methods; Partial differential equations", } @InProceedings{Elman:1990:IML, author = "Howard C. Elman and Gene H. Golub", title = "Block iterative methods for cyclically reduced nonselfadjoint elliptic problems", crossref = "Kincaid:1990:IML", pages = "91--105", year = "1990", MRclass = "65F10", MRnumber = "1 038 090", bibdate = "Fri Dec 20 17:21:26 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @TechReport{Elman:1990:LIMa, author = "Howard C. Elman and Gene H. Golub", title = "Line Iterative Methods for Cyclically Reduced Discrete Convection-Diffusion Problems", type = "Technical Report", number = "CS-TR-2403, UMIACS-TR-90-16", institution = inst-U-MARYLAND-CS, address = inst-U-MARYLAND-CS:adr, pages = "29", month = "????", year = "1990", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", abstract = "We perform an analytic and empirical study of line iterative methods for solving the discrete convection-diffusion equation. The methodology consists of performing one step of the cyclic reduction method, followed by iteration on the resulting cyclic reduction method, followed by iteration on the resulting reduced system using line orderings of the reduced grid. Two classes of iterative methods are considered: block stationary methods, such as the block Gauss--Seidel and SOR methods, and preconditioned generalized minimum residual methods with incomplete LU preconditioners. New analysis extends convergence bounds for constant coefficient problems to problems with separable variable coefficients. In addition, analytic results show that iterative methods based on incomplete LU preconditioners have faster convergence rates on incomplete LU preconditioners have faster convergence rates than block Jacobi relaxation methods. Numerical experiments examine additional properties of the two classes of methods, including the effects of flow, discretization, and grid ordering on performance.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "Iterative methods (Mathematics); Numerical analysis", } @InProceedings{Elman:1990:LIMb, author = "Howard C. Elman and Gene H. Golub", title = "Line iterative methods for cyclically reduced nonselfadjoint elliptic problems", crossref = "ARO:1990:TSA", pages = "457--466", year = "1990", MRclass = "65F10 (65N20)", MRnumber = "1 057 847", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Ferng:1990:ALM, author = "W. R. Ferng and G. H. Golub and R. J. Plemmons", title = "Adaptive {Lanczos} methods for recursive condition estimation", journal = j-PROC-SPIE, volume = "1348", pages = "326--337", month = "????", year = "1990", CODEN = "PSISDG", ISSN = "0277-786X (print), 1996-756X (electronic)", ISSN-L = "0277-786X", bibdate = "Mon Sep 9 11:37:15 MDT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", abstract = "This paper proposes an adaptive Lanczos Estimator scheme for tracking the condition number of the modified matrix over time. Applications to recursive least squares computations using the covariance method with sliding data windows are considered. Comparisons are made with other adaptive and non-adaptive condition estimators for recursive least squares problems. Numerical experiments are reported.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., North Carolina State Univ., Raleigh, NC, USA", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "B0290H (Linear algebra); B6140 (Signal processing and detection); C1240 (Adaptive system theory); C1260 (Information theory); C4140 (Linear algebra)", fjournal = "Proceedings of the SPIE --- The International Society for Optical Engineering", keywords = "Adaptive Lanczos Estimator; Covariance method; Modified matrix; Recursive condition estimation; Recursive least squares computations; RLS method; Signal processing; Sliding data windows", thesaurus = "Adaptive filters; Least squares approximations; Matrix algebra; Parameter estimation; Signal processing; Variational techniques", } @InProceedings{Gander:1990:SLE, author = "Walter Gander and G. H. Golub and Dominik Gruntz", title = "Solving linear equations by extrapolation", crossref = "Kowalik:1990:SNA", pages = "279--293", year = "1990", MRclass = "65F10", MRnumber = "91j:65060", MRreviewer = "R. P. Tewarson", bibdate = "Sun Jan 14 09:09:38 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1990:DVK, author = "Gene Golub and Bo K{\aa}gstr{\"o}m and Axel Ruhe and Paul {Van Dooren}", title = "Dedication to {Vera N. Kublanovskaya} on her 70th Birthday", journal = j-SIAM-J-MAT-ANA-APPL, volume = "11", number = "4", pages = "vii--ix", month = oct, year = "1990", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/0611033", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "01A70", MRnumber = "91j:01043", bibdate = "Fri Oct 17 06:15:04 2003", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @InProceedings{Golub:1990:IML, author = "Gene H. Golub and John E. de Pillis", title = "Toward an effective two-parameter {SOR} method", crossref = "Kincaid:1990:IML", pages = "107--119", year = "1990", MRclass = "65F10", MRnumber = "038 091", bibdate = "Sun Jan 14 10:13:28 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1990:MMI, author = "Gene H. Golub and Martin H. Gutknecht", title = "Modified Moments for Indefinite Weight Functions", journal = j-NUM-MATH, volume = "57", number = "6\slash 7", pages = "607--624", month = jul, year = "1990", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "30E05 (41A10 65F99)", MRnumber = "91i:30034", MRreviewer = "Jia Rong Yu", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Paper presented at the Conference on Approximation Theory and Numerical Linear Algebra, 30 March -- 1 April, 1989, Kent, Ohio.", abstract = "The problem of generating the recurrence coefficients of orthogonal polynomials from the moments or from modified moments of the weight function is well understood for positive weight distributions. The authors extend this theory and the basic algorithms to the case of an indefinite weight function. While the generic indefinite case is formally not much different from the positive definite case, there exist nongeneric degenerate situations, and these require a different more complicated treatment. The understanding of these degenerate situations makes it possible to construct a stable approximate solution of an ill-conditioned problem. The application to adaptive iterative methods for linear systems of equations is anticipated.", acknowledgement = ack-nhfb # " and " # ack-sf, affiliation = "Dept. of Comput. Sci., Stanford Univ., CA, USA", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "C4140 (Linear algebra)", corpsource = "Dept. of Comput. Sci., Stanford Univ., CA, USA", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "adaptive iterative methods; Adaptive iterative methods; degenerate situations; Degenerate situations; ill-conditioned problem; Ill-conditioned problem; indefinite weight functions; Indefinite weight functions; iterative methods; linear algebra; linear systems; Linear systems; orthogonal polynomials; Orthogonal polynomials; polynomials", thesaurus = "Iterative methods; Linear algebra; Polynomials", treatment = "T Theoretical or Mathematical", } @InCollection{Golub:1990:PRJ, author = "Gene Golub", title = "Prologue. Reflections on {Jim Wilkinson}", crossref = "Cox:1990:RNC", pages = "1--5", year = "1990", MRclass = "01A70", MRnumber = "92b:01057a", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Berry:1991:ELS, author = "Michael Berry and Gene Golub", title = "Estimating the Largest Singular Values of Large Sparse Matrices via Modified Moments", journal = j-NUMER-ALGORITHMS, volume = "1", number = "4", pages = "353--374 (or 353--373??)", month = nov, year = "1991", CODEN = "NUALEG", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", MRclass = "65F15 (65D32 65F50 65Y05)", MRnumber = "93a:65046", MRreviewer = "Cs. J. Heged{\H{u}}s", bibdate = "Mon Sep 9 11:25:40 MDT 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least squares, which is available by anonymous ftp from {\tt math.liu.se} in {\tt pub/references}.", abstract = "The authors describe a procedure for determining a few of the largest singular values of a large sparse matrix. The method by Golub and Kent (1989) which uses the method of modified moments for estimating the eigenvalues of operators used in iterative methods for the solution of linear systems of equations is appropriately modified in order to generate a sequence of bidiagonal matrices whose singular values approximate those of the original sparse matrix. A simple Lanczos recursion is proposed for determining the corresponding left and right singular vectors. The potential asynchronous computation of the bidiagonal matrices using modified moments with the iterations of an adapted Chebyshev semi-iterative (CSI) method is an attractive feature for parallel computers. Comparisons in efficiency and accuracy with an appropriate Lanczos algorithm (with selective re-orthogonalization) are presented on large sparse (rectangular) matrices arising from applications such as information retrieval and seismic reflection tomography. This procedure is essentially motivated by the theory of moments and Gauss quadrature.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN, USA", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "B0290F (Interpolation and function approximation); B0290H (Linear algebra); C4130 (Interpolation and function approximation); C4140 (Linear algebra)", fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", keywords = "Adaptive Chebyshev semi-iterative method; Asynchronous computation; Eigenvalues; Gauss quadrature; Information retrieval; Iterative methods; Lanczos recursion; Large sparse matrices; Largest singular values estimation; Linear systems of equations; Modified moments; nla, sparse, svd; Parallel computers; Seismic reflection tomography; Singular vectors", pubcountry = "Switzerland", thesaurus = "Chebyshev approximation; Eigenvalues and eigenfunctions; Iterative methods; Matrix algebra", } @InProceedings{Boley:1991:MNL, author = "D. Boley and G. H. Golub", title = "A modified non-symmetric {Lanczos} algorithm and applications", crossref = "Vaccaro:1991:SSP", pages = "189--196", month = "????", year = "1991", bibdate = "Mon Sep 9 11:37:15 MDT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", abstract = "Gives a brief description of a non-symmetric Lanczos algorithm that does not require strict bi-orthogonality among the generated vectors. Several applications are mentioned. For example, it is shown how the vectors generated are algebraically related to `controllable space' and `observable space' for a related linear dynamical system. The algorithm described is particularly appropriate for large sparse problems.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Minnesota, Univ., Minneapolis, MN, USA", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "B0290H (Linear algebra); C4140 (Linear algebra)", keywords = "Controllable space; Large sparse problems; Linear dynamical system; Matrix eigenvalue computation; Modified nonsymmetric Lanczos algorithm; Observable space", thesaurus = "Eigenvalues and eigenfunctions; Matrix algebra", } @Article{Boley:1991:NLA, author = "Daniel Boley and Gene Golub", title = "The nonsymmetric {Lanczos} algorithm and controllability", journal = j-SYST-CONTROL-LETT, volume = "16", number = "2", pages = "97--105", month = feb, year = "1991", CODEN = "SCLEDC", ISSN = "0167-6911 (print), 1872-7956 (electronic)", ISSN-L = "0167-6911", MRclass = "93B05 (93B40)", MRnumber = "92e:93004", MRreviewer = "Alexander N. Shoshitaishvili", bibdate = "Fri Dec 20 17:23:54 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", abstract = "Gives a brief description of a nonsymmetric Lanczos algorithm that does not require strict bi-orthogonality among the generated vectors. The authors show how the vectors generated are algebraically related to reachable space and observable space for a related linear dynamical system. The algorithm described is particularly appropriate for large sparse systems.", acknowledgement = ack-nhfb # " and " # ack-sf, affiliation = "Comput. Sci. Dept., Minnesota Univ., Minneapolis, MN, USA", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "C1110 (Algebra); C1120 (Analysis); C1310 (Analysis and synthesis methods); C1320 (Stability)", fjournal = "Systems and Control Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01676911", keywords = "Controllability; Large sparse systems; Linear dynamical system; Nonsymmetric Lanczos algorithm; Observability; Observable space; Reachable space; Vectors", pubcountry = "Netherlands", thesaurus = "Algebra; Controllability; Linear systems; Observability; Vectors", } @Article{Boley:1991:NLF, author = "Daniel L. Boley and Sylvan Elhay and Gene H. Golub and Martin H. Gutknecht", title = "Nonsymmetric {Lanczos} and finding orthogonal polynomials associated with indefinite weights", journal = j-NUMER-ALGORITHMS, volume = "1", number = "1", pages = "21--43", month = "????", year = "1991", CODEN = "NUALEG", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", MRclass = "65F15 (65F30 65F50 65G05)", MRnumber = "93f:65033", MRreviewer = "Alexander S. Babanin", bibdate = "Sun Jan 14 08:49:25 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", abstract = "The nonsymmetric Lanczos algorithm reduces a general matrix to tridiagonal by generating two sequences of vectors which satisfy a mutual bi-orthogonality property. The process can proceed as long as the two vectors generated at each stage are not mutually orthogonal, otherwise the process breaks down. The authors propose a variant that does not break down by grouping the vectors into clusters and enforcing the bi-orthogonality property only between different clusters, but relaxing the property within clusters. They show how this variant of the matrix Lanczos algorithm applies directly to a problem of computing a set of orthogonal polynomials and associated indefinite weights with respect to an indefinite inner product, given the associated moments. The authors discuss the close relationship between the modified Lanczos algorithm and the modified Chebyshev algorithm. They further show the connection between this last problem and checksum-based error correction schemes for fault-tolerant computing.", acknowledgement = ack-nhfb # " and " # ack-sf, affiliation = "Dept. of Comput. Sci., Minnesota Univ., Minneapolis, MN, USA", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "B0290H (Linear algebra); B6120B (Codes); C4140 (Linear algebra)", fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", keywords = "Checksum-based error correction; Fault-tolerant computing; Indefinite inner product; Indefinite weights; Matrix Lanczos algorithm; Modified Chebyshev algorithm; Modified Lanczos algorithm; Mutual bi-orthogonality property; Nonsymmetric Lanczos algorithm; Orthogonal polynomials; Tridiagonal matrix", pubcountry = "Switzerland", thesaurus = "Error correction codes; Matrix algebra; Polynomials", } @Article{DeMoor:1991:RSV, author = "Bart L. R. {De Moor} and Gene H. Golub", title = "The Restricted Singular Value Decomposition: Properties and Applications", journal = j-SIAM-J-MAT-ANA-APPL, volume = "12", number = "3", pages = "401--425", month = jul, year = "1991", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/0612029", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A09 (15A18 15A21 15A24 47A99)", MRnumber = "92k:15012", MRreviewer = "Zdzislaw W. Trzaska", bibdate = "Sun Jan 14 08:07:16 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", keywords = "nla, gsvd", } @InProceedings{Elhay:1991:UDOa, author = "Sylvan Elhay and G. H. Golub and Jaroslav Kautsk{\'y}", title = "Updating and downdating of orthogonal polynomials with data fitting applications", crossref = "Golub:1991:NLA", pages = "149--172", year = "1991", MRclass = "65D15 (65F30)", MRnumber = "92j:65017", bibdate = "Sun Jan 14 09:02:43 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", abstract = "Derives and assesses new methods for updating and downdating least squares polynomial fits to discrete data using polynomials orthogonal on all the data points being used. Rather than fixing on one basis throughout, the methods adaptively update and downdate both the least squares fit and the polynomial basis. This is achieved by performing similarity transformations on the tridiagonal Jacobi matrices representing the basis.", acknowledgement = ack-nhfb # " and " # ack-sf, affiliation = "Dept. of Comput. Sci., Adelaide Univ., SA, Australia", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "B6140 (Signal processing and detection); C1260 (Information theory)", keywords = "Data fitting applications; Data points; Downdating; Least squares polynomial fits; Orthogonal polynomials; Similarity transformations; Tridiagonal Jacobi matrices; Updating", thesaurus = "Data compression; Least squares approximations; Matrix algebra; Polynomials", } @Article{Elhay:1991:UDOb, author = "Sylvan Elhay and Gene H. Golub and Jaroslav Kautsk{\'y}", title = "Updating and downdating of orthogonal polynomials with data fitting applications", journal = j-SIAM-J-MAT-ANA-APPL, volume = "12", number = "2", pages = "327--353", month = apr, year = "1991", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/0612024", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65D20 (65F05)", MRnumber = "91m:65054", bibdate = "Sun Jan 14 09:07:02 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Elman:1991:IMC, author = "Howard C. Elman and Gene H. Golub", title = "Iterative methods for cyclically reduced nonselfadjoint linear systems. {II}", journal = j-MATH-COMPUT, volume = "56", number = "193", pages = "215--242", month = jan, year = "1991", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2008538", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F10 (65N22)", MRnumber = "91e:65051", MRreviewer = "Harry Yserentant", bibdate = "Sun Jan 14 09:10:54 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database", abstract = "For pt.~I see ibid., vol.~54, p.~671--700 (1990). The authors perform an analytic and experimental study of line iterative methods for solving linear systems arising from finite difference discretizations of nonself-adjoint elliptic partial differential equations on two-dimensional domains. The methods consist of performing one step of cyclic reduction, followed by solution of the resulting reduced system by line relaxation. They augment previous analyses of one-line methods, and derive a new convergence analysis for two-line methods, showing that both classes of methods are highly effective for solving the convection-diffusion equation. In addition, they compare the experimental performance of several variants of these methods, and show that the methods can be implemented efficiently on parallel architectures.", acknowledgement = ack-nhfb # " and " # ack-sf, affiliation = "Dept. of Comput. Sci., Maryland Univ., College Park, MD, USA", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "B0290P (Differential equations); C4170 (Differential equations)", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "2D domains; Convection-diffusion equation; Convergence analysis; Finite difference discretizations; Line iterative methods; Line relaxation; Linear systems; Nonself-adjoint elliptic partial differential equations; Parallel architectures", thesaurus = "Convergence of numerical methods; Iterative methods; Parallel algorithms; Partial differential equations", } @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-NUMER-ALGORITHMS, volume = "1", number = "1", pages = "1--20", month = "????", year = "1991", CODEN = "NUALEG", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", MRclass = "65F10 (65F20 65F35 93E10 94A12)", MRnumber = "92h:65053", MRreviewer = "De Hui Chen", bibdate = "Fri Nov 6 18:06:29 MST 1998", bibsource = "http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", abstract = "Estimates for the condition number of a matrix are useful in many areas of scientific computing, including: recursive least squares computations, optimization, eigenanalysis, and general nonlinear problems solved by linearization techniques where matrix modification techniques are used. The purpose of this paper is to propose an adaptive Lanczos estimator scheme, which the authors call ale, for tracking the condition number of the modified matrix over time. Applications to recursive least squares (RLS) computations using the covariance method with sliding data windows are considered. ale is fast for relatively small n-parameter problems arising in RLS methods in control and signal processing, and is adaptive over time, i.e., estimates at time t are used to produce estimates at time t+1. Comparisons are made with other adaptive and non-adaptive condition estimators for recursive least squares problems. Numerical experiments are reported indicating that ale yields a very accurate recursive condition estimator.", acknowledgement = ack-nhfb # " and " # ack-sf, affiliation = "Dept. of Math., North Carolina State Univ., Raleigh, NC, USA", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "B0290F (Interpolation and function approximation); B0290H (Linear algebra); B6140 (Signal processing and detection); C1260 (Information theory); C4130 (Interpolation and function approximation); C4140 (Linear algebra)", corpsource = "Dept. of Math., North Carolina State Univ., Raleigh, NC, USA", fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", keywords = "Adaptive Lanczos estimator; adaptive Lanczos estimator; Adaptive Lanczos methods; adaptive Lanczos methods; Covariance method; covariance method; least squares approximations; matrix algebra; Matrix condition number; matrix condition number; Matrix modification; matrix modification; numerical methods; Recursive condition estimation; recursive condition estimation; Recursive least squares computations; recursive least squares computations; signal processing; Sliding data windows; sliding data windows", pubcountry = "Switzerland", thesaurus = "Least squares approximations; Matrix algebra; Numerical methods; Signal processing", treatment = "T Theoretical or Mathematical", xxpages = "1--19", } @Article{Fischer:1991:GPW, author = "Bernd Fischer and Gene H. Golub", title = "On generating polynomials which are orthogonal over several intervals", journal = j-MATH-COMPUT, volume = "56", number = "194", pages = "711--730", month = apr, year = "1991", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2008403", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "33C45", MRnumber = "92d:33015", MRreviewer = "J. Prasad", bibdate = "Sun Jan 14 09:06:36 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://www.jstor.org/stable/2008403", abstract = "The authors consider the problem of generating the recursion coefficients of orthogonal polynomials for a given weight function. The weight function is assumed to be the weighted sum of weight functions, each supported on its own interval. Some of these intervals may coincide, overlap or are contiguous. They discuss three algorithms. Two of them are based on modified moments, whereas the other is based on an explicit expression for the desired coefficients. Several examples, illustrating the numerical performance of the various methods, are presented.", acknowledgement = ack-nhfb # " and " # ack-sf, affiliation = "Inst. fur Angewandte Math., Hamburg Univ., Germany", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "Explicit expression; Generating polynomials; Modified moments; Numerical performance; Recursion coefficients; Weight function; Weighted sum", thesaurus = "Polynomials", } @TechReport{Freund:1991:ISLa, author = "Roland W. Freund and Gene H. Golub and No{\"e}l M. Nachtigal", title = "Iterative Solution of Linear Systems", type = "Technical Report", number = "NA-91-05", institution = "Computer Science Department, Stanford University", address = "Stanford, CA, USA", month = "????", year = "1991", bibdate = "Sun Jan 14 08:46:41 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @InCollection{Gander:1991:CEP, author = "Walter Gander and Gene H. Golub and Urs {von Matt}", title = "A constrained eigenvalue problem", crossref = "Golub:1991:NLA", pages = "677--686", year = "1991", MRclass = "65F15", MRnumber = "92k:65067", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1991:DJW, author = "G. Golub and B. Parlett", title = "Dedication to {J. Wallace Givens}", journal = j-SIAM-J-MAT-ANA-APPL, volume = "12", number = "1", pages = "U1--U1", month = jan, year = "1991", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Thu Jun 6 10:13:11 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Golub:1991:HMN, author = "Gene H. Golub", title = "A history of modern numerical linear algebra", journal = j-MITT-MATH-GES-HAMBURG, volume = "12", number = "4", pages = "949--960", year = "1991/1992", CODEN = "MNGBAK", ISSN = "0340-4358", MRclass = "65-03 (01A60 65Fxx)", MRnumber = "93c:65002", bibdate = "Sun Jan 14 08:25:42 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Mathematische Wissenschaften gestern und heute. 300 Jahre Mathematische Gesellschaft in Hamburg, Teil 4 (Hamburg, 1990).", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "Mitteilungen der Mathematischen Gesellschaft in Hamburg", } @InProceedings{Golub:1991:IMC, author = "G. H. Golub and R. S. Tuminaro", title = "Iterative Methods for Cyclically Reduced Non-Self-Adjoint Linear Systems", crossref = "Anonymous:1991:PIS", pages = "7--8", year = "1991", bibdate = "Mon Aug 26 10:38:41 MDT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Golub:1991:QCL, author = "Gene H. Golub and Urs {von Matt}", title = "Quadratically Constrained Least Squares and Quadratic Problems", journal = j-NUM-MATH, volume = "59", number = "6", pages = "561--580", month = sep, year = "1991", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/BF01385796", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65F20 (65F50 65K10)", MRnumber = "92f:65049", MRreviewer = "R. P. Tewarson", bibdate = "Sun Jan 14 09:05:23 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", abstract = "The article considers the following problem: Compute a vector x such that //Ax-b///sub 2/-min, subject to the constraint //x///sub 2/= alpha. A new approach to this problem based on Gauss quadrature is given. The method is especially well suited when the dimensions of A are large and the matrix is sparse. It is also possible to extend this technique to a constrained quadratic form: For a symmetric matrix A it considers the minimization of x/sup T/Ax-2b/sup T/x subject to the constraint //x///sub 2/= alpha. Some numerical examples are given.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Stanford Univ., CA, USA", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "C1110 (Algebra); C1180 (Optimisation techniques); C4140 (Linear algebra)", corpsource = "Dept. of Comput. Sci., Stanford Univ., CA, USA", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "constraints; Gauss quadrature; lsq; matrix algebra; minimisation; Minimization; minimization; nla; nllsq; nlop; Quadratically constrained least squares problems; quadratically constrained least squares problems; Quadratically constrained quadratic problems; quadratically constrained quadratic problems; Sparse matrix; sparse matrix; Symmetric matrix; symmetric matrix; Vector; vector", thesaurus = "Matrix algebra; Minimisation", treatment = "T Theoretical or Mathematical", } @Book{VanHuffel:1991:TLS, author = "Sabine {Van Huffel} and Joos Vandewalle", title = "The total least squares problem. Computational aspects and analysis", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xiv + 300", year = "1991", ISBN = "0-89871-275-0", ISBN-13 = "978-0-89871-275-9", LCCN = "QA275.H84 1991", MRclass = "65-00 (00A69 65-01)", MRnumber = "93b:65001", MRreviewer = "R. P. Tewarson", bibdate = "Sun Jan 14 08:25:42 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Foreword by Gene H. Golub.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @Article{Arbenz:1992:LAS, author = "Peter Arbenz and Gene H. Golub", title = "{$ Q R $}-Like Algorithms for Symmetric Arrow Matrices", journal = j-SIAM-J-MAT-ANA-APPL, volume = "13", number = "2", pages = "655--658", month = apr, year = "1992", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/0613039", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F15", MRnumber = "92k:65064", bibdate = "Sun Jan 14 08:58:46 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", keywords = "nla, arrowhead matrix, QR algorithm, eig", } @Article{Bojanczyk:1992:PSD, author = "A. Bojanczyk and G. Golub and P. {Van Dooren}", title = "The periodic {Schur} decomposition: algorithms and applications", journal = j-PROC-SPIE, volume = "1770", pages = "31--42", month = "????", year = "1992", CODEN = "PSISDG", ISSN = "0277-786X (print), 1996-756X (electronic)", ISSN-L = "0277-786X", bibdate = "Mon Sep 9 11:06:23 MDT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", abstract = "The authors derive a unitary eigendecomposition for a sequence of matrices which they call the periodic Schur decomposition. They prove its existence and discuss its application to the solution of periodic difference arising in control. It is shown how the classical QR algorithm can be extended to provide a stable algorithm for computing this generalized decomposition. The decomposition is also applied to cyclic matrices and two-point boundary value problems.", acknowledgement = ack-nhfb, affiliation = "Dept. Electr. Eng., Cornell Univ., Ithaca, NY, USA", author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", classification = "C1110 (Algebra); C1120 (Analysis); C1340G (Time-varying systems); C4140 (Linear algebra); C4170 (Differential equations)", fjournal = "Proceedings of the SPIE --- The International Society for Optical Engineering", keywords = "Cyclic matrices; Matrix sequence; Periodic difference; Periodic Schur decomposition; QR algorithm; Stable algorithm; Time-varying control systems; Two-point boundary value problems; Unitary eigendecomposition", thesaurus = "Boundary-value problems; Difference equations; Eigenvalues and eigenfunctions; Matrix algebra; Time-varying systems", } @Article{Boley:1992:AFT, author = "Daniel L. Boley and Richard P. Brent and Gene H. Golub and Franklin T. Luk", title = "Algorithmic Fault Tolerance Using the {Lanczos} Method", journal = j-SIAM-J-MAT-ANA-APPL, volume = "13", number = "1", pages = "312--332", month = jan, year = "1992", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/0613023", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F15 (94B05)", MRnumber = "93f:65034", MRreviewer = "Herbert J. Bernstein", bibdate = "Tue Jan 21 08:54:30 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", acknowledgement = ack-nhfb # " and " # ack-sf, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Carey:1992:NAS, author = "Cheryl Carey and Hsin-Chu Chen and G. H. Golub and Ahmed Sameh", title = "A new approach for solving symmetric eigenvalue problems", journal = j-COMPUT-SYST-ENG, volume = "3", number = "6", pages = "671--679", month = dec, year = "1992", CODEN = "COSEEO", ISSN = "0956-0521 (print), 1873-6211 (electronic)", ISSN-L = "0956-0521", bibdate = "Tue Jan 21 08:54:30 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", abstract = "Presents a new approach for the solution to a series of slightly perturbed symmetric eigenvalue problems (A+BS/sub i/B/sup T/)x= lambda x, 0