%! /TeXDict 200 dict def TeXDict begin /Mtrx matrix def /@start { /StartTime usertime def vmstatus pop /@VMused exch def pop 72 720 translate } def /@letter { /letter where { pop letter 72 720 translate } if } def /@legal { /legal where { pop legal 72 936 translate } if } def /@note { /note where { pop note 72 720 translate } if } def /@a4 { /a4 where { pop a4 72 765 translate } if } def /@landscape { [ 0 1 -1 0 0 0 ] concat -648 0 translate } def /@manualfeed { /manualfeed where { /manualfeed true put } if } def /@duplex { /setduplexmode where { /setduplexmode true put } if } def /@copies { /#copies exch def } def /@startdoc { dup 72 exch div dup neg scale 0 0 transform round exch round exch itransform translate Mtrx currentmatrix pop currentdict /isoddpage known { /SecondMtrx matrix def 8.5 exch mul 0 translate SecondMtrx currentmatrix pop }{ pop } ifelse /@TeXSave save def } def /@restore /restore load def /restore { vmstatus pop dup @VMused lt {pop @VMused} if exch pop exch @restore /@VMused exch def } bind def /@pri { ( ) print ( ) cvs print }def /@newfont { /newname exch def newname 7 dict def newname load begin /FontType 3 def dup neg matrix scale /FontMatrix exch def /FontBBox [0 0 1 1] def /BitMaps 256 array def /BuildChar {CharBuilder} def /Encoding 256 array def 0 1 255 {Encoding exch /.undef put} for end newname newname load definefont pop } bind def /ch-image {ch-data 0 get} bind def /ch-width {ch-data 1 get} bind def /ch-height {ch-data 2 get} bind def /ch-xoff {ch-data 3 get} bind def /ch-yoff {ch-data 4 get} bind def /ch-tfmw {ch-data 5 get} bind def /CharBuilder { exch /BitMaps get exch get /ch-data exch def ch-data null ne { ch-tfmw 0 ch-xoff neg ch-yoff neg ch-width ch-xoff sub ch-height ch-yoff sub setcachedevice ch-width ch-height true [1 0 0 1 ch-xoff ch-yoff] {ch-image} imagemask } if } bind def /@dc{ /ch-code exch def dup 0 get length 2 lt { pop [ <00> 1 1 0 0 8.00 ] } if /ch-data exch def currentfont /BitMaps get ch-code ch-data put currentfont /Encoding get ch-code dup ( ) cvs cvn put } bind def /@pc { pop /ch-data exch def currentpoint translate ch-width ch-height true [1 0 0 -1 ch-xoff ch-yoff ] {ch-image} imagemask } bind def /@sf { setfont } def /@flushfonts { @TeXSave restore /@TeXSave save def} def /@bop0 { pop } bind def /@bop1 { pop Mtrx setmatrix /SaveImage save def } def /@eop { showpage SaveImage restore } def /p { moveto } bind def /r { 0 rmoveto } bind def /s { show pop } bind def /ks { 2 1 counttomark 2 sub { -1 roll } for counttomark 2 idiv { show 0 rmoveto } repeat show pop } bind def /m { mark } bind def /ru { /dy exch 1 sub neg def /dx exch 1 sub def gsave currentpoint newpath moveto dx 0 rlineto 0 dy rlineto dx neg 0 rlineto closepath fill grestore } bind def /@end { (Time used: ) print usertime StartTime sub @pri (VM used: ) print @VMused @pri (. Unused: ) print vmstatus @VMused sub @pri pop pop (\n) print flush end } def /DraftFirst { gsave initmatrix newpath /Helvetica-Bold findfont setfont (Draft) dup stringwidth pop 8.875 exch div dup 72 mul dup scale 52.3 rotate 2.5 exch div -.35 translate 0.95 setgray 0 0 moveto show grestore } bind def /DraftMore { gsave initmatrix newpath /Helvetica-Bold findfont 72 scalefont setfont 0.95 setgray 576 702 moveto (Draft) stringwidth exch neg exch neg rmoveto (Draft) show grestore } bind def /@draft { /@bop1 { 1 le {DraftFirst} {DraftMore} ifelse Mtrx setmatrix /SaveImage save def } bind def } bind def /@twoup { initmatrix [ 0 1 -1 0 0 0 ] concat 36 -87 translate 5.5 8.5 div dup scale /isoddpage true def /@eop { isoddpage not {showpage} if SaveImage restore /isoddpage isoddpage not def } def /@bop1 { pop isoddpage { SecondMtrx setmatrix } { Mtrx setmatrix } ifelse /SaveImage save def } def /@end { isoddpage not { showpage } if end } def } def /@beginspecial { SpecialDict begin gsave /SpecialSave save def currentpoint transform initgraphics itransform translate 0 0 moveto SpecialDefaults IfMacSetUp } def /@setspecial { hof vof translate setclipper hsc vsc scale angl rotate } def /@endspecial { SpecialSave restore grestore end } def /@beginfullpage { gsave /SpecialSave save def SpecialDict begin /showpage {} def initgraphics } def /@endfullpage { clear end SpecialSave restore grestore showpage } def /SpecialDict 50 dict def SpecialDict begin /Inch { 72 mul} bind def /SpecialDefaults { /hsi 8.5 Inch def /vsi 11 Inch def /hof 0 def /vof 0 def /hsc 1 def /vsc 1 def /angl 0 def /CLIP false def } def /@hsize {/hsi exch def /CLIP true def} def /@vsize {/vsi exch def /CLIP true def} def /@hoffset {/hof exch def} def /@voffset {/vof exch def} def /@hscale {/hsc exch def} def /@vscale {/vsc exch def} def /@rotate {/angl exch def} def /setclipper { CLIP { newpath 0 0 moveto hsi 0 rlineto 0 vsi rlineto hsi neg 0 rlineto closepath clip } if } def end /IfMacSetUp { userdict /md known { userdict /md get type /dicttype eq { md begin /txpose{ 1 -1 scale } bind def /cp {pop pop} bind def end } if } if } def end /TeXDict where {/TeXDict get begin} { (Need to load basic TeXDict first\n) print currentfile flushfile} ifelse /@texmakefont { /TeXsize exch def [ TeXsize 0 0 TeXsize neg 0 0 ] makefont def } bind def /@ps2texfont { dup FontDirectory exch known { exch pop findfont } { ReEncodeForTeX } ifelse exch @texmakefont } bind def /ReEncodeForTeX { /newfontname exch def /basefontname exch def /TeXstr 30 string def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall basefontdict /MathFontName known not { /TeXvec basefontname TeXstr cvs (Courier) search { pop pop pop TeXcourvec } { pop TeXnormalvec } ifelse def TeXvec aload pop TeXvec length 2 idiv { newfont /Encoding get 3 1 roll put } repeat } if newfontname newfont definefont } bind def /TeXnormalvec [ 8#014 /fi 8#015 /fl 8#020 /dotlessi 8#022 /grave 8#023 /acute 8#024 /caron 8#025 /breve 8#026 /macron 8#027 /ring 8#030 /cedilla 8#031 /germandbls 8#032 /ae 8#033 /oe 8#034 /oslash 8#035 /AE 8#036 /OE 8#037 /Oslash 8#042 /quotedblright 8#074 /exclamdown 8#076 /questiondown 8#134 /quotedblleft 8#136 /circumflex 8#137 /dotaccent 8#173 /endash 8#174 /emdash 8#175 /hungarumlat 8#176 /tilde 8#177 /dieresis ] def /TeXcourvec [ 8#016 /exclamdown 8#017 /questiondown 8#020 /dotlessi 8#022 /grave 8#023 /acute 8#024 /caron 8#025 /breve 8#026 /macron 8#027 /ring 8#030 /cedilla 8#031 /germandbls 8#032 /ae 8#033 /oe 8#034 /oslash 8#035 /AE 8#036 /OE 8#037 /Oslash 8#074 /less 8#076 /greater 8#134 /backslash 8#136 /circumflex 8#137 /underscore 8#173 /braceleft 8#174 /bar 8#175 /braceright 8#177 /dieresis ] def /ObliqueFont { /ObliqueAngle exch def /ObliqueBaseName exch def /ObliqueFontName exch def /ObliqueTransform [1 0 ObliqueAngle sin ObliqueAngle cos div 1 0 0] def /basefontdict ObliqueBaseName findfont ObliqueTransform makefont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName ObliqueFontName put ObliqueFontName newfont definefont pop } bind def /SmallCapsFont { /SmallCapsBaseName exch def /SmallCapsFontName exch def /basefontdict SmallCapsBaseName findfont def /newfont basefontdict maxlength 10 add dict def newfont begin /FontName SmallCapsFontName def /FontBaseDict basefontdict 1000 scalefont def /FontSCDict FontBaseDict .8 scalefont def /FontType 3 def /BuildChar {SmallCapChar} def /FontMatrix dup basefontdict exch get def /FontBBox dup basefontdict exch get def /Encoding dup basefontdict exch get def end SmallCapsFontName newfont definefont pop } bind def /SmallCapChar { /achar (A) def achar exch 0 exch put begin achar 0 get dup 97 ge exch 122 le and { achar 0 achar 0 get 32 sub put FontSCDict } { FontBaseDict } ifelse setfont achar stringwidth FontBBox setcachedevice newpath 0 0 moveto achar show end } bind def /MathEncodingVec [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon1 /Phi /Psi /Omega /alpha /beta /gamma /delta /epsilon /zeta /nu /theta /iota /kappa /lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon /phi /chi /psi /omega /epsilon /theta1 /omega1 /rho /sigma /phi1 /arrowleft /arrowleft /arrowright /arrowright /suchthat /congruent /proportional /angle /zero /one /two /three /four /five /six /seven /eight /nine /period /comma /less /slash /greater /asteriskmath /partialdiff /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /registerserif /copyrightserif /trademarkserif /logicalor /logicaland /section /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /dotlessi /j /weierstrass /macron /breve ] def /MathCharVec [ 71 68 81 76 88 80 83 161 70 89 87 97 98 103 100 101 122 110 113 105 107 108 109 110 120 112 114 115 116 117 102 99 121 119 101 74 118 114 115 106 172 172 174 174 39 64 181 208 48 49 50 51 52 53 54 55 56 57 46 44 60 47 62 42 182 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 210 211 212 218 217 167 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 245 106 195 197 198 ] def /MathDictVec [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 ] def /MathOblique { 3 copy ObliqueFont pop pop MathFont } bind def /MathFont { /MathSymName exch def /MathBaseName exch def /MathFontName exch def /basefontdict MathBaseName findfont def /newfont basefontdict maxlength 10 add dict def newfont begin /FontName MathFontName def /FontDictArray [ basefontdict 1000 scalefont MathSymName findfont 950 scalefont /Symbol findfont 950 scalefont ] def /FontType 3 def /BuildChar {MathFontChar} def /FontMatrix dup basefontdict exch get def /FontBBox dup basefontdict exch get def /Encoding dup basefontdict exch get dup length array copy def /WhichFont MathDictVec def /WhichChar MathCharVec def MathEncodingVec Encoding copy pop /achar (A) def end MathFontName newfont definefont pop } bind def /MathFontChar { exch begin achar exch 0 exch put FontDictArray WhichFont achar 0 get get get setfont achar dup 0 get WhichChar exch get 0 exch put achar stringwidth FontBBox setcachedevice newpath 0 0 moveto achar show end } bind def end /psf$TeXscale { 65536 div } def /DocumentInitState [ matrix currentmatrix currentlinewidth currentlinecap currentlinejoin currentdash currentgray currentmiterlimit ] cvx def /startTexFig { /psf$SavedState save def userdict maxlength dict begin currentpoint transform DocumentInitState setmiterlimit setgray setdash setlinejoin setlinecap setlinewidth setmatrix itransform moveto /psf$ury exch psf$TeXscale def /psf$urx exch psf$TeXscale def /psf$lly exch psf$TeXscale def /psf$llx exch psf$TeXscale def /psf$y exch psf$TeXscale def /psf$x exch psf$TeXscale def currentpoint /psf$cy exch def /psf$cx exch def /psf$sx psf$x psf$urx psf$llx sub div def /psf$sy psf$y psf$ury psf$lly sub div def psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub translate /DefFigCTM matrix currentmatrix def /initmatrix { DefFigCTM setmatrix } def /defaultmatrix { DefFigCTM exch copy } def /initgraphics { DocumentInitState setmiterlimit setgray setdash setlinejoin setlinecap setlinewidth setmatrix DefFigCTM setmatrix } def /showpage { initgraphics } def /erasepage { initgraphics } def /copypage {} def } bind def /clipFig { currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll exch lineto exch lineto exch lineto closepath clip newpath moveto } bind def /doclip { psf$llx 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[<3F800060E000F07000783800301C00001C00001C00000E00000E0003CE000C2E001C17001C0F00 3C07003C07003C03803C03803C03803C03801E01C01E01C01E01C00E01C00F00E00700E00380E0 01C1E000E270003C60> 20 29 -2 9 21] 103 @dc [<3001C07003303803103807083803083803881C03841C01C01C01C01C01C00E00E00E00E00E00E0 8E00E04700704700704780604740602630C01C0F80> 22 20 -4 0 26] 110 @dc [<1F8020604010E008F00CF00C700E000E003E03FC07F80FF00F800C000C060C070C030601030200 FC> 16 20 -3 0 19] 115 @dc [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @dc [<300300380070070066003803806200380380E100380380610038038071001C01C070801C01C038 001C01C038001C01C038000E00E01C000E00E01C000E00E01C008E00E01C004700700E00470070 0E004780680E004740640C002630C318001C0F80F000> 33 20 -4 0 37] 109 @dc [<07C000187000301800700E00700F00F00700F00780F003C0F003C0F003C07801E07801E07801E0 3C01E01C01E01E01C00E01C003018001C300007C00> 19 20 -4 0 23] 111 @dc [<07C3800C26401C1E20180E20180E201C0E201C07101C07001C07001C07000E03800E03800E0380 8703804701C04301C04381C02301C03300E00E00C0> 20 20 -4 0 24] 117 @dc [ 20 1 -4 -12 23] 123 @dc [ 30 31 -3 0 31] 80 @dc [<00FE00000381C000060020000C0018001800040038000200380001007000010070000080700000 80F0000080F0000000F0000000F0000000F0000000780000007800000078000000780000003C00 00003C0000001E0000101E0000100F000018070000180380001801C0001800C0001C0060003C00 38003C001C004C000781860000FE02> 31 33 -6 1 33] 67 @dc [ 35 31 -3 0 35] 75 @dc [<00FC0000038304000E00CC001C002E0018003E0038001E0070001E0070000F0070000F0070000F 00F0000F00F0000780F0000780F000FFF0F0000000780000007800000078000000780000003C00 00003C0000001E0000201E0000200E00003007000030038000300380003001C0003800E0007800 300078001C00980007030C0000FC04> 30 33 -6 1 35] 71 @dc [<0F0700308C80705C40703C40F01C40F01C40F00E20F00E00F00E00F00E00780700780700780700 3807003C03801C03800E03800707800389C000F1C00001C00001C00000E00000E00000E00000E0 0000700000700000700000700003F8000078> 21 32 -4 0 23] 100 @dc [ 25 31 -3 0 29] 76 @dc [<07C000183800300400700200700100F00000F00000F00000F00000F00000780000780000780000 3C02001C07001E07800E078003008001C100007E00> 17 20 -4 0 21] 99 @dc [ 35 31 -3 0 34] 78 @dc [ 23 29 0 9 23] 112 @dc cmr10.329 @sf [<000003E0FFFC0F100FC01E0807803E0407807E0407807C0407807C0007807C0007807C00078078 000780780007807800078070000780F0000780E0000781C00007FF80000780F000078078000780 3C0007801E0007801E0007801F0007801F0007801F0007801F0007801E0007801E0007803C0007 8078000F80F000FFFF8000> 30 32 -2 1 33] 82 @dc cmti10.329 @sf [ 35 31 -3 0 34] 72 @dc [<1F0031C060E06070E038E03CE01CE01EE01EE01E700F700F700F700F380F380F3C0E3A0E1D0C1C F01C001C000E000E000E000E0007000700070007003F800780> 16 32 -5 0 21] 98 @dc [<601E00E0310070310070708070708070708038384038700038700038E0001FC0001E00001D0000 1C80000E40C00E21E00E11E00E08E00704200703C0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 19 32 -3 0 21] 107 @dc [<3C0000660000F300007B000031800001800001C00001C00000C00000E00000E00000E00000E000 007000007000007000007000007000007000003800003800003800003800003800001C00001C00 001C00001C0001FFE0000E00000E00000E00000E00000E0000070000070000071800033C00033C 00019C000078> 22 41 2 9 14] 102 @dc [ 8 20 -5 0 14] 58 @dc [<01000000018000000380000003C0000003C0000003E0000003D0000003D0000003C8000003C800 0003C4000003C2000007C200000781000007810000078080000780400007804000078020000780 200007801000078008000F8008000F0004000F0004000F0002000F0001000F0001000F0000800F 0000C00F8000E0FFF007FC> 30 32 -9 1 34] 86 @dc [<38006400E200E200E200E200710070007000700038003800380038001C001C001C001C000E000E 000E000E00070007000700070003800380038003801FC003C0> 10 32 -4 0 12] 108 @dc [<7FE0FFE07FF0> 12 3 -3 -8 16] 45 @dc [ 28 31 -8 0 33] 84 @dc [<600700E00CC0700C40701C20700C20700E20380E103807003807003807001C03801C03801C0380 1C03800E01C00E01C00F01C00E8180076300071E00070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -3 0 23] 104 @dc cmr10.329 @sf [<001F800000F0F00001C0380007801E000F000F000E0007001E0007803C0003C03C0003C07C0003 E07C0003E0780001E0F80001F0F80001F0F80001F0F80001F0F80001F0F80001F0F80001F0F800 01F0F80001F0780001E0780001E07C0003E03C0003C03C0003C01E0007800E0007000F000F0007 801E0001C0380000F0F000001F8000> 28 33 -3 1 35] 79 @dc [ 23 20 0 0 24] 120 @dc 43 @bop1 cmr10.329 @sf 1919 -77 p m (43) s 74 67 p m ([13]) s 168 67 p m (T.Y.) 17 (Li,) 19 (Zhonggang) 17 (Zeng,) 19 (and) 18 (Luan) 19 (Cong.) 28 (Solving) 19 (eigen) 0 (v) -2 (alue) 18 (problems) 19 (of) 18 (real) 18 (nonsym-) ks 168 167 p m (metric) 14 (matrices) 14 (with) 14 (real) 14 (homotopies.) 18 (Preprin) 0 (t,) 13 (Mic) 0 (higan) 14 (State) 13 (Univ) 0 (ersit) 0 (y) -3 (,) 12 (E.) 13 (Lansing,) 15 (MI) ks 168 266 p m (48824-1027) -1 (,) 13 (1990.) ks 74 403 p m ([14]) s 168 403 p m (G.) 18 (P) 0 (eters) 18 (and) 20 (J.H.) 19 (Wilkinson.) 34 (In) 0 (v) 0 (erse) 17 (iteration,) 20 (ill-c) 1 (onditi) 1 (oned) 22 (equations) 19 (and) 20 (Newton's) ks 168 503 p m (metho) 1 (d.) ks cmti10.329 @sf 20 r m (SIAM) 15 (R) -1 (eview) ks cmr10.329 @sf m (,) 13 (21:339{36) -1 (0,) 13 (1979.) ks 74 640 p m ([15]) s 168 640 p m (B.) 14 (T.) 14 (Smith,) 15 (J.) 14 (M.) 14 (Bo) 0 (yle,) 14 (J.) 14 (J.) 15 (Dongarra,) 12 (B.) 15 (S.) 14 (Garb) 1 (o) 0 (w,) 12 (Y.) 14 (Ik) 0 (eb) 1 (e,) 15 (V.) 14 (C.) 14 (Klema,) 15 (and) 14 (C.) 14 (B.) ks 168 740 p m (Moler.) s cmti10.329 @sf 36 r m (Matrix) 21 (Eigensystem) 20 (R) -1 (outines) 20 ({) 21 (EISP) -2 (A) -2 (CK) 19 (Guide) ks cmr10.329 @sf m (,) 22 (v) 0 (olume) 20 (6) 20 (of) ks cmti10.329 @sf 21 r m (L) -1 (e) -3 (ctur) -1 (e) 19 (Notes) 21 (in) ks 168 839 p m (Computer) 17 (Scienc) -2 (e) ks cmr10.329 @sf m (.) 18 (Springer-V) -3 (erlag,) 15 (Berlin,) 16 (1976.) ks 74 976 p m ([16]) s 168 976 p m (J.) 17 (Wilkinson) 18 (and) 18 (C.) 16 (Reinsc) 0 (h.) ks cmti10.329 @sf 26 r m (Handb) -1 (o) -2 (ok) 16 (for) 19 (A) 0 (utomatic) 17 (Computation:) 25 (V) -2 (olume) 17 (II) 17 (-) 18 (Line) -1 (ar) ks 168 1076 p m (A) 0 (lgebr) -3 (a) ks cmr10.329 @sf m (.) 18 (Springer-V) -3 (erlag,) 16 (New) 15 (Y) -3 (ork,) 14 (1971.) ks 74 1213 p m ([17]) s 168 1213 p m (J.) 15 (H.) 15 (Wilkinson.) ks cmti10.329 @sf 21 r m (The) 16 (A) 0 (lgebr) -2 (aic) 14 (Eigenvalue) 16 (Pr) -1 (oblem) ks cmr10.329 @sf m (.) 18 (Oxford) 15 (Univ) 0 (ersit) 0 (y) 14 (Press,) 14 (1965.) ks @eop 42 @bop0 1.000000 /cmbx10.432 @newfont cmbx10.432 @sf [ 48 41 -3 0 52] 82 @dc [<001FF00000FFFE0003F81F0007E003800FC001C01F8000E03F8000E07F0000007F0000007F0000 00FF000000FF000000FF000000FFFFFFE0FFFFFFE0FF0007E0FF0007E07F0007E07F0007C07F00 0FC03F800FC01F800F800F801F8007C01F0003F07E0001FFF800003FE000> 27 27 -2 0 32] 101 @dc [<7FFF807FFF807FFF8007F00007F00007F00007F00007F00007F00007F00007F00007F00007F000 07F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007F000FFFFC0FFFFC0 FFFFC007F00007F00007F00007F00007F00007F00007F00007F03E07F07F03F07F03F87F01F87F 00FE3E003FFC0007F0> 24 42 -2 0 21] 102 @dc [ 24 27 -2 0 28] 114 @dc [ 33 27 -3 0 38] 110 @dc [<001FE00000FFFC0003F01E0007E007000FC003801F8001C03F8001C07F8000007F0000007F0000 00FF000000FF000000FF000000FF000000FF000000FF000000FF0000007F0000007F0000007F80 0E003F801F001F803F800FC03F8007E03F8003F01F0000FFFE00001FF800> 26 27 -2 0 31] 99 @dc [ 22 27 -2 0 27] 115 @dc cmr10.329 @sf [<7FC3FE0700E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E0 0700E00700E00700E00700E00700E00700E0FFFFE0070000070000070000070000070000070000 0701E00701E00381E001C0C000E0C0003F00> 23 32 0 0 25] 12 @dc cmti10.329 @sf [ 5 5 -5 0 14] 46 @dc cmr10.329 @sf [ 31 32 -1 0 34] 65 @dc [<7FE7FE0700E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E0 0700E00700E00700E00700E00700E00700E0FFFFE00700E00700E00700E00700E00700E00700E0 0700E00700E00381E001C1E000E0E0003FE0> 23 32 0 0 25] 13 @dc cmti10.329 @sf [ 30 31 -3 0 32] 66 @dc [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 24] 74 @dc [ 30 31 -3 0 30] 70 @dc 42 @bop1 cmr10.329 @sf 1919 -77 p m (42) s cmbx10.432 @sf 74 67 p m (References) s cmr10.329 @sf 97 230 p m ([1]) s 168 230 p m (J.) 16 (R.) 17 (Bunc) 0 (h,) 16 (C.) 16 (P) -3 (.) 15 (Nielsen,) 19 (and) 17 (D.) 16 (C.) 16 (Sorensen.) 24 (Rank-one) 17 (mo) 1 (di\014cation) 18 (of) 16 (the) 17 (symmetric) ks 168 330 p m (eigenproblem.) s cmti10.329 @sf 21 r m (Numer.) 17 (Math.) ks cmr10.329 @sf m (,) 15 (31:31{48) -1 (,) 13 (1978.) ks 97 466 p m ([2]) s 168 466 p m (P) -3 (.) 21 (A.) 22 (Businger.) 42 (Numerically) 24 (stable) 23 (de\015ation) 23 (of) 22 (Hessen) 0 (b) 1 (erg) 22 (and) 23 (symmetric) 22 (tridiagonal) ks 168 566 p m (matrices.) s cmti10.329 @sf 19 r m (BIT) s cmr10.329 @sf m (,) 14 (11:262{270) -1 (,) 13 (1971.) ks 97 702 p m ([3]) s 168 702 p m (J.) 20 (Cupp) 1 (en.) 39 (A) 20 (divide) 23 (and) 21 (conquer) 22 (metho) 1 (d) 21 (for) 20 (the) 21 (symmetric) 21 (tridiagonal) 22 (eigenproblem.) ks cmti10.329 @sf 168 802 p m (Numer.) 16 (Math.) ks cmr10.329 @sf m (,) 15 (36:177{195) -1 (,) 13 (1981.) ks 97 938 p m ([4]) s 168 938 p m (J.) 17 (Dongarra.) 27 (Impro) 0 (ving) 17 (the) 18 (accuracy) 18 (of) 18 (computed) 18 (matrix) 18 (eigen) 0 (v) -2 (alues.) 28 (T) -3 (ec) 0 (hnical) 18 (Rep) 1 (ort) ks 168 1038 p m (ANL-80-84,) 14 (Argonne) 15 (National) 16 (Lab.,) 15 (August) 15 (1980.) ks 97 1174 p m ([5]) s 168 1174 p m (J.) 14 (Dongarra,) 12 (C.) 14 (Moler,) 14 (and) 15 (J.) 14 (Wilkinson.) 20 (Impro) 0 (ving) 14 (the) 14 (accuracy) 15 (of) 13 (computed) 15 (eigen) 0 (v) -2 (alues) ks 168 1273 p m (and) 15 (eigen) 0 (v) 0 (ectors.) ks cmti10.329 @sf 18 r m (SIAM) 15 (J.) 16 (Numer.) 16 (A) 0 (nal.) ks cmr10.329 @sf m (,) 13 (20:23{45,) 13 (1982.) ks 97 1410 p m ([6]) s 168 1410 p m (J.) 21 (Dongarra) 21 (and) 22 (D.) 21 (Sorensen.) 40 (A) 22 (fully) 23 (parallel) 23 (algorithm) 22 (for) 21 (the) 22 (symmetric) 22 (eigen) 0 (v) -2 (alue) ks 168 1509 p m (problem.) s cmti10.329 @sf 20 r m (SIAM) 15 (J.) 16 (Sci.) 16 (Statist.) 15 (Comput.) ks cmr10.329 @sf m (,) 16 (8:s139{s15) -1 (4,) 13 (1987.) ks 97 1646 p m ([7]) s 168 1646 p m (J.) 15 (Dongarra,) 14 (D.) 15 (Sorensen,) 16 (K.) 16 (Connolly) -3 (,) 16 (and) 16 (J.) 15 (P) 0 (atterson.) 19 (Programming) 15 (metho) 1 (dology) 16 (and) ks 168 1745 p m (p) 1 (erformance) 11 (issues) 11 (for) 10 (adv) -2 (anced) 11 (computer) 11 (arc) 0 (hitectures.) ks cmti10.329 @sf 12 r m (Par) -1 (al) 2 (lel) 10 (Computing) ks cmr10.329 @sf m (,) 11 (8:41{58,) 10 (1988.) ks 97 1882 p m ([8]) s 168 1882 p m (G.) 14 (Golub) 15 (and) 15 (C.) 14 (V) -3 (an) 14 (Loan.) ks cmti10.329 @sf 19 r m (Matrix) 16 (Computations) ks cmr10.329 @sf m (.) 19 (Johns) 15 (Hopkins) 16 (Univ) 0 (ersit) 0 (y) 13 (Press,) 14 (Balti-) ks 168 1981 p m (more,) 14 (MD,) 14 (second) 16 (edition,) 16 (1989.) ks 97 2117 p m ([9]) s 168 2117 p m (G.) 19 (Golub) 20 (and) 20 (J.H.) 19 (Wilkinson.) 35 (Ill-cond) 1 (iti) 1 (oned) 22 (eigensystems) 20 (and) 20 (the) 20 (computation) 20 (of) 19 (the) ks 168 2217 p m (Jordan) 15 (canonical) 16 (form.) ks cmti10.329 @sf 19 r m (SIAM) 15 (R) -1 (eview) ks cmr10.329 @sf m (,) 14 (18:578{6) -1 (19,) 13 (1976.) ks 74 2353 p m ([10]) s 168 2353 p m (G.) 14 (H.) 15 (Golub.) 20 (Some) 15 (mo) 1 (di\014ed) 17 (matrix) 15 (eigen) 0 (v) -2 (alue) 15 (problems.) ks cmti10.329 @sf 20 r m (SIAM) 15 (R) -1 (ev.) ks cmr10.329 @sf m (,) 14 (15:318{3) -1 (34,) 13 (1973.) ks 74 2490 p m ([11]) s 168 2490 p m (L.E) 13 (Jessup.) 17 (A) 13 (case) 13 (against) 13 (a) 13 (divide) 15 (and) 13 (conquer) 14 (approac) 0 (h) 12 (for) 12 (the) 14 (nonsymmetric) 13 (eigen) 0 (v) -2 (alue) ks 168 2589 p m (problem.) 20 (Preprin) 0 (t,) 14 (Oak) 15 (Ridge) 17 (National) 15 (Lab) 1 (oratory) -3 (,) 13 (Oak) 16 (Ridge,) 16 (TN) 15 (37831,) 13 (1991.) ks 74 2726 p m ([12]) s 168 2726 p m (K.) 15 (Knopp.) ks cmti10.329 @sf 20 r m (The) -1 (ory) 15 (of) 17 (F) -2 (unctions) ks cmr10.329 @sf -1 r m (.) 18 (Do) 0 (v) -1 (er) 13 (Publications,) 17 (New) 15 (Y) -3 (ork,) 14 (NY,) 15 (1945.) ks @eop 41 @bop0 1.000000 /cmmi10.329 @newfont cmmi10.329 @sf [<001000001800001800001800000C00000C00000C00000C00000600000600000600000200000200 000200000300000300000300000280000280000280000240000240800420C00420400C10301C10 3FF8101FF8080FF00803E004> 22 30 -1 10 24] 13 @dc cmr10.329 @sf [<7FFFFFE0FFFFFFF000000000000000000000000000000000000000000000000000000000000000 00FFFFFFF07FFFFFE0> 28 12 -3 -5 35] 61 @dc cmmi10.329 @sf [ 21 32 -3 0 27] 21 @dc [<0F8000184000302000701000701800F00800F00800F00C00F00400F00400780600780600780600 3C06001C06001E06000E0E00070E0001FC00007C0000F80001F00003C000038000038000030000 03800001800001808000C080006100001E00> 17 32 -2 0 20] 14 @dc [<70F8F8F870> 5 5 -4 0 13] 58 @dc [<0F8000186000301800600C00E00E00E00700E00700E00380E00380E003807001C07001C07001C0 3801C01C01C01E03800F078007FFFE01FFFE007FFE> 23 20 -2 0 26] 27 @dc cmr10.329 @sf [<0020004000800100020006000C000C00180018003000300030007000600060006000E000E000E0 00E000E000E000E000E000E000E000E000E0006000600060007000300030003000180018000C00 0C00060002000100008000400020> 11 46 -3 12 18] 40 @dc cmmi10.329 @sf [ 36 31 -2 0 38] 72 @dc 1.000000 /cmsy8.300 @newfont cmsy8.300 @sf [<40C0E06070703038383C1C1E1E0E0F0F06> 8 17 -1 -1 10] 48 @dc cmmi10.329 @sf [<40201010080804040474FCFCF870> 6 14 -4 9 13] 59 @dc [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @dc cmr10.329 @sf [<800040002000100008000C00060006000300030001800180018001C000C000C000C000E000E000 E000E000E000E000E000E000E000E000E000E000C000C000C001C0018001800180030003000600 06000C0008001000200040008000> 11 46 -3 12 18] 41 @dc 1.000000 /cmsy10.329 @newfont cmsy10.329 @sf [ 26 2 -4 -10 35] 0 @dc [<000F0038006000E001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C003 8007001E00F8001E000700038001C001C001C001C001C001C001C001C001C001C001C001C001C0 01C001C000E000600038000F> 16 45 -3 11 23] 102 @dc [ 16 45 -3 11 23] 103 @dc cmr10.329 @sf [<381C7C3EFC7EFC7EB85C804080408040402040202010201010080804> 15 14 -5 -18 23] 92 @dc [<402020101008100808040804040204020402743AFC7EFC7EF87C7038> 15 14 -2 -18 23] 34 @dc [<3F006180F0C0F06060700070007000700070007000700070007000700070007000700070007000 7000700070007000700070007000F007F0007000000000000000000000000000E001F001F001F0 00E0> 12 40 2 9 14] 106 @dc cmmi10.329 @sf [ 22 31 -1 0 20] 73 @dc [ 36 31 -2 0 37] 78 @dc cmr10.329 @sf [<7FE3FF000700700007007000070070000700700007007000070070000700700007007000070070 00070070000700700007007000070070000700700007007000070070000700700007007000FFFF FF80070070000700700007007000070070000700700007007000070070000300F0300380F87801 C0787800F06E30001F83E0> 29 32 0 0 27] 11 @dc cmmi10.329 @sf [<1801E03803101C03081C07081C07041C03840E03820E01C00E01C00E01C00700E00700E00700E0 8700E043807043807043C07023A0602318C01E0780> 23 20 -2 0 27] 110 @dc cmsy10.329 @sf [<400004C0000C6000183000301800600C00C006018003030001860000CC00007800003000003000 00780000CC000186000303000601800C00C0180060300030600018C0000C400004> 22 24 -6 1 35] 2 @dc cmmi10.329 @sf [<0FC01838300470027001F000F000F000F000F0007800780078003C041C0E1E0F0E0F070101C200 7C> 16 20 -2 0 20] 99 @dc [<07C000187000301800700E00700F00F00700F00780F003C0F003C0F003C07801E07801E07801E0 3C01E01C01E01E01C00E01C003018001C300007C00> 19 20 -2 0 22] 111 @dc [<0F0780308C40705C40703C20F01C20F01C20F00E10F00E00F00E00F00E00780700780700780700 3807003C03801C03800E03800707800389C000F1C00001C00001C00000E00000E00000E00000E0 0000700000700000700000700003F8000078> 21 32 -2 0 24] 100 @dc cmsy8.300 @sf [<0F8007C010E01E6020303810400860088004C00C80078004800380048007000480078004C00C80 04401840082070301019E01C200F8007C0> 30 14 -2 0 35] 49 @dc cmsy10.329 @sf [<80003F008000FF808001FFC0C007C0E0E00F0070703E00303FF800101FF000100FC00010000000 000000000080003F008000FF808001FFC0C007C0E0E00F0070703E00303FF800101FF000100FC0 0010> 28 20 -3 -2 35] 25 @dc cmmi10.329 @sf [<1801800F0038038018801C01C018401C01C038401C01C038201C01C01C200E00E01C100E00E00E 000E00E00E000E00E00E0007007007000700700700070070070087007007004380380380438038 038043C034030023A032030023186186001E07C07C00> 36 20 -2 0 40] 109 @dc [<0F0780308C40705C40703C20F01C20F01C20F00E10F00E00F00E00F00E00780700780700780700 3807003C03801C03800E03800707800389C000F180> 20 20 -2 0 24] 97 @dc [<383C00446300E2C080F1C080F1C04061C04000E02000E00000E00000E000007000007000007000 4070002038602038F01038F01034700C622003C1C0> 20 20 -2 0 26] 120 @dc cmsy10.329 @sf [ 2 45 -5 11 13] 106 @dc cmmi10.329 @sf [<01F0780007098600060781000E0780800E0380800E0380400E0380400E0380200E0380200E0380 200701C0100701C0100701C0108381C0104380E01841C0E03821C0E0782180E0F8118070F00F00 6060> 29 20 -2 0 33] 119 @dc 1.000000 /cmmi8.300 @newfont cmmi8.300 @sf [<1C0032003200310031001800180018000C008C004600460024001C000000000000000000000000 00030003800300> 9 23 -1 0 12] 105 @dc 1.000000 /cmr8.300 @newfont cmr8.300 @sf [ 13 21 -2 0 18] 50 @dc cmr10.329 @sf [ 16 20 -1 0 20] 122 @dc cmmi10.329 @sf [ 33 31 -2 0 38] 68 @dc 1.000000 /cmex10.300 @newfont cmex10.300 @sf [ 13 37 -16 38 37] 56 @dc [<007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C00 7C007C007C007C007C00F800F800F800F001F001E003E003C0078007000E001C003800F000C000 F00038001C000E000700078003C003E001E001F000F000F800F800F8007C007C007C007C007C00 7C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C> 14 77 -7 76 37] 60 @dc [<0018007800F001E003C007800F001F001E003E003C007C007C007800F800F800F800F800F800F8 00F800F800F800F800F800F800F800F800F800F800F800F800F800F800F800F800F800> 13 37 -16 36 37] 58 @dc cmsy8.300 @sf [ 2 33 -4 8 10] 106 @dc cmmi8.300 @sf [<03C7C00C2C200818101818101818081818080C0C040C0C040C0C04860C0446060646060626060E 1C0204> 23 14 -1 0 25] 119 @dc 1.000000 /cmmi6.300 @newfont cmmi6.300 @sf [<306864646030309898587000000000000C04> 6 18 -2 0 11] 105 @dc [<603860643062303230303030181898189C189A1871F0> 15 11 -2 0 19] 110 @dc cmsy10.329 @sf [ 26 36 -4 7 35] 20 @dc cmmi10.329 @sf [ 26 26 -4 2 35] 62 @dc [ 44 31 -2 0 44] 77 @dc 41 @bop1 cmr10.329 @sf 1919 -77 p m (41) s 74 67 p m (In) 16 (fact) 15 (in) 16 (this) 15 (particular) 16 (case) 15 (w) 0 (e) 14 (ha) 0 (v) 0 (e) ks cmmi10.329 @sf 963 167 p m (\015) s cmr10.329 @sf 14 r m (=) s cmmi10.329 @sf 13 r m (\025) s cmr10.329 @sf 74 289 p m (and) s cmmi10.329 @sf 960 388 p m (\016) s cmr10.329 @sf 15 r m (=) 13 (1) ks cmmi10.329 @sf m (:) s cmr10.329 @sf 74 510 p m (Clearly:) s cmmi10.329 @sf 748 610 p m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmsy8.300 @sf 836 592 p m (0) s cmmi10.329 @sf 846 610 p m (;) 8 (U) ks cmsy8.300 @sf 903 592 p m (0) s cmr10.329 @sf 914 610 p m (\)) 12 (=) ks cmmi10.329 @sf 13 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) 1 (;) 8 (U) ks cmr10.329 @sf 5 r m (\)) s cmsy10.329 @sf 8 r m (\000) 11 (f) ks cmmi10.329 @sf m (\025) s cmsy10.329 @sf m (g) s cmmi10.329 @sf m (:) s cmr10.329 @sf 74 732 p m (Therefore,) 14 (ha) 0 (ving) 14 (\\remo) 0 (v) -2 (ed") ks cmmi10.329 @sf 13 r m (\025) s cmr10.329 @sf 14 r m (from) 13 (the) 15 (sp) 1 (ectrum) 14 (w) 0 (e) 13 (can) 15 (get) 14 (further) 14 (eigenpairs.) 21 (W) -3 (e) 13 (note) 14 (that,) ks 74 832 p m (just) 18 (as) 18 (in) 19 (the) 18 (case) ks cmmi10.329 @sf 19 r m (U) s cmr10.329 @sf 22 r m (=) s cmmi10.329 @sf 18 r m (I) s cmr10.329 @sf 4 r m (,) s cmmi10.329 @sf 18 r m (H) s cmsy8.300 @sf 666 817 p m (0) s cmr10.329 @sf 696 832 p m (and) s cmmi10.329 @sf 18 r m (U) s cmsy8.300 @sf 823 817 p m (0) s cmr10.329 @sf 853 832 p m (are) 18 (v) 0 (ery) 17 (c) 0 (heap) 17 (to) 18 (obtain) 18 (once) ks cmmi10.329 @sf 19 r m (N) s cmr10.329 @sf 23 r m (has) 18 (b) 1 (een) 19 (determined.) ks 74 931 p m (Indeed,) s cmmi10.329 @sf 22 r m (H) s cmsy8.300 @sf 282 916 p m (0) s cmr10.329 @sf 312 931 p m (di\013ers) 19 (from) 19 (the) ks cmmi10.329 @sf 19 r m (n) s cmsy10.329 @sf 13 r m (\000) s cmr10.329 @sf 14 r m (1) s cmsy10.329 @sf 12 r m (\002) s cmmi10.329 @sf 13 r m (n) s cmsy10.329 @sf 13 r m (\000) s cmr10.329 @sf 14 r m (1) 18 (principal) 22 (submatrix) 19 (of) ks cmmi10.329 @sf 19 r m (H) s cmr10.329 @sf 23 r m (in) 20 (the) 19 (last) 20 (column) 20 (only) -3 (,) ks 74 1031 p m (whereas) s cmmi10.329 @sf 18 r m (U) s cmsy8.300 @sf 285 1016 p m (0) s cmr10.329 @sf 315 1031 p m (is) 19 (the) ks cmmi10.329 @sf 18 r m (n) s cmsy10.329 @sf 13 r m (\000) s cmr10.329 @sf 12 r m (1) s cmsy10.329 @sf 12 r m (\002) s cmmi10.329 @sf 13 r m (n) s cmsy10.329 @sf 12 r m (\000) s cmr10.329 @sf 13 r m (1) 18 (principal) 20 (submatrix) 19 (of) ks cmmi10.329 @sf 18 r m (U) s cmr10.329 @sf 5 r m (.) 29 (The) 18 (computation) 19 (of) ks cmmi10.329 @sf 18 r m (N) s cmr10.329 @sf 22 r m (requires) 19 (a) ks 74 1130 p m (matrix-v) 0 (ector) 13 (m) 0 (ultiply) -3 (.) ks 124 1272 p m (It) 14 (is) 14 (also) 14 (easy) 14 (to) 13 (v) 0 (erify) 13 (that) 13 (de\015ating) 15 (t) 0 (w) -1 (o) 12 (consecutiv) 0 (e) 13 (complex) 15 (conjugate) 14 (eigenpairs) 15 (results) 14 (in) ks 74 1371 p m (real) s cmmi10.329 @sf 16 r m (H) s cmsy8.300 @sf 205 1356 p m (0) s cmr10.329 @sf 231 1371 p m (and) s cmmi10.329 @sf 15 r m (U) s cmsy8.300 @sf 355 1356 p m (0) s cmr10.329 @sf 367 1371 p m (.) s 124 1512 p m (The) 15 (condition) 17 (n) 0 (um) 0 (b) 1 (er) 13 (of) ks cmmi10.329 @sf 15 r m (N) s cmr10.329 @sf 20 r m (migh) 0 (t) 14 (raise) 15 (concern.) 21 (W) -3 (e) 14 (ha) 0 (v) -1 (e) ks cmmi10.329 @sf 771 1648 p m (cond) s cmsy8.300 @sf 864 1655 p m (1) s cmr10.329 @sf 901 1648 p m (\() s cmmi10.329 @sf m (N) s cmr10.329 @sf 5 r m (\)) s cmsy10.329 @sf 11 r m (\031) s cmmi10.329 @sf 13 r m (max) s cmr10.329 @sf m (\() s cmsy10.329 @sf m (j) s cmmi10.329 @sf m (w) s cmmi8.300 @sf 1192 1655 p m (i) s cmsy10.329 @sf 1205 1648 p m (j) s cmr10.329 @sf m (\)) s cmr8.300 @sf 1236 1630 p m (2) s cmmi10.329 @sf 1255 1648 p m (:) s cmr10.329 @sf 74 1784 p m (It) 17 (is) 18 (therefore) 17 (easy) 17 (to) 16 (detect) 17 (an) 17 (ill-cond) 1 (iti) 1 (oned) ks cmmi10.329 @sf 19 r m (N) s cmr10.329 @sf 5 r m (.) 25 (W) -3 (e) 16 (prop) 1 (ose) 17 (to) 17 (handle) 18 (this) 18 (situation) 17 (in) 18 (the) ks 74 1884 p m (generalized) 15 (case) 13 (in) 14 (the) 13 (follo) 0 (wing) 13 (manner.) 19 (Let) ks cmmi10.329 @sf 13 r m (D) s cmr10.329 @sf 14 r m (b) 1 (e) 14 (a) 13 (diagonal) 13 (matrix) 13 (with) 14 (its) 13 (diagonal) 13 (elemen) 0 (ts) ks cmmi10.329 @sf 74 1984 p m (d) s cmmi8.300 @sf 98 1991 p m (i) s cmr10.329 @sf 127 1984 p m (de\014ned) 17 (b) 0 (y) ks cmex10.300 @sf 754 1997 p m (8) s 754 2034 p m (<) s 754 2109 p m (:) s cmmi10.329 @sf 846 2047 p m (d) s cmmi8.300 @sf 870 2054 p m (i) s cmr10.329 @sf 897 2047 p m (=) 13 (1) ks cmmi10.329 @sf m (;) s cmr10.329 @sf 32 r m (if) s cmsy8.300 @sf 1074 2026 p m (j) s cmmi8.300 @sf m (w) s cmmi6.300 @sf 1109 2031 p m (i) s cmsy8.300 @sf 1122 2026 p m (j) s 1069 2038 p 67 2 ru 1069 2065 p m (j) s cmmi8.300 @sf m (w) s cmmi6.300 @sf 1104 2069 p m (n) s cmsy8.300 @sf 1126 2065 p m (j) s cmsy10.329 @sf 1153 2047 p m (\024) s cmr10.329 @sf 13 r m (1) s cmmi10.329 @sf 812 2119 p m (d) s cmmi8.300 @sf 836 2126 p m (i) s cmr10.329 @sf 862 2119 p m (=) s cmsy10.329 @sf 13 r m (\000) s cmmi8.300 @sf 950 2102 p m (w) s cmmi6.300 @sf 975 2106 p m (n) s 950 2109 p 47 2 ru cmmi8.300 @sf 954 2135 p m (w) s cmmi6.300 @sf 979 2140 p m (i) s cmmi10.329 @sf 1002 2119 p m (;) s cmr10.329 @sf 32 r m (if) s cmsy8.300 @sf 1108 2098 p m (j) s cmmi8.300 @sf m (w) s cmmi6.300 @sf 1143 2103 p m (i) s cmsy8.300 @sf 1156 2098 p m (j) s 1104 2110 p 67 2 ru 1104 2137 p m (j) s cmmi8.300 @sf m (w) s cmmi6.300 @sf 1139 2141 p m (n) s cmsy8.300 @sf 1160 2137 p m (j) s cmmi10.329 @sf 1188 2119 p m (>) s cmr10.329 @sf 13 r m (1) s 74 2205 p m (then) 16 (clearly) ks cmmi10.329 @sf 695 2305 p m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (D) 1 (N) 5 (H) 4 (M) 2 (;) 8 (D) 0 (N) 5 (U) 5 (M) ks cmr10.329 @sf 5 r m (\)) 11 (=) ks cmmi10.329 @sf 13 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) 1 (;) 8 (U) ks cmr10.329 @sf 5 r m (\)) s cmmi10.329 @sf m (;) s cmr10.329 @sf 74 2427 p m (since) s cmmi10.329 @sf 16 r m (D) s cmr10.329 @sf 15 r m (is) 14 (non-singular.) 21 (The) 14 (m) 0 (ultiplication) 16 (b) 0 (y) ks cmmi10.329 @sf 13 r m (D) s cmr10.329 @sf 15 r m (cancels) 16 (all) 15 (the) 14 (large) 14 (en) 0 (tries) 14 (in) 15 (the) 14 (last) 14 (column) ks 74 2526 p m (of) s cmmi10.329 @sf 15 r m (N) s cmr10.329 @sf 5 r m (.) 19 (It) 16 (is) 15 (easy) 15 (to) 15 (see) 16 (that) 14 (\(16\)) 14 (and) 16 (\(17\)) 14 (are) 14 (satis\014ed) 16 (when) 16 (the) 15 (pre-m) 0 (ultiplication) 17 (is) 16 (done) 16 (with) ks cmmi10.329 @sf 74 2626 p m (D) 1 (N) ks cmr10.329 @sf 21 r m (instead) 18 (of) ks cmmi10.329 @sf 16 r m (N) s cmr10.329 @sf 5 r m (.) 25 (The) 17 (disadv) -2 (an) 0 (tage) 15 (of) 16 (ha) 0 (ving) 16 (to) 17 (prem) 0 (ultiply) 17 (b) 0 (y) ks cmmi10.329 @sf 16 r m (D) s cmr10.329 @sf 18 r m (is) 17 (that) 16 (after) 16 (the) 17 (de\015ation) ks 74 2726 p m (of) 15 (t) 0 (w) -1 (o) 13 (complex) 16 (conjugate) 15 (eigenpairs,) 16 (the) 15 (resulting) ks cmmi10.329 @sf 16 r m (H) s cmsy8.300 @sf 1128 2711 p m (0) s cmr10.329 @sf 1155 2726 p m (and) s cmmi10.329 @sf 15 r m (U) s cmsy8.300 @sf 1279 2711 p m (0) s cmr10.329 @sf 1306 2726 p m (migh) 0 (t) 14 (still) 16 (b) 1 (e) 16 (complex.) ks @eop 40 @bop0 cmsy10.329 @sf [<4020C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C0 30C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030 C030C030C030C030C030C0304020> 12 46 -5 12 23] 107 @dc cmmi10.329 @sf [<3C0000620000F3000079800031800001C00000C00000E00000E00000E00000E000007000007000 007000007000007000003800003800003800003800003800001C00001C00001C00001C00001C00 000E00000E0000FFF0000E00000E00000E0000070000070000070000070000030C00039E00019E 0000CE00007C> 23 41 -2 9 22] 102 @dc [<07E00C1818003000700070007000F000F000F0007FF07800780038003C001C000E00070001C000 7E> 15 20 -2 0 18] 15 @dc cmbx10.432 @sf [<7FFFFE7FFFFE7FFFFE00FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE00 00FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE00 00FE0000FE0000FE0000FE0000FE0000FE00F8FE00FFFE00FFFE0007FE00007E00001E00000E00> 23 39 -5 0 34] 49 @dc [<003F800001FFF00007E0FC000FC07E001F803F001F803F003F001F803F001F807F001FC07F001F C07F001FC07F001FC0FF001FE0FF001FE0FF001FE0FF001FE0FF001FE0FF001FE0FF001FE0FF00 1FE0FF001FE0FF001FE0FF001FE0FF001FE0FF001FE0FF001FE0FF001FE07F001FC07F001FC07F 001FC07F001FC03F001F803F001F801F803F001F803F000FC07E0007E0FC0001FFF000003F8000> 27 39 -3 0 34] 48 @dc [ 45 41 -3 0 53] 68 @dc [<7FFF1FFFC07FFF1FFFC07FFF1FFFC007F001FC0007F001FC0007F001FC0007F001FC0007F001FC 0007F001FC0007F001FC0007F001FC0007F001FC0007F001FC0007F001FC0007F001FC0007F001 FC0007F001FC0007F001FC0007F001FC0007F001FC0007F001FC0007F001FC0007F001FC0007F0 01FC00FFFFFFFC00FFFFFFFC00FFFFFFFC0007F001FC0007F001FC0007F001FC0007F001FC0007 F001FC0007F001FC0007F001FC0007F001FC0007F001FC0003F801FC0001F801FC0000FC01FC00 007F81FC00001FFFFC000001FFFC00> 34 42 -1 0 38] 13 @dc [<01FC03FC0FFF0FFC3F839FFC7F00DF807E007F80FE003F80FE003F80FE003F80FE003F807F003F 803F003F803F803F800FE03F8007FC3F8000FFFF80000FFF8000003F8000003F8000003F800700 3F800F803F801FC03F001FC07E001FC07E000F81F80007FFF00001FF8000> 30 27 -2 0 33] 97 @dc [<001F8000FFC001F86003F87003F03807F03807F03807F03807F03807F03807F03807F00007F000 07F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007F000FFFFF0FFFFF0 1FFFF007F00003F00003F00001F00000F00000F00000F000007000007000007000007000> 21 38 -1 0 27] 116 @dc [ 15 43 -3 0 20] 105 @dc [<003FE00001FFFC0007F07F000FC01F801F800FC03F800FE03F800FE07F0007F07F0007F0FF0007 F8FF0007F8FF0007F8FF0007F8FF0007F8FF0007F8FF0007F8FF0007F87F0007F07F0007F07F00 07F03F0007E03F800FE01F800FC00FC01F8003F07E0001FFFC00003FE000> 29 27 -2 0 34] 111 @dc [ 33 42 -3 0 38] 104 @dc [<007FF00003FFFE000FC01F801F0007C03C0001E07C0001F0F80000F8F80000F8F80000F8F80000 F87C0001F83E0007F01FFFFFF007FFFFE00FFFFFC01FFFFF801FFFFF003FFFF8003E0000003C00 0000380000003800000018FF80001FFFE0000FC1F8001F80FC001F007C003F007E007F007F007F 007F007F007F007F007F007F007F007F007F003F007E101F007C381F80FC7C0FC1FE7C03FFE7F8 00FF81F0> 30 40 -2 13 34] 103 @dc [ 15 42 -3 0 20] 108 @dc [ 25 27 -2 0 31] 122 @dc [<003FC3FF8000FFF3FF8003F03BFF8007C00FF8000F8007F8001F8003F8003F8003F8007F0003F8 007F0003F8007F0003F800FF0003F800FF0003F800FF0003F800FF0003F800FF0003F800FF0003 F800FF0003F8007F0003F8007F0003F8007F0003F8003F8003F8001F8003F8000FC007F80007E0 0FF80003F03FF80000FFFBF800001FE3F800000003F800000003F800000003F800000003F80000 0003F800000003F800000003F800000003F800000003F800000003F800000003F800000003F800 00003FF80000003FF80000003FF800> 33 42 -2 0 38] 100 @dc cmmi8.300 @sf [<300F00300880181880181840180C40180C000C0C000C06000C06008E060046020047020044C600 383C00> 18 14 -1 0 21] 110 @dc cmsy10.329 @sf [<400000C000006000006000003000003000001800001800000C00000C0000060000060000060000 03000003000001800001800000C00000C000006000006000003000003000001800001800000C00 000C000006000006000003000003000001800001800001800000C00000C0000060000060000030 00003000001800001800000C00000C> 22 44 -6 11 0] 54 @dc cmmi10.329 @sf [<01E0000618000E04000E04000C02000E01000E01000E00800E00800E0080070040070040070040 83804043806041C0E021C1E02183E01183C00F0180> 19 20 -2 0 22] 118 @dc [ 16 45 -3 11 23] 61 @dc [<03E1E00613100E0F100C07080C07080E07080E03840E03800E03800E03800701C00701C00701C0 8381C04380E041C0E021C0E02180E01180700F0060> 22 20 -2 0 26] 117 @dc cmr10.329 @sf [ 25 31 -2 0 30] 70 @dc cmmi10.329 @sf [<07C018383004700270017000F000F000F000F0007C007BF0780C38023C011C010E01070101C200 7C> 16 20 -2 0 21] 101 @dc cmr8.300 @sf [<7FF007000700070007000700070007000700070007000700070007000700070007000700FF0007 000300> 12 21 -2 0 18] 49 @dc cmsy8.300 @sf [ 20 2 -3 -7 27] 0 @dc cmex10.300 @sf [ 22 75 -12 74 36] 48 @dc [<00000C0000180000380000300000600000E00000C00001C0000380000380000700000700000E00 000E00001C00001C0000380000380000780000700000F00000F00000E00001E00001E00003C000 03C00003C00003C0000780000780000780000F80000F00000F00000F00001F00001F00001E0000 1E00001E00003E00003E00003E00003E00003C00003C00003C00007C00007C00007C00007C0000 7C00007C00007C00007C0000780000780000F80000F80000F80000F80000F80000F80000F80000 F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000> 22 75 -12 72 36] 64 @dc 1.000000 /cmr10.432 @newfont cmr10.432 @sf [<007F000001C1C0000780F0000F0078000E0038001C001C003C001E003C001E003C001E0078000F 0078000F0078000F0078000F00F8000F80F8000F80F8000F80F8000F80F8000F80F8000F80F800 0F80F8000F80F8000F80F8000F80F8000F80F8000F80F8000F80F8000F80F8000F8078000F0078 000F0078000F0078000F003C001E003C001E003C001E001C001C000E0038000F0078000780F000 01C1C000007F0000> 25 41 -2 1 30] 48 @dc cmmi10.329 @sf [<07C01C1838323004617003E07000E0F000E0F000E0F000F0F000F0F000E87800E47800E47800E2 3C00E21C00E21E00C10E01C107018101C300007C00> 24 20 -2 0 29] 11 @dc cmex10.300 @sf [<00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C 00007C00007C00007C00007C0000780000780000F80000F80000F80000F80000F80000F80000F8 0000F80000F00000F00000F00001F00001F00001F00001F00001E00001E00001E00003E00003E0 0003C00003C00003C00007C0000780000780000780000F00000F00000F00000F00001E00001E00 001C00003C00003C0000380000780000700000700000E00000E00001C00001C000038000038000 0700000700000E00000C00001C0000180000300000700000600000C00000> 22 75 -1 74 36] 49 @dc [ 22 75 -1 72 36] 65 @dc 40 @bop1 cmr10.329 @sf 1919 -77 p m (40) s 74 67 p m (A) 15 (p) 1 (ossible) 17 (stopping) 16 (criterion) 16 (for) 15 (this) 15 (sc) 0 (heme) 15 (is) 15 (the) 16 (condition) ks cmsy10.329 @sf 695 169 p m (k) s cmmi10.329 @sf m (H) 4 (x) ks cmmi8.300 @sf 786 176 p m (i) s cmsy10.329 @sf 809 169 p m (\000) s cmmi10.329 @sf 10 r m (\025) s cmmi8.300 @sf 881 176 p m (i) s cmmi10.329 @sf 895 169 p m (U) 5 (x) ks cmmi8.300 @sf 957 176 p m (i) s cmsy10.329 @sf 971 169 p m (k) s 695 189 p 300 2 ru 801 230 p m (k) s cmmi10.329 @sf m (x) s cmmi8.300 @sf 850 237 p m (i) s cmsy10.329 @sf 864 230 p m (k) s 1011 199 p m (\024) s cmmi10.329 @sf 13 r m (f) s cmr10.329 @sf 5 r m (\() s cmmi10.329 @sf m (n) s cmr10.329 @sf m (\)) s cmsy10.329 @sf m (k) s cmmi10.329 @sf m (H) s cmsy10.329 @sf 4 r m (kk) s cmmi10.329 @sf m (U) s cmsy10.329 @sf 5 r m (k) s cmmi10.329 @sf m (\017;) s cmr10.329 @sf 74 331 p m (where) s cmmi10.329 @sf 14 r m (f) s cmr10.329 @sf 5 r m (\() s cmmi10.329 @sf m (n) s cmr10.329 @sf m (\)) 13 (is) 14 (a) 13 (mo) 1 (dest) 13 (function) 14 (of) ks cmmi10.329 @sf 13 r m (n) s cmr10.329 @sf m (.) 20 (It) 13 (is) 14 (easy) 13 (to) 13 (see) 13 (that) 13 (starting) 13 (from) 12 (t) 0 (w) -1 (o) 11 (complex) 14 (conjugate) ks 74 430 p m (initial) 24 (guesses) 21 (the) 22 (algorithm) 22 (will) 23 (compute) 22 (complex) 22 (conjugate) 21 (corrections,) 23 (therefore) 21 (allo) 0 (wing) ks 74 530 p m (similar) 17 (sa) 0 (vings) 14 (to) 14 (those) 15 (in) 16 (the) 15 (case) ks cmmi10.329 @sf 16 r m (U) s cmr10.329 @sf 17 r m (=) s cmmi10.329 @sf 13 r m (I) s cmr10.329 @sf 4 r m (.) s cmbx10.432 @sf 74 712 p m (10) s 212 712 p m (De\015ation) 22 (in) 22 (the) 22 (generalized) 21 (case) ks cmr10.329 @sf 74 899 p m (The) 13 (metho) 1 (d) 12 (of) 12 (de\015ation) 13 (presen) 0 (ted) 12 (in) 13 (section) 13 (3.1) 12 (generalizes) 14 (to) 11 (this) 13 (case) 13 (in) 13 (the) 12 (follo) 0 (wing) 12 (manner.) ks 74 998 p m (Let) s cmmi10.329 @sf 16 r m (H) 4 (x) ks cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 14 r m (\025U) 5 (x) ks cmr10.329 @sf 16 r m (\(of) 15 (course,) 15 (in) 17 (practice) 16 (w) 0 (e) 15 (only) 16 (ha) 0 (v) 0 (e) 14 (an) 15 (appro) 0 (ximate) 15 (eigenpair\).) 23 (Then) 16 (it) 16 (is) 16 (true) ks 74 1098 p m (that) 16 (if) ks cmmi10.329 @sf 16 r m (w) s cmr10.329 @sf 15 r m (=) s cmmi10.329 @sf 15 r m (U) 5 (x) ks cmr10.329 @sf 16 r m (then) s cmmi10.329 @sf 17 r m (w) s cmmi8.300 @sf 530 1105 p m (n) s cmsy10.329 @sf 567 1098 p m (6) s cmr10.329 @sf m (=) 15 (0:) 21 (Indeed,) 18 (if) ks cmmi10.329 @sf 17 r m (w) s cmmi8.300 @sf 912 1105 p m (n) s cmr10.329 @sf 949 1098 p m (=) 15 (0,) 16 (then) 16 (it) 17 (can) 16 (b) 1 (e) 17 (sho) 0 (wn) 15 (that) ks cmmi10.329 @sf 15 r m (w) s cmr10.329 @sf 17 r m (is) 17 (zero) 16 (using) 17 (the) ks 74 1197 p m (fact) 15 (that) ks cmmi10.329 @sf 14 r m (H) s cmr10.329 @sf 19 r m (is) 16 (unreduced.) ks cmmi10.329 @sf 21 r m (U) s cmr10.329 @sf 20 r m (b) 1 (eing) 17 (non) 15 (singular) 16 (implies) 17 (that) ks cmmi10.329 @sf 15 r m (x) s cmr10.329 @sf 15 r m (is) 16 (zero) 15 (whic) 0 (h) 15 (is) 16 (not) 14 (true.) ks 74 1339 p m (Let) s cmex10.300 @sf 843 1366 p save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pc restore cmsy10.329 @sf 897 1411 p m (\000) s cmmi10.329 @sf m (v) s cmr10.329 @sf 915 1466 p m (1) s cmex10.300 @sf 977 1366 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1022 1438 p m (=) s cmmi10.329 @sf 13 r m (w) 1 (=w) ks cmmi8.300 @sf 1160 1445 p m (n) s cmmi10.329 @sf 1183 1438 p m (;) s cmr10.329 @sf 74 1558 p m (and) s cmmi10.329 @sf 900 1658 p m (u) s cmr10.329 @sf 13 r m (=) s cmex10.300 @sf 987 1586 p save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pc restore cmmi10.329 @sf 1041 1631 p m (v) s cmr10.329 @sf 1041 1686 p m (1) s cmex10.300 @sf 1085 1586 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1125 1658 p m (:) s cmr10.329 @sf 74 1777 p m (W) -3 (e) 13 (kno) 0 (w) 13 (that) ks cmmi10.329 @sf 13 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) 1 (;) 8 (U) ks cmr10.329 @sf 5 r m (\)) 12 (is) 15 (the) 14 (same) 14 (as) ks cmmi10.329 @sf 14 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (N) 5 (H) 4 (M) 2 (;) 8 (N) 4 (U) 5 (M) ks cmr10.329 @sf 5 r m (\)) 12 (for) 13 (an) 0 (y) 13 (non-singular) ks cmmi10.329 @sf 16 r m (M) s cmr10.329 @sf 19 r m (and) s cmmi10.329 @sf 14 r m (N) s cmr10.329 @sf 5 r m (.) 19 (F) -3 (or) 12 (our) ks 74 1877 p m (purp) 1 (oses,) 16 (w) 0 (e) 13 (tak) 0 (e) ks cmmi10.329 @sf 813 1977 p m (M) s cmr10.329 @sf 17 r m (=) 13 ([) ks cmmi10.329 @sf m (e) s cmr8.300 @sf 956 1984 p m (1) s cmmi10.329 @sf 976 1977 p m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 1057 1977 p m (;) 8 (e) ks cmmi8.300 @sf 1099 1984 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1167 1977 p m (;) 8 (x) ks cmr10.329 @sf m (]) s 74 2096 p m (and) s cmmi10.329 @sf 810 2196 p m (N) s cmr10.329 @sf 17 r m (=) 13 ([) ks cmmi10.329 @sf m (e) s cmr8.300 @sf 946 2203 p m (1) s cmmi10.329 @sf 966 2196 p m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 7 (.) ks cmmi10.329 @sf 1047 2196 p m (;) 8 (e) ks cmmi8.300 @sf 1089 2203 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1157 2196 p m (;) 8 (u) ks cmr10.329 @sf m (]) s cmmi10.329 @sf m (:) s cmr10.329 @sf 74 2316 p m (Then) 16 (it) 15 (is) 16 (easy) 15 (to) 15 (v) 0 (erify) 14 (that) 14 (w) 0 (e) 14 (ha) 0 (v) 0 (e) ks cmmi10.329 @sf 459 2448 p m (N) 5 (H) 4 (M) ks cmr10.329 @sf 16 r m (=) s cmex10.300 @sf 651 2363 p m (0) s 651 2438 p m (@) s cmmi10.329 @sf 723 2401 p m (H) s cmsy8.300 @sf 765 2386 p m (0) s 811 2430 p 2 69 ru cmr10.329 @sf 852 2401 p m (0) s 688 2432 p 227 2 ru 811 2487 p 2 57 ru cmr10.432 @sf 728 2502 p m (0) s cmmi10.329 @sf 773 2466 p m (\013) s 811 2511 p 2 66 ru 850 2494 p m (\015) s cmex10.300 @sf 914 2363 p m (1) s 914 2438 p m (A) s cmmi10.329 @sf 958 2448 p m (;) 33 (N) 5 (U) 5 (M) ks cmr10.329 @sf 17 r m (=) s cmex10.300 @sf 1191 2363 p m (0) s 1191 2438 p m (@) s cmmi10.329 @sf 1258 2406 p m (U) s cmsy8.300 @sf 1294 2391 p m (0) s 1336 2435 p 2 69 ru cmr10.329 @sf 1377 2406 p m (0) s 1227 2437 p 213 2 ru 1336 2492 p 2 57 ru cmr10.432 @sf 1267 2498 p m (0) s 1336 2507 p 2 57 ru cmmi10.329 @sf 1378 2490 p m (\016) s cmex10.300 @sf 1440 2363 p m (1) s 1440 2438 p m (A) s cmmi10.329 @sf 1484 2448 p m (;) s cmr10.329 @sf 1883 2448 p m (\(16\)) s 74 2579 p m (where) s cmmi10.329 @sf 16 r m (H) s cmsy8.300 @sf 248 2564 p m (0) s cmr10.329 @sf 274 2579 p m (is) 16 (upp) 1 (er-Hessen) 0 (b) 1 (erg,) ks cmmi10.329 @sf 15 r m (U) s cmsy8.300 @sf 735 2564 p m (0) s cmr10.329 @sf 762 2579 p m (is) 16 (upp) 1 (er-triangular) 16 (and) ks cmmi10.329 @sf 915 2681 p m (\015) s 915 2701 p 27 2 ru 917 2742 p m (\016) s cmr10.329 @sf 958 2711 p m (=) s cmmi10.329 @sf 13 r m (\025:) s cmr10.329 @sf 1883 2711 p m (\(17\)) s @eop 39 @bop0 cmr8.300 @sf [<07C01C703018701C600C600CE00EE00EE00EE00EE00EE00EE00EE00EE00E600C600C701C301818 3007C0> 15 21 -1 0 18] 48 @dc cmmi8.300 @sf [ 15 23 -2 0 18] 107 @dc cmr8.300 @sf [<003000003000003000003000003000003000003000003000003000003000003000FFFFFCFFFFFC 003000003000003000003000003000003000003000003000003000003000003000> 22 24 -2 4 27] 43 @dc cmmi8.300 @sf [<7FFC0003C00001C00001C00001C00001C00000E00000E00000E00000E000007000007000007000 007000003800003800803804403804401C04601C04201C04381C0E1FFFFE> 23 23 -1 0 21] 84 @dc cmr10.329 @sf [<80E063F03F181C04> 14 4 -4 -26 23] 126 @dc cmsy10.329 @sf [<003FF800FFF803C0000700000C0000180000300000300000600000600000C00000C00000C00000 FFFFF8FFFFF8C00000C00000C000006000006000003000003000001800000C000007000003C000 00FFF8003FF8> 21 28 -4 3 30] 50 @dc cmmi10.329 @sf [ 26 31 -2 0 31] 76 @dc cmmi8.300 @sf [<3F00C180C0C0E0606060006003E00FC01E003800187018700C2007C0> 12 14 -2 0 16] 115 @dc cmmi10.329 @sf [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @dc [ 24 30 -1 10 27] 22 @dc [<1800003800001C00001C00001C00001C00000E00000E00000E00000E0000070000070000070000 87000043830043878043C78023C3802321001E1E00> 17 20 -2 0 21] 114 @dc cmsy10.329 @sf [<0100000000020000000002000000000400000000080000000010000000002000000000FFFFFFFF F8FFFFFFFFF8200000000010000000000800000000040000000002000000000200000000010000 0000> 37 16 -4 -3 45] 32 @dc cmr10.329 @sf [<000600000006000000060000000600000006000000060000000600000006000000060000000600 000006000000060000000600000006000000060000FFFFFFF0FFFFFFF000060000000600000006 000000060000000600000006000000060000000600000006000000060000000600000006000000 0600000006000000060000> 28 32 -3 5 35] 43 @dc [<40202010101008080878F8F8F0700000000000000000000070F8F8F870> 5 29 -4 9 13] 59 @dc 39 @bop1 cmr10.329 @sf 1919 -77 p m (39) s 74 67 p m (Without) 17 (loss) 18 (of) 17 (generalit) 0 (y) -3 (,) 16 (w) 0 (e) 16 (can) 18 (assume) ks cmmi10.329 @sf 17 r m (H) s cmr10.329 @sf 21 r m (to) 17 (b) 1 (e) 18 (unreduced) 19 (and) ks cmmi10.329 @sf 17 r m (U) s cmr10.329 @sf 22 r m (to) 17 (b) 1 (e) 18 (non-singular) 19 (since) ks 74 167 p m (otherwise) 21 (the) 20 (problem) 21 (reduces) 21 (to) 20 (a) 20 (smaller) 21 (problem.) 36 (Then) 21 (our) 20 (algorithm) 20 (generalizes) 22 (easily) -3 (.) ks 74 266 p m (Indeed,) 17 (set) ks cmmi10.329 @sf 823 366 p m (H) s cmr8.300 @sf 861 373 p m (0) s cmr10.329 @sf 893 366 p m (=) s cmmi10.329 @sf 13 r m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (\013) 0 (e) ks cmmi8.300 @sf 1088 373 p m (k) s cmr8.300 @sf 1 r m (+1) s cmmi10.329 @sf 1154 366 p m (e) s cmmi8.300 @sf 1175 348 p m (T) s 1175 377 p m (k) s cmmi10.329 @sf 1203 366 p m (;) s cmr10.329 @sf 74 486 p m (and) 16 (consider) 16 (solutions) 16 (of) 14 (\(or) 15 (appro) 0 (ximations) 14 (of) 15 (these\)) ks cmmi10.329 @sf 855 619 p m (H) s cmr8.300 @sf 893 626 p m (0) s cmmi10.329 @sf 913 619 p m (x) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (\025U) 5 (x;) ks cmr10.329 @sf 1883 619 p m (\(15\)) s 74 751 p m (as) 11 (initial) 14 (appro) 0 (ximations) 10 (to) 11 (the) 12 (sough) 0 (t) 10 (eigenpairs.) 20 (More) 10 (precisely) -3 (,) 13 (solving) 13 (\(15\)) 10 (reduces) 12 (to) 11 (solving) ks cmmi10.329 @sf 667 884 p m (H) s cmr8.300 @sf 705 891 p m (11) s cmmi10.329 @sf 743 884 p m (x) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (\025U) s cmr8.300 @sf 887 891 p m (11) s cmmi10.329 @sf 924 884 p m (x) 25 (and) 26 (H) ks cmr8.300 @sf 1114 891 p m (22) s cmmi10.329 @sf 1151 884 p m (x) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (\025U) s cmr8.300 @sf 1295 891 p m (22) s cmmi10.329 @sf 1332 884 p m (x:) s cmr10.329 @sf 74 1017 p m (Let's) 20 (denote) 21 (these) 20 (solutions) 21 (b) 0 (y) 19 (\() 3 (~) ks cmmi10.329 @sf 745 1017 p m (x) s cmr8.300 @sf 771 1024 p m (1) s cmmi10.329 @sf 790 1017 p m (;) 8 (\025) ks cmr8.300 @sf 838 1024 p m (1) s cmr10.329 @sf 857 1017 p m (\)) s cmmi10.329 @sf m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 7 (.) ks cmmi10.329 @sf 955 1017 p m (;) s cmr10.329 @sf 8 r m (\() 3 (~) ks cmmi10.329 @sf 994 1017 p m (x) s cmmi8.300 @sf 1020 1024 p m (n) s cmmi10.329 @sf 1043 1017 p m (;) 8 (\025) ks cmmi8.300 @sf 1091 1024 p m (n) s cmr10.329 @sf 1113 1017 p m (\)) 20 (\(w) 0 (e) 18 (ha) 0 (v) 0 (e) ks cmmi10.329 @sf 18 r m (n) s cmr10.329 @sf 21 r m (solutions) 20 (b) 1 (ecause) 22 (of) 19 (our) 20 (as-) ks 74 1116 p m (sumption) 25 (that) ks cmmi10.329 @sf 23 r m (U) s cmr10.329 @sf 29 r m (is) 25 (non-singular\).) 48 (These) 25 (can) 24 (b) 1 (e) 25 (used) 24 (to) 24 (construct) 24 (initial) 26 (appro) 0 (ximations) ks 74 1216 p m (\() s cmmi10.329 @sf m (x) s cmr8.300 @sf 118 1223 p m (1) s cmmi10.329 @sf 138 1216 p m (;) 8 (\025) ks cmr8.300 @sf 186 1223 p m (1) s cmr10.329 @sf 204 1216 p m (\)) s cmmi10.329 @sf m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 7 (.) ks cmmi10.329 @sf 302 1216 p m (;) s cmr10.329 @sf 8 r m (\() s cmmi10.329 @sf m (x) s cmmi8.300 @sf 367 1223 p m (n) s cmmi10.329 @sf 390 1216 p m (;) 8 (\025) ks cmmi8.300 @sf 438 1223 p m (n) s cmr10.329 @sf 460 1216 p m (\)) 22 (to) 22 (the) 23 (eigenpairs) 23 (of) 22 (the) 23 (original) 24 (generalized) 24 (eigenproblem) 24 (in) 23 (m) 0 (uc) 0 (h) 21 (the) ks 74 1316 p m (same) 15 (w) 0 (a) -1 (y) 13 (w) 0 (e) 14 (did) 16 (in) 16 (the) 16 (case) ks cmmi10.329 @sf 15 r m (U) s cmr10.329 @sf 18 r m (=) s cmmi10.329 @sf 13 r m (I) s cmr10.329 @sf 4 r m (.) 19 (More) 14 (precisely) -3 (,) 16 (w) 0 (e) 14 (tak) 0 (e) ks 789 1448 p m (\() s cmmi10.329 @sf m (x) s cmmi8.300 @sf 833 1455 p m (i) s cmmi10.329 @sf 847 1448 p m (;) 8 (\025) ks cmmi8.300 @sf 895 1455 p m (i) s cmr10.329 @sf 907 1448 p m (\)) 13 (=) 13 (\() ks cmex10.300 @sf 1004 1376 p save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pc restore cmr10.329 @sf 1060 1421 p m (~) s cmmi10.329 @sf 1057 1421 p m (x) s cmmi8.300 @sf 1083 1428 p m (i) s cmr10.329 @sf 1066 1476 p m (0) s cmex10.300 @sf 1118 1376 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1158 1448 p m (;) 8 (\025) ks cmmi8.300 @sf 1206 1455 p m (i) s cmr10.329 @sf 1219 1448 p m (\)) s cmmi10.329 @sf m (;) s cmr10.329 @sf 74 1581 p m (if) s cmmi10.329 @sf 16 r m (\025) s cmmi8.300 @sf 143 1588 p m (i) s cmsy10.329 @sf 169 1581 p m (2) s cmmi10.329 @sf 13 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmr8.300 @sf 296 1588 p m (11) s cmmi10.329 @sf 332 1581 p m (;) 8 (U) ks cmr8.300 @sf 384 1588 p m (11) s cmr10.329 @sf 421 1581 p m (\)) 15 (and) ks 789 1680 p m (\() s cmmi10.329 @sf m (x) s cmmi8.300 @sf 833 1687 p m (i) s cmmi10.329 @sf 847 1680 p m (;) 8 (\025) ks cmmi8.300 @sf 895 1687 p m (i) s cmr10.329 @sf 907 1680 p m (\)) 13 (=) 13 (\() ks cmex10.300 @sf 1004 1608 p save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pc restore cmr10.329 @sf 1066 1653 p m (0) s 1060 1708 p m (~) s cmmi10.329 @sf 1057 1708 p m (x) s cmmi8.300 @sf 1083 1715 p m (i) s cmex10.300 @sf 1118 1608 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1158 1680 p m (;) 8 (\025) ks cmmi8.300 @sf 1206 1687 p m (i) s cmr10.329 @sf 1219 1680 p m (\)) s cmmi10.329 @sf m (;) s cmr10.329 @sf 74 1801 p m (if) s cmmi10.329 @sf 16 r m (\025) s cmmi8.300 @sf 143 1808 p m (i) s cmsy10.329 @sf 169 1801 p m (2) s cmmi10.329 @sf 13 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmr8.300 @sf 296 1808 p m (22) s cmmi10.329 @sf 332 1801 p m (;) 8 (U) ks cmr8.300 @sf 384 1808 p m (22) s cmr10.329 @sf 421 1801 p m (\)) 15 (\(an) 15 (appropriate) 15 (n) 0 (um) 0 (b) 1 (er) 13 (of) 15 (zeros) 15 (in) 16 (eac) 0 (h) 14 (case\).) ks 124 1942 p m (Finally) 24 (solving) 23 (the) 22 (generalized) 24 (eigen) 0 (v) -2 (alue) 22 (problem) 23 (\(14\)) 21 (ab) 1 (o) 0 (v) -1 (e) 20 (is) 23 (the) 22 (same) 22 (as) 22 (solving) 23 (the) ks 74 2041 p m (problem) s cmex10.300 @sf 832 2069 p save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pc restore cmmi10.329 @sf 886 2114 p m (H) 4 (x) ks cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (\025U) 5 (x) ks cmr10.329 @sf 12 r m (=) 13 (0) ks cmmi10.329 @sf 886 2169 p m (L) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (x) s cmr10.329 @sf m (\)) 12 (=) 13 (1) ks 74 2261 p m (where) s cmmi10.329 @sf 17 r m (L) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (x) s cmr10.329 @sf m (\)) 16 (is) 17 (a) 16 (scalar) 17 (equation,) 17 (whic) 0 (h) 16 (w) 0 (e) 16 (tak) 0 (e) 14 (to) 16 (b) 1 (e) 18 (a) 16 (normalizing) 18 (condition:) ks cmmi10.329 @sf 24 r m (e) s cmmi8.300 @sf 1682 2246 p m (T) s 1682 2272 p m (s) s cmmi10.329 @sf 1710 2261 p m (x) s cmr10.329 @sf 15 r m (=) 15 (1.) 24 (Then) ks 74 2361 p m (for) 15 (eac) 0 (h) 14 (initial) 17 (eigenpair) 17 (\() ks cmmi10.329 @sf m (x) s cmmi8.300 @sf 616 2368 p m (i) s cmmi10.329 @sf 630 2361 p m (;) 8 (\025) ks cmmi8.300 @sf 678 2368 p m (i) s cmr10.329 @sf 690 2361 p m (\),) 15 (successiv) 0 (e) 15 (corrections) 16 (can) 15 (b) 1 (e) 16 (computed) 15 (via) ks cmex10.300 @sf 335 2421 p save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pc restore cmmi10.329 @sf 389 2466 p m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 10 r m (\025) s cmmi8.300 @sf 513 2473 p m (i) s cmmi10.329 @sf 527 2466 p m (U) s cmsy10.329 @sf 604 2466 p m (\000) s cmmi10.329 @sf m (U) 5 (x) ks cmmi8.300 @sf 701 2473 p m (i) s cmmi10.329 @sf 452 2522 p m (e) s cmmi8.300 @sf 473 2507 p m (T) s 473 2533 p m (s) s cmr10.329 @sf 649 2522 p m (0) s cmex10.300 @sf 736 2421 p save [ 21 124 -1 122 33] 33 @pc restore 777 2421 p save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pc restore cmmi10.329 @sf 832 2466 p m (y) s 830 2522 p m (\026) s cmex10.300 @sf 879 2421 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 924 2493 p m (=) s cmex10.300 @sf 972 2421 p save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pc restore cmmi10.329 @sf 1026 2466 p m (r) s cmmi8.300 @sf 1047 2473 p m (i) s cmr10.329 @sf 1032 2522 p m (0) s cmex10.300 @sf 1081 2421 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1121 2493 p m (;) 33 (\025) ks cmmi8.300 @sf 1194 2500 p m (i) s cmsy10.329 @sf 1220 2493 p m ( ) s cmmi10.329 @sf 13 r m (\025) s cmmi8.300 @sf 1305 2500 p m (i) s cmr10.329 @sf 1329 2493 p m (+) s cmmi10.329 @sf 10 r m (\026) s cmr10.329 @sf 26 r m (;) s cmmi10.329 @sf 32 r m (x) s cmmi8.300 @sf 1498 2500 p m (i) s cmsy10.329 @sf 1525 2493 p m ( ) s cmmi10.329 @sf 13 r m (x) s cmmi8.300 @sf 1609 2500 p m (i) s cmr10.329 @sf 1633 2493 p m (+) s cmmi10.329 @sf 11 r m (y) s cmr10.329 @sf 74 2626 p m (where) s cmmi10.329 @sf 838 2726 p m (r) s cmmi8.300 @sf 859 2733 p m (i) s cmr10.329 @sf 886 2726 p m (=) s cmmi10.329 @sf 13 r m (\025) s cmmi8.300 @sf 961 2733 p m (i) s cmmi10.329 @sf 974 2726 p m (U) 5 (x) ks cmmi8.300 @sf 1036 2733 p m (i) s cmsy10.329 @sf 1060 2726 p m (\000) s cmmi10.329 @sf 11 r m (H) 4 (x) ks cmmi8.300 @sf 1174 2733 p m (i) s cmmi10.329 @sf 1187 2726 p m (:) s @eop 38 @bop0 cmr10.329 @sf [ 16 45 -3 11 23] 47 @dc [<0000078000000FC000001FE000001FE000003FF0000038700000383000003010001FB01000F0F0 1001E0380007A03E000F204F000E2047001E1087803C0F03C03C0003C07C0003E0780001E07800 01E0F80001F0F80001F0F80001F0F80001F0F80001F0F80001F0F80001F0F80001F0F80001F078 0001E07C0003E07C0003E03C0003C03C0003C01E0007800E0007000F000F0007801E0001C03800 00F0F000001F8000> 28 41 -3 9 35] 81 @dc [<07E00F801C183860380670307801C0107003C008F003C008F0074000F00E2000F01E1000701C10 0070380800307808001870040008F0020004E0020003E0010001C0010001C00080038001C003C0 03E003A00FFC031000000708000007080000070400000704000007020000070200000702000007 02000003020000018400000084000000780000> 30 34 -2 1 35] 38 @dc [<7FE3FE3FF007007007000700700700070070070007007007000700700700070070070007007007 000700700700070070070007007007000700700700070070070007007007000700700700070070 0700070070070007007007000700700700FFFFFFFF000700700000070070000007007000000700 700000070070000007007000000700F00F000300F00F000380F80F0001C07C060000F04F040000 1F81F800> 36 32 0 0 38] 14 @dc cmbx10.432 @sf [<01FE000007FF80000FFFE0001E03F0001F01F8003F807C003F807E003F803F003F803F001F003F 8000003F8000001FC000001FC000001FC000001FE0007E1FE003FF9FE007C1DFE00F807FE01F80 7FE03F003FE07F003FE07F001FE0FF001FE0FF001FE0FF001FE0FF001FE0FF001FC0FF001FC0FF 001FC0FF001F807F001F807F003F003F803F001F807E000FE0FC0007FFF80001FFF000007F8000> 27 39 -3 0 34] 57 @dc [<0001C000000003E000000003E000000007F000000007F00000000FF80000000FF80000000FF800 00001FDC0000001FDC0000003FDE0000003F8E0000007F8F0000007F070000007F07000000FE03 800000FE03800001FC01C00001FC01C00003FC01E00003F800E00007F800F00007F000700007F0 007000FFFE03FF80FFFE03FF80FFFE03FF80> 33 27 -1 0 36] 118 @dc [<003FC3FF8001FFF3FF8003F03BFF8007E00FF80007E007F8000FE007F8000FE003F8000FE003F8 000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003 F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE0 03F800FFE03FF800FFE03FF800FFE03FF800> 33 27 -3 0 38] 117 @dc [ 33 39 -2 12 38] 112 @dc [<0E01FC00000F07FF80000F9E07E0000FF803F0000FF001F8000FE000FC000FE000FE000FE0007F 000FE0007F000FE0007F000FE0007F800FE0007F800FE0007F800FE0007F800FE0007F800FE000 7F800FE0007F800FE0007F000FE0007F000FE0007F000FE000FE000FE000FC000FF000F8000FF8 01F0000FFE07E0000FE7FF80000FE1FE00000FE00000000FE00000000FE00000000FE00000000F E00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE0000000 FFE0000000FFE0000000FFE0000000> 33 42 -2 0 38] 98 @dc [ 53 27 -3 0 60] 109 @dc 1.000000 /cmbx12.300 @newfont cmbx12.300 @sf [<03F8000FFE001C0F801E03C03F01E03F00F03F00F83F00F81E007C00007C00007C00207E07FC7E 0FFE7E1E037E3E01FE7C00FE7C00FEFC007EFC007EFC007EFC007EFC007CFC007CFC007C7C0078 7C00F83E00F01E01F00F83E007FF8001FE00> 23 32 -2 0 28] 57 @dc [<387CFEFEFE7C38> 7 7 -4 0 16] 46 @dc [<7FFFE07FFFE001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F800 01F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F800 01F800FFF800FFF80001F800007800001800> 19 32 -4 0 28] 49 @dc [ 34 34 -2 0 40] 66 @dc [<07E03F1FF87F7E0CF87E02F0FC01F0FC01F0FC01F0FC01F07E01F03F01F01FC1F003FDF0003FF0 0001F00001F01E01F03F01F03F01E03F03E03F07C01FFF8007FC00> 24 22 -2 0 27] 97 @dc [ 17 22 -2 0 22] 115 @dc [ 11 36 -2 0 16] 105 @dc [<00FE0007FF800FC0E01F00603E00307E00007E00007C0000FC0000FC0000FC0000FC0000FC0000 FC00007C00007C01E07E03F03E03F01F03F00F83F007FFE000FF80> 20 22 -2 0 25] 99 @dc [ 11 35 -2 0 16] 108 @dc [<01FF000FFFE03F01F87C007C78003CF0001EF0001EF0001EF0001E70003E3800FC1FFFFC0FFFF8 1FFFF03FFF8038000030000030000013FC001FFF001F0F803E07C03C03C07C03E07C03E07C03E0 7C03E07C03E03C03C03E07CF1F0F8F0FFF7F03FC1E> 24 33 -2 11 28] 103 @dc [<00FE0007FFC00F83E01F01F03E00F87C007C7C007CFC007EFC007EFC007EFC007EFC007EFC007E FC007E7C007C7C007C7C007C3E00F81E00F00F83E007FFC000FE00> 23 22 -2 0 28] 111 @dc [ 19 22 -2 0 23] 114 @dc [<00F80003FE0007C3000F83000F81800F81800F81800F81800F81800F80000F80000F80000F8000 0F80000F80000F80000F80000F80000F80000F8000FFFF00FFFF003F80000F8000078000078000 038000038000018000018000018000018000> 17 32 -1 0 22] 116 @dc [ 26 35 -2 0 31] 104 @dc [ 43 22 -2 0 48] 109 @dc 38 @bop1 cmr10.329 @sf 1919 -77 p m (38) s 74 67 p m (The) 16 (follo) 0 (wing) 15 (are) 14 (some) 15 (results) 16 (from) 14 (the) 16 (In) 0 (tel) 15 (iPSC/860) 14 (implemen) 0 (tation.) ks 508 201 p m (Order) s 648 218 p 2 57 ru 674 201 p m (No.) 20 (of) 14 (pro) 1 (cs.) ks 957 218 p 2 57 ru 983 201 p m (Lev) 0 (els) ks 1129 218 p 2 57 ru 1155 201 p m (Ratio) 15 (HQR2/D&C) ks 483 220 p 1073 2 ru 532 258 p m (100) s 648 275 p 2 57 ru 792 258 p m (1) s 957 275 p 2 57 ru 1033 258 p m (1) s 1129 275 p 2 57 ru 1302 258 p m (1.15) s 648 331 p 2 57 ru 792 314 p m (2) s 957 331 p 2 57 ru 1033 314 p m (1) s 1129 331 p 2 57 ru 1314 314 p m (1.9) s 648 387 p 2 57 ru 792 370 p m (4) s 957 387 p 2 57 ru 1033 370 p m (2) s 1129 387 p 2 57 ru 1314 370 p m (3.3) s 648 444 p 2 57 ru 792 427 p m (8) s 957 444 p 2 57 ru 1033 427 p m (3) s 1129 444 p 2 57 ru 1314 427 p m (5.1) s 532 483 p m (400) s 648 500 p 2 57 ru 792 483 p m (1) s 957 500 p 2 57 ru 1033 483 p m (1) s 1129 500 p 2 57 ru 1302 483 p m (1.24) s 648 557 p 2 57 ru 792 540 p m (2) s 957 557 p 2 57 ru 1033 540 p m (1) s 1129 557 p 2 57 ru 1314 540 p m (2.4) s 648 613 p 2 57 ru 792 596 p m (4) s 957 613 p 2 57 ru 1033 596 p m (2) s 1129 613 p 2 57 ru 1314 596 p m (3.2) s 648 670 p 2 57 ru 792 653 p m (8) s 957 670 p 2 57 ru 1033 653 p m (3) s 1129 670 p 2 57 ru 1314 653 p m (6.0) s 648 726 p 2 57 ru 781 709 p m (16) s 957 726 p 2 57 ru 1033 709 p m (4) s 1129 726 p 2 57 ru 1314 709 p m (8.4) s 532 766 p m (600) s 648 783 p 2 57 ru 792 766 p m (8) s 957 783 p 2 57 ru 1033 766 p m (3) s 1129 783 p 2 57 ru 1314 766 p m (7.5) s 648 839 p 2 57 ru 781 822 p m (16) s 957 839 p 2 57 ru 1033 822 p m (4) s 1129 839 p 2 57 ru 1302 822 p m (13.5) s 648 896 p 2 57 ru 781 879 p m (32) s 957 896 p 2 57 ru 1033 879 p m (5) s 1129 896 p 2 57 ru 1320 879 p m (23) s 648 952 p 2 57 ru 781 935 p m (64) s 957 952 p 2 57 ru 1033 935 p m (6) s 1129 952 p 2 57 ru 1320 935 p m (32) s 74 1066 p m (W) -3 (e) 18 (observ) 0 (e) 18 (here) 19 (that) 18 (the) 19 (sp) 1 (eedups) 20 (realized) 20 (b) 0 (y) 18 (our) 18 (algorithm) 19 (o) 0 (v) -1 (er) 17 (the) 19 (QR) 19 (algorithm,) 20 (do) 18 (not) ks 74 1166 p m (remain) 19 (linear) 20 (for) 18 (a) 18 (large) 19 (n) 0 (um) 0 (b) 1 (er) 17 (of) 18 (pro) 1 (cessors.) 30 (This) 19 (is) 20 (due) 19 (to) 18 (the) 19 (fact) 18 (that) 18 (our) 18 (algorithm) 19 (is) ks 74 1266 p m (m) 0 (uc) 0 (h) 12 (less) 14 (e\016cien) 0 (t) 14 (on) 14 (small) 14 (matrices,) 14 (and) 14 (w) 0 (e) 12 (had) 14 (to) 13 (w) 0 (ork) 12 (with) 14 (small) 15 (matrices) 14 (when) 14 (the) 14 (n) 0 (um) 0 (b) 1 (er) ks 74 1365 p m (of) 17 (pro) 1 (cessors) 17 (b) 1 (ecame) 17 (large.) 26 (F) -3 (or) 15 (example,) 18 (with) 17 (a) 17 (matrix) 17 (of) 16 (order) 17 (600) 16 (and) 18 (using) 17 (64) 17 (pro) 1 (cessors,) ks 74 1465 p m (matrices) 15 (of) 15 (a) 0 (v) -1 (erage) 13 (size) 16 (20) 15 (had) 15 (to) 15 (b) 1 (e) 16 (solv) 0 (ed) 14 (on) 15 (eac) 0 (h) 15 (no) 1 (de) 15 (at) 15 (lev) 0 (el) 16 (5.) ks cmbx10.432 @sf 74 1650 p m (9) s 177 1650 p save [<007FFFFFE000007FFFFFE000007FFFFFE00000003FC0000000003FC0000000003FC0000000003F C0000000003FC0000000003FC0000000003FC0000000003FC0000000003FC0000000003FC00000 00003FC0000000003FC0000000003FC0000000003FC0000000003FC0000000003FC0000000003F C0000000003FC0000000003FC0000000003FC0000000003FC0000000003FC00000E0003FC000E0 E0003FC000E0E0003FC000E0E0003FC000E0E0003FC000E0F0003FC001E0F0003FC001E070003F C001C078003FC003C078003FC003C07E003FC007C07F803FC03FC07FFFFFFFFFC07FFFFFFFFFC0 7FFFFFFFFFC0> 43 40 -2 0 48] 84 @pc restore 48 r m (he) 23 (generalize) -1 (d) 21 (eigen) -1 (v) -3 (al) -1 (ue) 21 (problem) ks cmr10.329 @sf 74 1836 p m (W) -3 (e) 11 (sho) 0 (w) 10 (here) 12 (ho) 0 (w) 10 (the) 12 (ideas) 13 (b) 1 (ehind) 13 (our) 12 (algorithm) 11 (can) 12 (b) 1 (e) 13 (used) 12 (to) 11 (solv) 0 (e) 11 (the) 12 (generalized) 13 (eigen) 0 (v) -2 (alue) ks 74 1935 p m (problem.) s cmbx12.300 @sf 74 2099 p m (9.1) s 202 2099 p m (Basic) 18 (algorithm) ks cmr10.329 @sf 74 2269 p m (Giv) 0 (en) 15 (an) 15 (upp) 1 (er-Hessen) 0 (b) 1 (erg) 16 (matrix) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 18 r m (and) 16 (an) 15 (upp) 1 (er-triangular) 16 (matrix) ks cmmi10.329 @sf 15 r m (U) s cmr10.329 @sf 5 r m (:) s cmmi10.329 @sf 531 2414 p m (H) s cmr10.329 @sf 16 r m (=) s cmex10.300 @sf 633 2330 p m (0) s 633 2405 p m (@) s cmmi10.329 @sf 694 2368 p m (H) s cmr8.300 @sf 732 2375 p m (11) s 793 2397 p 2 69 ru cmmi10.329 @sf 834 2368 p m (H) s cmr8.300 @sf 872 2375 p m (12) s 669 2399 p 281 2 ru 793 2454 p 2 57 ru cmr10.432 @sf 709 2469 p m (0) s cmmi10.329 @sf 755 2433 p m (\013) s 793 2478 p 2 66 ru 834 2461 p m (H) s cmr8.300 @sf 872 2468 p m (22) s cmex10.300 @sf 949 2330 p m (1) s 949 2405 p m (A) s cmmi10.329 @sf 993 2414 p m (;) 45 (U) ks cmr10.329 @sf 18 r m (=) s cmex10.300 @sf 1148 2330 p m (0) s 1148 2405 p m (@) s cmmi10.329 @sf 1209 2372 p m (U) s cmr8.300 @sf 1240 2379 p m (11) s 1302 2402 p 2 69 ru cmmi10.329 @sf 1343 2372 p m (U) s cmr8.300 @sf 1374 2379 p m (12) s 1184 2404 p 267 2 ru 1302 2458 p 2 57 ru cmr10.432 @sf 1228 2464 p m (0) s 1302 2473 p 2 57 ru cmmi10.329 @sf 1343 2456 p m (U) s cmr8.300 @sf 1374 2463 p m (22) s cmex10.300 @sf 1451 2330 p m (1) s 1451 2405 p m (A) s cmmi10.329 @sf 1495 2414 p m (;) s cmr10.329 @sf 74 2560 p m (w) 0 (e) 14 (w) 0 (an) -1 (t) 13 (to) 15 (solv) 0 (e) 14 (the) 15 (generalized) 17 (eigen) 0 (v) -2 (alue) 16 (problem,) ks cmmi10.329 @sf 863 2705 p m (H) 4 (x) ks cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (\025U) 5 (x:) ks cmr10.329 @sf 1883 2705 p m (\(14\)) s @eop 37 @bop0 cmr10.329 @sf [ 31 31 -1 0 34] 88 @dc 37 @bop1 cmr10.329 @sf 1919 -77 p m (37) s 459 65 p m (Order) s 600 82 p 2 57 ru 625 65 p m (HQR2) s 775 82 p 2 57 ru 801 65 p m (D&C) s 928 82 p 2 57 ru 953 65 p m (Ratio) 16 (HQR2/D&C) ks 1353 82 p 2 57 ru 1379 65 p m (Distinct) s cmmi10.329 @sf 16 r m (\025) s 434 84 p 1170 2 ru cmr10.329 @sf 483 122 p m (100) s 600 139 p 2 57 ru 648 122 p m (1.04) s 775 139 p 2 57 ru 812 122 p m (1.12) s 928 139 p 2 57 ru 1112 122 p m (.93) s 1353 139 p 2 57 ru 1456 122 p m (99) s 483 178 p m (200) s 600 195 p 2 57 ru 648 178 p m (9.31) s 775 195 p 2 57 ru 812 178 p m (9.18) s 928 195 p 2 57 ru 1101 178 p m (1.01) s 1353 195 p 2 57 ru 1445 178 p m (196) s 483 235 p m (300) s 600 252 p 2 57 ru 648 235 p m (34.1) s 775 252 p 2 57 ru 812 235 p m (28.1) s 928 252 p 2 57 ru 1112 235 p m (1.2) s 1353 252 p 2 57 ru 1445 235 p m (293) s 483 291 p m (400) s 600 308 p 2 57 ru 648 291 p m (94.0) s 775 308 p 2 57 ru 812 291 p m (65.3) s 928 308 p 2 57 ru 1112 291 p m (1.4) s 1353 308 p 2 57 ru 1445 291 p m (395) s 483 347 p m (500) s 600 364 p 2 57 ru 654 347 p m (196) s 775 364 p 2 57 ru 818 347 p m (136) s 928 364 p 2 57 ru 1112 347 p m (1.4) s 1353 364 p 2 57 ru 1445 347 p m (490) s 472 404 p m (1000) s 600 421 p 2 57 ru 643 404 p m (1741) s 775 421 p 2 57 ru 818 404 p m (992) s 928 421 p 2 57 ru 1112 404 p m (1.7) s 1353 421 p 2 57 ru 1434 404 p m (1000) s 74 522 p m (In) 18 (an) 17 (implemen) 0 (tation) 17 (on) 17 (a) 17 (shared) 17 (memory) 16 (mac) 0 (hine,) 17 (the) 17 (storage) 16 (allo) 1 (cated) 18 (to) 17 (the) 17 (Jacobian) 18 (\(in) ks 74 621 p m (serial) 15 (mo) 1 (de\)) 13 (is) 14 (m) 0 (ultiplied) 15 (b) 0 (y) 13 (the) 13 (n) 0 (um) 0 (b) 1 (er) 12 (of) 13 (pro) 1 (cessors) 14 (used;) 14 (this) 14 (is) 14 (mean) 0 (t) 12 (to) 13 (prev) 0 (en) 0 (t) 11 (concurren) 0 (t) ks 74 721 p m (write) 20 (to) 19 (the) 20 (same) 20 (memory) 19 (lo) 1 (cations.) 35 (The) 20 (follo) 0 (wing) 20 (are) 20 (some) 19 (results) 20 (from) 20 (the) 20 (Allian) 0 (t) 20 (FX/8) ks 74 821 p m (implemen) 0 (tation.) 20 (The) 16 (Allian) 0 (t) 15 (FX/8) 15 (is) 15 (a) 15 (parallel) 17 (mac) 0 (hine) 15 (with) 16 (8) 14 (v) 0 (ector) 14 (pro) 1 (cessors.) ks 508 934 p m (Order) s 648 951 p 2 57 ru 674 934 p m (No.) 20 (of) 14 (pro) 1 (cs.) ks 957 951 p 2 57 ru 983 934 p m (Lev) 0 (els) ks 1129 951 p 2 57 ru 1155 934 p m (Ratio) 15 (HQR2/D&C) ks 483 953 p 1073 2 ru 532 991 p m (100) s 648 1008 p 2 57 ru 792 991 p m (2) s 957 1008 p 2 57 ru 1033 991 p m (1) s 1129 1008 p 2 57 ru 1314 991 p m (1.7) s 648 1064 p 2 57 ru 792 1047 p m (4) s 957 1064 p 2 57 ru 1033 1047 p m (2) s 1129 1064 p 2 57 ru 1314 1047 p m (2.4) s 648 1121 p 2 57 ru 792 1104 p m (8) s 957 1121 p 2 57 ru 1033 1104 p m (3) s 1129 1121 p 2 57 ru 1314 1104 p m (4.0) s 74 1215 p m (The) 17 (results) 16 (on) 16 (the) 16 (Allian) 0 (t) 17 (w) 0 (ere) 15 (in) 17 (general) 16 (disapp) 1 (oin) 0 (ting.) 24 (The) 16 (storage) 15 (sc) 0 (heme) 16 (for) 15 (the) 16 (Jacobian) ks 74 1314 p m (that) 22 (w) 0 (e) 20 (used) 23 (on) 22 (that) 21 (mac) 0 (hine) 22 (seems) 22 (to) 22 (ha) 0 (v) -1 (e) 20 (inhibi) 1 (ted) 24 (the) 22 (compiler's) 23 (v) 0 (ector) 21 (optimizations.) ks 74 1414 p m (HQR2,) 16 (running) 16 (on) 15 (a) 15 (single) 16 (pro) 1 (cessor) ks cmti10.329 @sf 15 r m (was) s cmr10.329 @sf 16 r m (v) 0 (ector-optimized.) ks 124 1555 p m (The) 16 (follo) 0 (wing) 16 (are) 15 (some) 16 (results) 16 (from) 15 (the) 16 (In) 0 (tel) 15 (iPSC/2) 16 (implemen) 0 (tation.) 22 (The) 16 (largest) 16 (size) 16 (used) ks 74 1655 p m (w) 0 (as) 14 (dictated) 15 (b) 0 (y) 14 (the) 16 (memory) 14 (capacit) 0 (y) 15 (of) 14 (a) 15 (single) 17 (no) 1 (de.) ks 508 1766 p m (Order) s 648 1783 p 2 57 ru 674 1766 p m (No.) 20 (of) 14 (pro) 1 (cs.) ks 957 1783 p 2 57 ru 983 1766 p m (Lev) 0 (els) ks 1129 1783 p 2 57 ru 1155 1766 p m (Ratio) 15 (HQR2/D&C) ks 483 1785 p 1073 2 ru 532 1823 p m (100) s 648 1840 p 2 57 ru 792 1823 p m (1) s 957 1840 p 2 57 ru 1033 1823 p m (1) s 1129 1840 p 2 57 ru 1302 1823 p m (1.22) s 648 1895 p 2 57 ru 792 1878 p m (2) s 957 1895 p 2 57 ru 1033 1878 p m (1) s 1129 1895 p 2 57 ru 1314 1878 p m (2.2) s 648 1952 p 2 57 ru 792 1935 p m (4) s 957 1952 p 2 57 ru 1033 1935 p m (2) s 1129 1952 p 2 57 ru 1314 1935 p m (3.7) s 648 2008 p 2 57 ru 792 1991 p m (8) s 957 2008 p 2 57 ru 1033 1991 p m (3) s 1129 2008 p 2 57 ru 1314 1991 p m (6.0) s 648 2065 p 2 57 ru 781 2048 p m (16) s 957 2065 p 2 57 ru 1033 2048 p m (4) s 1129 2065 p 2 57 ru 1314 2048 p m (8.2) s 532 2104 p m (200) s 648 2121 p 2 57 ru 792 2104 p m (1) s 957 2121 p 2 57 ru 1033 2104 p m (1) s 1129 2121 p 2 57 ru 1302 2104 p m (1.16) s 648 2178 p 2 57 ru 792 2161 p m (2) s 957 2178 p 2 57 ru 1033 2161 p m (1) s 1129 2178 p 2 57 ru 1314 2161 p m (2.2) s 648 2234 p 2 57 ru 792 2217 p m (4) s 957 2234 p 2 57 ru 1033 2217 p m (2) s 1129 2234 p 2 57 ru 1314 2217 p m (3.5) s 648 2291 p 2 57 ru 792 2274 p m (8) s 957 2291 p 2 57 ru 1033 2274 p m (3) s 1129 2291 p 2 57 ru 1314 2274 p m (5.2) s 648 2347 p 2 57 ru 781 2330 p m (16) s 957 2347 p 2 57 ru 1033 2330 p m (4) s 1129 2347 p 2 57 ru 1314 2330 p m (9.1) s 532 2387 p m (300) s 648 2404 p 2 57 ru 792 2387 p m (1) s 957 2404 p 2 57 ru 1033 2387 p m (1) s 1129 2404 p 2 57 ru 1302 2387 p m (1.25) s 648 2460 p 2 57 ru 792 2443 p m (2) s 957 2460 p 2 57 ru 1033 2443 p m (1) s 1129 2460 p 2 57 ru 1314 2443 p m (2.2) s 648 2516 p 2 57 ru 792 2499 p m (4) s 957 2516 p 2 57 ru 1033 2499 p m (2) s 1129 2516 p 2 57 ru 1314 2499 p m (3.2) s 648 2573 p 2 57 ru 792 2556 p m (8) s 957 2573 p 2 57 ru 1033 2556 p m (3) s 1129 2573 p 2 57 ru 1314 2556 p m (6.3) s 648 2629 p 2 57 ru 781 2612 p m (16) s 957 2629 p 2 57 ru 1033 2612 p m (4) s 1129 2629 p 2 57 ru 1314 2612 p m (9.8) s 648 2686 p 2 57 ru 781 2669 p m (32) s 957 2686 p 2 57 ru 1033 2669 p m (5) s 1129 2686 p 2 57 ru 1302 2669 p m (13.2) s 648 2742 p 2 57 ru 781 2725 p m (64) s 957 2742 p 2 57 ru 1033 2725 p m (6) s 1129 2742 p 2 57 ru 1302 2725 p m (21.3) s @eop 36 @bop0 cmbx10.432 @sf [<007FC00003FFF8000FFFFC001FC03E003F000F007C0007807C0003C0F80003C0F80003E0F80003 E0F80003E0F80007E0F80007E078001FE07C007FE03C01FFC01E03FFC00F0FFF8007FFFF0001FF FE0001FFFC0003FFF80007FFE0000FFFF8001FFE3C001FFC1E003FF01F003FC00F003F000F803F 000F803E000F803E000F801E000F801E001F000F003F0007C07E0003FFFC0001FFF000003FC000> 27 39 -3 0 34] 56 @dc cmmi10.329 @sf [<01FC0000078380000E00E0001C00700038003C0038001E0078000F007000070070000380F00003 C0F00001C0F00001E0F00000E0F00000F0F00000F0780000787800007878000078780000783C00 00383C0000381C0000381E0000380E00003807000038078000380380007001C0007000E0006000 3000E0001C01C0000707000001FC00> 29 33 -2 1 35] 79 @dc 36 @bop1 cmr10.329 @sf 1919 -77 p m (36) s 74 67 p m (the) 11 (matrix) 11 (reside) 13 (on) 11 (the) 11 (same) 11 (pro) 1 (cessor.) 18 (Therefore) 11 (storage) 10 (sc) 0 (hemes) 11 (more) 11 (adv) -2 (an) 0 (ta) -1 (geous) 9 (for) 11 (linear) ks 74 167 p m (system) 10 (solving,) 12 (suc) 0 (h) 9 (as) 10 (wrap) 10 (mapping) 11 (of) 10 (columns) 11 (or) 10 (ro) 0 (ws,) 9 (could) 11 (not) 10 (b) 1 (e) 11 (used.) 19 (The) 10 (comm) 0 (unication) ks 74 266 p m (b) 1 (et) 0 (w) 0 (een) 13 (pro) 1 (cessors) 14 (for) 14 (this) 14 (second) 15 (implemen) 0 (tation) 15 (is) 15 (more) 13 (in) 0 (tensiv) 0 (e.) 19 (Comm) 0 (unication) 14 (is) 15 (needed) ks 74 366 p m (when) 15 (solving) 14 (the) 14 (linear) 16 (systems) 13 (arising) 15 (in) 15 (Newton's) 13 (iterations) 14 (as) 14 (w) 0 (ell) 13 (as) 14 (for) 13 (the) 14 (de\015ation) 15 (phase.) ks 74 466 p m (Also) 18 (b) 1 (ecause) 19 (of) 18 (the) 18 (storage) 16 (sc) 0 (heme,) 18 (w) 0 (e) 17 (can) 18 (exp) 1 (ect) 18 (the) 18 (pro) 1 (cessors) 18 (to) 17 (b) 1 (ecome) 19 (successiv) 0 (ely) 18 (idle) ks 74 565 p m (during) 21 (the) 20 (factorization) 19 (of) 19 (the) 20 (Jacobian) 21 (and) 20 (the) 20 (bac) 0 (k) 18 (solv) 0 (e) 19 (for) 19 (the) 20 (correction.) 34 (Ho) 0 (w) -1 (ev) -1 (er,) 18 (w) 0 (e) ks 74 665 p m (ha) 0 (v) 0 (e) 16 (implemen) 0 (ted) 20 (an) 18 (e\016cien) 0 (t) 18 (sc) 0 (heme) 18 (where) 19 (the) 19 (Jacobian) 19 (is) 19 (repartitioned) 19 (b) 0 (y) 18 (ro) 0 (ws) 16 (b) 1 (efore) 19 (the) ks 74 765 p m (bac) 0 (k) 13 (solv) 0 (e) 14 (tak) 0 (es) 13 (place:) 20 (the) 15 (\\resh) 0 (u) ks save [<7FE3FE3FF007007007000700700700070070070007007007000700700700070070070007007007 000700700700070070070007007007000700700700070070070007007007000700700700070070 0700070070070007007007000700700700FFFFFFFF000700700700070070070007007007000700 7007000700700700070070070007007007000300F007000380F80F0001C07C0F0000F06F070000 1F81FF00> 36 32 0 0 38] 15 @pc restore 38 r m (ing") 13 (of) 14 (the) 15 (submatrices) 15 (tak) 0 (es) 12 (place) 16 (b) 1 (et) 0 (w) 0 (een) 13 (pro) 1 (cessors) 14 (that) ks 74 864 p m (b) 1 (ecame) 16 (idle) 17 (after) 14 (doing) 16 (their) 16 (part) 14 (of) 15 (the) 15 (Gaussian) 16 (elimination.) ks cmbx10.432 @sf 74 1049 p m (8) s 177 1049 p save [ 47 41 -3 0 54] 78 @pc restore 54 r m (ume) -1 (ri) -1 (cal) 20 (Results) 22 (and) ks 23 r save [ 39 41 -3 0 47] 80 @pc restore 46 r m (erform) -1 (ance) ks cmr10.329 @sf 74 1235 p m (In) 23 (this) 22 (section) 23 (w) 0 (e) 20 (presen) 0 (t) 21 (the) 22 (results) 23 (of) 21 (the) 22 (implemen) 0 (tation) 23 (of) 21 (the) 22 (algorithm) 22 (on) 22 (a) 22 (n) 0 (um) 0 (b) 1 (er) ks 74 1335 p m (of) 22 (mac) 0 (hines.) 39 (The) 23 (serial) 22 (v) 0 (ersion) 21 (of) 22 (the) 22 (co) 1 (de) 22 (is) 23 (a) 0 (v) -2 (a) -1 (ilable) 22 (through) 22 (NETLIB) 23 (where) 22 (it's) 21 (called) ks 74 1434 p m (\\nonsymdc".) s 124 1575 p m (The) 21 (same) 21 (algorithm) 22 (has) 21 (b) 1 (een) 22 (run) 22 (on) 21 (the) 21 (IBM) 21 (RS/6000-550,) 21 (the) 22 (Allian) 0 (t) 21 (FX/8,) 22 (the) 21 (In) 0 (tel) ks 74 1675 p m (iPSC/2) 13 (and) 13 (the) 13 (In) 0 (tel) 12 (iPSC/860.) 19 (W) -3 (e) 12 (compared) 13 (our) 12 (results) 13 (to) 12 (those) 13 (of) 12 (HQR2) 14 (from) 12 (the) 12 (EISP) -3 (A) 0 (CK) ks 74 1775 p m (collection.) 32 (W) -3 (e) 18 (ha) 0 (v) 0 (e) 17 (used) 19 (randomly) 19 (generated) 18 (upp) 1 (er-Hessen) 0 (b) 1 (erg) 20 (matrices) 19 (in) 19 (these) 19 (tests,) 19 (with) ks 74 1874 p m (en) 0 (tries) 21 (uniformly) 23 (distributed) 23 (b) 1 (et) 0 (w) -1 (een) ks cmsy10.329 @sf 20 r m (\000) s cmr10.329 @sf m (1) 22 (and) 22 (1;) 24 (de\015ation) 22 (w) 0 (as) 19 (not) 22 (p) 1 (erformed.) 39 (The) 21 (storage) ks 74 1974 p m (requiremen) 0 (t) 21 (for) 21 (our) 21 (algorithm) 22 (in) 22 (a) 21 (serial) 22 (implemen) 0 (tation) 22 (is) 22 (4) ks cmmi10.329 @sf m (n) s cmr8.300 @sf 1371 1959 p m (2) s cmr10.329 @sf 1405 1974 p m (+) s cmmi10.329 @sf 15 r m (O) s cmr10.329 @sf 1 r m (\() s cmmi10.329 @sf m (n) s cmr10.329 @sf m (\),) 22 (whic) 0 (h) 21 (is) 22 (t) 0 (wice) 21 (the) ks 74 2074 p m (storage) 14 (requiremen) 0 (t) 15 (for) 14 (a) 15 (serial) 16 (implemen) 0 (tation) 16 (of) 15 (HQR2) 15 ([) 0 (15) ks 1285 2074 p m (].) s 124 2215 p m (The) 12 (follo) 0 (wing) 12 (are) 12 (the) 12 (results) 13 (from) 11 (the) 13 (IBM) 12 (RS/6000-550) 11 (implemen) 0 (tation.) 19 (The) 12 (IBM) 13 (RS/6000-) ks 74 2314 p m (550) 14 (is) 14 (a) 14 (single) 16 (pro) 1 (cessor) 14 (computer) 14 (with) 15 (a) 14 (RISC-based) 16 (Arc) 0 (hitecture.) 19 (In) 15 (the) 14 (last) 14 (column) 15 (w) 0 (e) 13 (ha) 0 (v) 0 (e) ks 74 2414 p m (giv) 0 (en) 13 (the) 14 (n) 0 (um) 0 (b) 1 (er) 12 (of) 13 (distinct) 15 (eigen) 0 (v) -2 (alues) 13 (that) 13 (w) 0 (as) 12 (computed) 14 (b) 0 (y) 13 (our) 13 (algorithm) 14 (\(the) 13 (test) 13 (matrices) ks 74 2514 p m (had) 14 (no) 13 (m) 0 (ultiple) 15 (eigen) 0 (v) -2 (alues\).) 18 (Eac) 0 (h) 13 (matrix) 13 (w) 0 (as) 11 (divided) 16 (in) 0 (to) 12 (t) 0 (w) -1 (o) 12 (subproblems,) 14 (i.e.,) 14 (only) 14 (one) 13 (zero) ks 74 2613 p m (w) 0 (as) 14 (in) 0 (tro) 1 (duced) 15 (on) 15 (the) 15 (sub) 1 (diagonal.) ks @eop 35 @bop0 cmbx12.300 @sf [<01E00003F00003F00003F00003F00003F00003F00003F00001F00001F00001F00000F00000F000 00F000007800007800003800001800001C00000C00000600C00300C00300C00180E000C0E00060 7FFFF07FFFF87FFFF87FFFFC7FFFFE7FFFFE780000600000> 23 34 -3 0 28] 55 @dc [ 21 32 -3 0 28] 50 @dc [<180FC0001C3FF8001EE07C001FC03E001F801F001F001F801F000F801F000FC01F000FC01F000F C01F000FC01F000FC01F000FC01F000FC01F000FC01F000F801F000F801F001F001F801E001FF0 7C001F3FF8001F0FE0001F0000001F0000001F0000001F0000001F0000001F0000001F0000001F 0000001F0000001F0000001F000000FF000000FF000000> 26 35 -2 0 31] 98 @dc [<01FC3FC007FF3FC00F81BE001F00FE001F007E001F003E001F003E001F003E001F003E001F003E 001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F00 3E00FF01FE00FF01FE00> 26 22 -2 0 31] 117 @dc [<00FF0003FFC00FC0701F00303E00187E00007C00007C0000FC0000FC0000FC0000FFFFF8FFFFF8 FC00F8FC00F87C00F87C00F03E01F01E01E00F87C007FF8000FE00> 21 22 -2 0 26] 101 @dc [<01FC3FC007FF3FC00F83BE001E00FE003E007E007C003E007C003E00FC003E00FC003E00FC003E 00FC003E00FC003E00FC003E00FC003E00FC003E007C003E007E003E003E003E001F007E000F81 FE0007FFBE0001FC3E0000003E0000003E0000003E0000003E0000003E0000003E0000003E0000 003E0000003E0000003E0000003E000001FE000001FE00> 26 35 -2 0 31] 100 @dc [<1F0000007F80000069C00000FC600000FC300000FC3800007818000000180000000C0000000C00 00000E0000000E0000001F0000001F0000003F8000003F8000007FC000007CC000007CC00000F8 600000F8600001F0300001F0300003E0180003E0180007E01C0007C00C000FC00E000F8006000F 800600FFE01FE0FFE01FE0> 27 32 -1 10 30] 121 @dc [ 26 32 -2 10 31] 112 @dc [ 26 22 -2 0 31] 110 @dc cmmi10.329 @sf [ 23 29 1 9 23] 112 @dc cmr8.300 @sf [<0FE030304018C00CE00EE00E000E000E000C0018003007E0006000380018001C701C701C601830 300FE0> 15 21 -1 0 18] 51 @dc 1.000000 /cmr6.300 @newfont cmr6.300 @sf [ 9 16 -2 0 15] 49 @dc [ 11 16 -1 0 15] 50 @dc 35 @bop1 cmr10.329 @sf 1919 -77 p m (35) s cmbx12.300 @sf 74 67 p m (7.2) s 202 67 p save [ 37 34 -2 0 43] 68 @pc restore 43 r m (istributed) 17 (mem) -1 (ory) 16 (implem) -2 (en) -1 (t) -1 (ation) ks cmr10.329 @sf 74 238 p m (The) 13 (curren) 0 (t) 11 (implemen) 0 (tation) 13 (on) 12 (distributed) 14 (memory) 12 (mac) 0 (hines) 13 (requires) 13 (that) 12 (the) 12 (matrix) 12 (b) 1 (e) 14 (stored) ks 74 337 p m (on) 18 (eac) 0 (h) 17 (pro) 1 (cessor.) 27 (This) 19 (ob) 0 (viously) 17 (puts) 18 (rather) 17 (sev) 0 (ere) 17 (constrain) 0 (ts) 17 (on) 17 (the) 18 (size) 19 (of) 17 (problems) 19 (that) ks 74 437 p m (can) 19 (b) 1 (e) 20 (solv) 0 (ed.) 30 (With) 19 (this) 19 (implemen) 0 (tation) 19 (ho) 0 (w) 0 (ev) -1 (er,) 17 (comm) 0 (unication) 18 (is) 20 (needed) 20 (only) 19 (during) 20 (the) ks 74 537 p m (de\015ation) 15 (phase.) 20 (This) 16 (implemen) 0 (tation) 14 (is) 15 (b) 1 (est) 15 (describ) 1 (ed) 17 (through) 14 (the) 15 (con) 0 (tribution) 14 (of) 14 (a) 14 (particular) ks 74 636 p m (pro) 1 (cessor.) 19 (Supp) 1 (ose) 13 (that) 11 (w) 0 (e) 10 (ha) 0 (v) -1 (e) 10 (4) 12 (pro) 1 (cessors) 11 (at) 11 (our) 12 (disp) 1 (osal,) ks cmmi10.329 @sf 13 r m (p) s cmr8.300 @sf 1308 643 p m (0) s cmmi10.329 @sf 1328 636 p m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 7 (.) ks cmmi10.329 @sf 1409 636 p m (;) 8 (p) ks cmr8.300 @sf 1453 643 p m (3) s cmr10.329 @sf 1483 636 p m (and) 12 (that) 11 (accordingly) 13 (the) ks 74 736 p m (matrix) s cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 19 r m (has) 15 (b) 1 (een) 16 (divided) 17 (in) 0 (to) 15 (4) 14 (subproblems:) ks cmmi10.329 @sf 21 r m (H) s cmr8.300 @sf 1076 743 p m (0) s cmmi10.329 @sf 1096 736 p m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 7 (.) ks cmmi10.329 @sf 1177 736 p m (;) 8 (H) ks cmr8.300 @sf 1236 743 p m (3) s cmr10.329 @sf 1254 736 p m (,) 15 (that) 15 (their) 15 (common) 15 (size) 16 (is) ks cmmi10.329 @sf 16 r m (n=) s cmr10.329 @sf m (4) 15 (and) ks 74 835 p m (that) 16 (they) 16 (o) 1 (ccur) 16 (in) 17 (this) 17 (order) 16 (on) 16 (the) 16 (diagonal) 16 (of) 16 (the) 16 (matrix.) 23 (W) -3 (e) 15 (describ) 1 (e) 18 (no) 0 (w) 14 (the) 16 (con) 0 (tribution) ks 74 935 p m (of) s cmmi10.329 @sf 15 r m (p) s cmr8.300 @sf 149 942 p m (2) s cmr10.329 @sf 184 935 p m (b) 0 (y) 14 (steps:) ks 124 1076 p m (1\)) 15 (Call) 15 (HQR2) 16 (to) 15 (solv) 0 (e) 14 (for) 15 (the) 15 (eigensystem) 16 (of) 15 (the) 15 (matrix) ks cmmi10.329 @sf 15 r m (H) s cmr8.300 @sf 1299 1083 p m (2) s cmr10.329 @sf 1318 1076 p m (.) s 124 1217 p m (2\)) 13 (Re\014ne) 16 (the) 14 (output) 14 (from) 14 (step) 14 (1) 14 (to) 13 (get) 14 (1) ks cmmi10.329 @sf m (=) s cmr10.329 @sf m (2) 13 (the) 14 (n) 0 (um) 0 (b) 1 (er) 13 (of) 14 (\(i.e.,) ks cmmi10.329 @sf 13 r m (n=) s cmr10.329 @sf m (4\)) 14 (eigenpairs) 15 (of) 14 (the) 14 (matrix) ks cmmi10.329 @sf 74 1317 p m (H) s cmr6.300 @sf 5 r m (1) s 117 1323 p 16 2 ru 117 1343 p m (2) s cmr10.329 @sf 139 1317 p m (:) s cmmi10.329 @sf 789 1434 p m (H) s cmr6.300 @sf 5 r m (1) s 832 1440 p 16 2 ru 832 1460 p m (2) s cmr10.329 @sf 867 1434 p m (=) s cmex10.300 @sf 915 1350 p m (0) s 915 1424 p m (@) s cmmi10.329 @sf 985 1388 p m (H) s cmr8.300 @sf 1023 1395 p m (2) s 1075 1417 p 2 69 ru cmmi10.329 @sf 1116 1388 p save [ 31 31 -2 0 34] 66 @pc restore 951 1419 p 241 2 ru 1075 1474 p 2 57 ru cmr10.432 @sf 991 1489 p m (0) s cmmi10.329 @sf 1036 1453 p m (\013) s 1075 1498 p 2 66 ru 1105 1481 p m (H) s cmr8.300 @sf 1143 1488 p m (3) s cmex10.300 @sf 1192 1350 p m (1) s 1192 1424 p m (A) s cmmi10.329 @sf 1236 1434 p m (;) s cmr10.329 @sf 74 1561 p m (where) s cmmi10.329 @sf 16 r m (H) s cmr6.300 @sf 5 r m (1) s 248 1567 p 16 2 ru 248 1587 p m (2) s cmr10.329 @sf 286 1561 p m (is) 15 (a) 15 (submatrix) 16 (of) ks cmmi10.329 @sf 14 r m (H) s cmr10.329 @sf 4 r m (.) s 124 1702 p m (3\)) 19 (Re\014ne) 21 (the) 19 (output) 19 (from) 19 (step) 20 (2) 19 (to) 19 (get) 19 (1) ks cmmi10.329 @sf m (=) s cmr10.329 @sf m (4) 18 (of) 19 (the) 20 (n) 0 (um) 0 (b) 1 (er) 17 (of) 20 (eigenpairs) 20 (\(i.e.,) ks cmmi10.329 @sf 20 r m (n=) s cmr10.329 @sf m (4\)) 19 (of) 19 (the) ks 74 1802 p m (matrix) s cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 4 r m (.) s 124 1943 p m (As) 12 (can) 12 (b) 1 (e) 13 (readily) 14 (realized) 13 (no) 13 (comm) 0 (unication) 11 (b) 1 (et) 0 (w) 0 (een) 11 (pro) 1 (cessors) 12 (is) 12 (needed) 14 (except) 13 (for) 11 (c) 0 (hec) 0 (king) ks 74 2042 p m (for) 19 (eigenpairs) 20 (to) 19 (whic) 0 (h) 19 (con) 0 (v) -1 (ergence) 18 (o) 1 (ccurred) 20 (from) 18 (more) 19 (than) 19 (one) 20 (initial) 21 (appro) 0 (ximation.) 31 (F) -3 (or) ks 74 2142 p m (example,) 18 (the) 17 (eigenpairs) 18 (of) ks cmmi10.329 @sf 16 r m (H) s cmr6.300 @sf 5 r m (1) s 657 2148 p 16 2 ru 657 2168 p m (2) s cmr10.329 @sf 696 2142 p m (are) 17 (generated) 17 (on) ks cmmi10.329 @sf 17 r m (p) s cmr8.300 @sf 1071 2149 p m (2) s cmr10.329 @sf 1107 2142 p m (and) s cmmi10.329 @sf 17 r m (p) s cmr8.300 @sf 1220 2149 p m (3) s cmr10.329 @sf 1240 2142 p m (,) 16 (and) 17 (therefore) 17 (w) 0 (e) 16 (need) 17 (to) 17 (c) 0 (hec) 0 (k) 15 (for) ks 74 2242 p m (duplicate) 15 (eigenpairs) 15 (\(on) 13 (eac) 0 (h) 13 (pro) 1 (cessor) 13 (separately) 13 (whic) 0 (h) 14 (requires) 14 (no) 13 (comm) 0 (unication,) 13 (and) 14 (across) ks 74 2341 p m (b) 1 (oth) 15 (whic) 0 (h) 16 (requires) 15 (comm) 0 (unication\).) ks 124 2482 p m (W) -3 (e) 15 (are) 17 (curren) 0 (tly) 15 (dev) 0 (eloping) 17 (another) 16 (implemen) 0 (tation) 17 (where) 17 (blo) 1 (c) 0 (ks) 16 (of) 16 (columns) 17 (of) 16 (the) 16 (matrix) ks 74 2582 p m (are) 11 (stored) 11 (on) 11 (di\013eren) 0 (t) 10 (pro) 1 (cessors.) 18 (This) 12 (storage) 10 (sc) 0 (heme) 10 (has) 11 (b) 1 (een) 13 (dictated) 11 (to) 11 (us) 11 (b) 0 (y) 10 (the) 11 (need) 12 (to) 11 (call) ks 74 2682 p m (HQR2) 15 (at) 14 (the) 15 (lo) 0 (w) 0 (est) 12 (lev) 0 (el:) 20 (indeed,) 16 (the) 15 (call) 16 (the) 14 (serial) 16 (HQR2) 15 (requires) 15 (that) 14 (con) 0 (tiguous) 14 (columns) 16 (of) ks @eop 34 @bop0 cmbx12.300 @sf [<80FF80C7FFE0FF00F8FC003CF0003CE0001EE0001EC0001FC0001FC0001F00003F00003F00007F 0003FF003FFE03FFFE0FFFFC1FFFF83FFFF07FFFC07FFF00FFE000FF0000FC0000FC000CF8000C F8000C78001C78001C7C003C3C007C1F03FC07FF8C01FC04> 24 34 -3 0 31] 83 @dc [ 19 34 -1 0 21] 73 @dc 34 @bop1 cmr10.329 @sf 1919 -77 p m (34) s cmbx10.432 @sf 74 67 p save [<00380000007C000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE00 00007E0000007E0000007E0000007E0000003E0000003E0000003F0000001F0000001F0000000F 0000000F00000007800000078000000380000001C0000000E000E000E000E0007000E000380070 001C0070000E0070000E007FFFFF007FFFFF807FFFFFC07FFFFFE03FFFFFF03FFFFFF03FFFFFF0 3E00000038000000> 28 41 -4 0 34] 55 @pc restore 177 67 p save [ 39 41 -3 0 47] 80 @pc restore 46 r m (arallel) s 20 r save [ 47 41 -2 0 52] 65 @pc restore 52 r m (lgorithm) -1 (s) 21 (Detail) -1 (s) 21 (and) ks 24 r save [ 39 41 -3 0 47] 80 @pc restore 46 r m (erform) -1 (ance) ks cmr10.329 @sf 74 253 p m (It) 15 (is) 16 (fairly) 16 (straigh) 0 (tfo) -1 (rw) -1 (a) -1 (rd) 14 (to) 14 (see) 15 (from) 15 (section) 15 (2) 15 (ho) 0 (w) 14 (to) 14 (obtain) 16 (a) 14 (parallel) 17 (algorithm.) 20 (W) -3 (e) 14 (discuss) ks 74 353 p m (here) 20 (certain) 20 (details.) 33 (The) 19 (giv) 0 (en,) 20 (generally) 20 (dense,) 21 (matrix) 19 (is) 19 (\014rst) 19 (reduced) 21 (to) 18 (upp) 1 (er-Hessen) 0 (b) 1 (erg) ks 74 453 p m (form) 17 (using) 17 (a) 17 (parallel) 19 (blo) 1 (c) 0 (k) 0 (ed) 16 (algorithm.) 25 (Next) 17 (comes) 17 (the) 18 (partitioning) 18 (phase) 17 (or) 17 (\\divide".) 26 (This) ks 74 552 p m (phase) 18 (amoun) 0 (ts) 15 (to) 17 (constructing) 17 (a) 17 (binary) 18 (tree) 18 (with) 17 (eac) 0 (h) 17 (no) 1 (de) 18 (represen) 0 (ting) 16 (a) 17 (partition) 18 (in) 0 (to) 16 (t) 0 (w) -1 (o) ks 74 652 p m (subproblems.) 21 (It) 13 (has) 14 (b) 1 (een) 15 (our) 13 (practice) 15 (to) 13 (partition) 14 (the) 13 (matrix) 14 (in) 0 (to) 13 (a) 13 (n) 0 (um) 0 (b) 1 (er) 12 (of) 13 (subproblems) 15 (\(at) ks 74 751 p m (the) 12 (lo) 0 (w) -1 (est) 9 (lev) 0 (el\)) 12 (equal) 12 (to) 11 (the) 11 (n) 0 (um) 0 (b) 1 (er) 10 (of) 11 (pro) 1 (cessors) 11 (a) 0 (v) -2 (ailable) 11 (on) 12 (the) 11 (target) 10 (mac) 0 (hine.) 19 (Eac) 0 (h) 10 (of) 11 (these) ks 74 851 p m (problems) 14 (ma) 0 (y) 12 (b) 1 (e) 15 (spa) 0 (wned) 13 (indep) 1 (enden) 1 (tly) 14 (without) 14 (fear) 13 (of) 14 (data) 13 (con\015icts;) 14 (the) 14 (computation) 14 (at) 13 (this) ks 74 951 p m (lev) 0 (el) 18 (\(the) 17 (lo) 0 (w) 0 (est) -1 (\)) 15 (consists) 18 (of) 17 (calls) 18 (to) 17 (the) 17 (EISP) -3 (A) 0 (CK) 16 (routine) 18 (HQR2.) 27 (The) 17 (tree) 18 (is) 17 (then) 18 (tra) 0 (v) -1 (ersed) ks 74 1050 p m (in) 15 (rev) 0 (erse) 13 (order) 14 (with) 15 (Newton's) 14 (metho) 1 (d) 14 (applied) 16 (at) 14 (eac) 0 (h) 13 (no) 1 (de) 15 (using) 15 (the) 15 (results) 14 (from) 14 (the) 14 (c) 0 (hildren) ks 74 1150 p m (as) 16 (initial) 18 (appro) 0 (ximations.) 21 (Note) 15 (here) 16 (that) 16 (the) 16 (computation) 15 (at) 16 (a) 15 (no) 1 (de) 17 (do) 1 (es) 16 (not) 16 (ha) 0 (v) -1 (e) 14 (to) 15 (w) 0 (ait) 15 (for) ks 74 1250 p m (b) 1 (oth) 14 (c) 0 (hildren) 15 (to) 14 (complete) 15 (in) 15 (order) 13 (to) 14 (start:) 18 (as) 14 (a) 13 (matter) 13 (of) 14 (fact,) 13 (it) 15 (can) 14 (start) 13 (as) 14 (so) 1 (on) 13 (as) 14 (one) 14 (c) 0 (hild) ks 74 1349 p m (has) 13 (computed) 14 (one) 13 (eigenpair) 14 (of) 13 (a) 13 (subproblem.) 20 (In) 14 (order) 13 (to) 12 (stress) 13 (this) 13 (p) 1 (oin) 0 (t,) 13 (w) 0 (e) 12 (men) 0 (tion) 12 (here) 14 (that) ks 74 1449 p m (this) 15 (is) 14 (quite) 15 (di\013eren) 0 (t) 13 (from) 14 (the) 14 (situation) 15 (in) 15 (the) 14 (symmetric) 14 (case) 14 ([) 0 (6) ks 1350 1449 p m (],) 14 (where) 14 (information) 15 (from) 13 (b) 1 (oth) ks 74 1548 p m (c) 0 (hildren) 21 (is) 19 (needed) 21 (b) 1 (efore) 20 (computations) 19 (can) 20 (start) 18 (at) 19 (the) 19 (no) 1 (de.) 34 (Ho) 0 (w) -1 (ev) -1 (er,) 18 (in) 20 (practice) 20 (w) 0 (e) 18 (ha) 0 (v) 0 (e) ks 74 1648 p m (allo) 0 (w) 0 (ed) 13 (computations) 13 (to) 14 (start) 12 (at) 14 (a) 13 (no) 1 (de) 15 (only) 15 (after) 13 (at) 13 (least) 14 (one) 14 (c) 0 (hild) 15 (has) 14 (completed;) 15 (the) 14 (need) 15 (to) ks 74 1748 p m (c) 0 (hec) 0 (k) 14 (for) 14 (duplicate) 17 (eigen) 0 (v) -2 (alues) 15 (and) 16 (de\015ate) 15 (if) 16 (necessary) 15 (has) 15 (imp) 1 (osed) 16 (further) 16 (sync) 0 (hronization.) ks 124 1889 p m (The) 19 (algorithm) 19 (has) 19 (b) 1 (een) 20 (implemen) 0 (ted) 19 (on) 19 (computers) 19 (with) 19 (a) 19 (shared) 19 (memory) 18 (and) 19 (computers) ks 74 1988 p m (with) 16 (distributed) 16 (memory) 15 (arc) 0 (hitectures.) ks cmbx12.300 @sf 74 2152 p m (7.1) s 202 2152 p m (Shared) s 19 r save [ 48 34 -2 0 53] 77 @pc restore 53 r m (emory) 16 (Implem) -1 (e) -1 (n) -1 (tati) -1 (on) ks cmr10.329 @sf 74 2322 p m (So) 13 (far) 13 (w) 0 (e) 12 (ha) 0 (v) 0 (e) 11 (used) 14 (SCHEDULE) 27 ([) 0 (7) ks 786 2322 p m (]) 13 (to) 13 (implemen) 0 (t) 13 (the) 14 (algorithm) 13 (on) 13 (shared) 14 (memory) 13 (computers.) ks 74 2422 p m (SCHEDULE) 20 (is) 21 (a) 20 (pac) 0 (k) -2 (ag) -1 (e) 18 (of) 20 (F) 0 (OR) -3 (TRAN) 19 (and) 20 (C) 20 (subroutines) 21 (designed) 21 (to) 19 (aid) 21 (in) 21 (programming) ks 74 2521 p m (explici) 1 (tly) 20 (parallel) 19 (algorithms) 17 (for) 17 (n) 0 (umerical) 18 (calculations.) 29 (An) 18 (imp) 1 (ortan) 0 (t) 16 (part) 18 (of) 17 (this) 18 (pac) 0 (k) -2 (age) 16 (is) ks 74 2621 p m (the) 17 (pro) 0 (vision) 16 (of) 16 (a) 16 (mec) 0 (hanism) 16 (for) 16 (dynamically) 18 (spa) 0 (wning) 16 (pro) 1 (cesses) 17 (ev) 0 (en) 16 (when) 17 (suc) 0 (h) 16 (a) 16 (capabilit) 0 (y) ks 74 2721 p m (is) 16 (not) 15 (presen) 0 (t) 14 (within) 16 (the) 16 (parallel) 16 (language) 16 (extensions) 16 (pro) 0 (vided) 15 (for) 14 (a) 15 (giv) 0 (en) 15 (mac) 0 (hine.) ks @eop 33 @bop0 cmmi8.300 @sf [<3018078030180440180C0C40180C0C20180C0620180C06000C0606000C0603000C0603008E0703 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0 (um) 0 (b) 1 (er) 15 (of) 16 (splits) ks cmmi10.329 @sf 18 r m (m) s cmr10.329 @sf m (,) 17 (with) ks cmmi10.329 @sf 17 r m (p) s cmr10.329 @sf 15 r m (=) 16 (2) ks cmmi8.300 @sf 1711 1142 p m (m) s cmr10.329 @sf 1760 1157 p m (and) s cmmi10.329 @sf 17 r m (k) s cmr10.329 @sf 17 r m (=) 15 (3) ks 74 1214 p m (\(see) 15 (expression) 16 (for) 15 (w) 0 (ork\).) ks 74 1526 p @beginspecial @setspecial 18945146 14208860 5262540 26773176 34995896 49731010 startTexFig %!PS-Adobe-2.0 %%Creator: sidani %%Title: MATLAB graph %%CreationDate: 07/26/91 06:29:29 %%Pages: 001 %%BoundingBox: 080 407 532 756 %%DocumentFonts: Times-Roman %%DocumentNeededFonts: Times-Roman %%EndComments % MathWorks dictionary /mathworks 50 dict begin % definition operators /bdef {bind def} bind def /xdef {exch def} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot {gsave} bdef /eplot {grestore} bdef % bounding box in default coordinates /dx 0 def /dy 0 def /sides {/dx urx llx sub def /dy ury lly sub def} bdef /llx 0 def /lly 0 def /urx 0 def /ury 0 def /bbox {/ury xdef /urx xdef /lly xdef /llx xdef sides} bdef % orientation switch /por true def /portrait {/por true def} bdef /landscape {/por false def} bdef % coordinate system mappings /px 8.5 72 mul def /py 11.0 72 mul def /port {dx py div dy px div scale} bdef /land {-90.0 rotate dy neg 0 translate dy py div dx px div scale} bdef /csm {llx lly translate por {port} {land} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [0 4] 0 setdash } bdef /DA { [4] 0 setdash } bdef /DD { [0 4 3 4] 0 setdash } bdef % macros for moveto and polyline /M {moveto} bdef /L {{lineto} repeat stroke} bdef % font control /font_spec () def /lfont currentfont def /sfont currentfont def /selfont {/font_spec xdef} bdef /savefont {font_spec findfont exch scalefont def} bdef /LF {lfont setfont} bdef /SF {sfont setfont} bdef % text display /sh {show} bdef /csh {dup stringwidth pop 2 div neg 0 rmoveto show} bdef /rsh {dup stringwidth pop neg 0 rmoveto show} bdef /r90sh {gsave currentpoint translate 90 rotate csh grestore} bdef currentdict end def %dictionary %%EndProlog %%BeginSetup mathworks begin % fonts for text, standard numbers and exponents %%IncludeFont: Times-Roman /Times-Roman selfont /lfont 20 savefont /sfont 14 savefont %line width, line cap, and joint spec .5 setlinewidth 1 setlinecap 1 setlinejoin end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 080 407 532 756 mathworks begin bpage %%EndPageSetup %%BeginObject: graph 1 bplot 80 407 532 756 bbox portrait csm SO 78.09 77.33 757.00 77.33 757.00 570.67 78.09 570.67 78.09 77.33 M 4 L LF 73.09 71.33 M (0) rsh 78.09 159.55 84.83 159.55 M 1 L 750.27 159.55 757.00 159.55 M 1 L 73.09 153.55 M (20) rsh 78.09 241.78 84.83 241.78 M 1 L 750.27 241.78 757.00 241.78 M 1 L 73.09 235.78 M (40) rsh 78.09 324.00 84.83 324.00 M 1 L 750.27 324.00 757.00 324.00 M 1 L 73.09 318.00 M (60) rsh 78.09 406.22 84.83 406.22 M 1 L 750.27 406.22 757.00 406.22 M 1 L 73.09 400.22 M (80) rsh 78.09 488.45 84.83 488.45 M 1 L 750.27 488.45 757.00 488.45 M 1 L 73.09 482.45 M (100) rsh 73.09 564.67 M (120) rsh 78.09 55.33 M (0) csh 175.08 77.33 175.08 82.53 M 1 L 175.08 565.47 175.08 570.67 M 1 L 175.08 55.33 M (20) csh 272.07 77.33 272.07 82.53 M 1 L 272.07 565.47 272.07 570.67 M 1 L 272.07 55.33 M (40) csh 369.05 77.33 369.05 82.53 M 1 L 369.05 565.47 369.05 570.67 M 1 L 369.05 55.33 M (60) csh 466.04 77.33 466.04 82.53 M 1 L 466.04 565.47 466.04 570.67 M 1 L 466.04 55.33 M (80) csh 563.03 77.33 563.03 82.53 M 1 L 563.03 565.47 563.03 570.67 M 1 L 563.03 55.33 M (100) csh 660.01 77.33 660.01 82.53 M 1 L 660.01 565.47 660.01 570.67 M 1 L 660.01 55.33 M (120) csh 757.00 55.33 M (140) csh 87.79 84.38 97.49 90.90 116.89 104.23 155.68 131.00 233.27 184.60 388.45 291.84 698.81 506.33 M 6 L 417.55 14.00 M (p) csh 14.00 324.00 M (speedup) r90sh eplot %%EndObject graph 1 epage end showpage %%Trailer endTexFig @endspecial 74 2524 p m (Figure) 17 (5:) 21 (Predicted) 18 (sp) 1 (eedup) 18 (o) 0 (v) -1 (er) 14 (QR) 17 (in) 17 (terms) 16 (of) 16 (the) 16 (n) 0 (um) 0 (b) 1 (er) 15 (of) 16 (pro) 1 (cessors) ks cmmi10.329 @sf 16 r m (p) s cmr10.329 @sf m (,) 16 (with) ks cmmi10.329 @sf 16 r m (m) s cmr10.329 @sf 14 r m (=) 15 (log) ks cmr8.300 @sf 1914 2535 p m (2) s cmmi10.329 @sf 1941 2524 p m (p) s cmr10.329 @sf 74 2580 p m (and) s cmmi10.329 @sf 16 r m (k) s cmr10.329 @sf 13 r m (=) 13 (3) 15 (\(see) 15 (expression) 16 (for) 15 (w) 0 (ork\).) ks @eop 32 @bop0 32 @bop1 cmr10.329 @sf 1919 -77 p m (32) s 74 159 p @beginspecial @setspecial 18945146 14208860 5262540 26773176 34995896 49731010 startTexFig %!PS-Adobe-2.0 %%Creator: sidani %%Title: MATLAB graph %%CreationDate: 07/26/91 06:27:26 %%Pages: 001 %%BoundingBox: 080 407 532 756 %%DocumentFonts: Times-Roman %%DocumentNeededFonts: Times-Roman %%EndComments % MathWorks dictionary /mathworks 50 dict begin % definition operators /bdef {bind def} bind def /xdef {exch def} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot {gsave} bdef /eplot {grestore} bdef % bounding box in default coordinates /dx 0 def /dy 0 def /sides {/dx urx llx sub def /dy ury lly sub def} bdef /llx 0 def /lly 0 def /urx 0 def /ury 0 def /bbox {/ury xdef /urx xdef /lly xdef /llx xdef sides} bdef % orientation switch /por true def /portrait {/por true def} bdef /landscape {/por false def} bdef % coordinate system mappings /px 8.5 72 mul def /py 11.0 72 mul def /port {dx py div dy px div scale} bdef /land {-90.0 rotate dy neg 0 translate dy py div dx px div scale} bdef /csm {llx lly translate por {port} {land} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [0 4] 0 setdash } bdef /DA { [4] 0 setdash } bdef /DD { [0 4 3 4] 0 setdash } bdef % macros for moveto and polyline /M {moveto} bdef /L {{lineto} repeat stroke} bdef % font control /font_spec () def /lfont currentfont def /sfont currentfont def /selfont {/font_spec xdef} bdef /savefont {font_spec findfont exch scalefont def} bdef /LF {lfont setfont} bdef /SF {sfont setfont} bdef % text display /sh {show} bdef /csh {dup stringwidth pop 2 div neg 0 rmoveto show} bdef /rsh {dup stringwidth pop neg 0 rmoveto show} bdef /r90sh {gsave currentpoint translate 90 rotate csh grestore} bdef currentdict end def %dictionary %%EndProlog %%BeginSetup mathworks begin % fonts for text, standard numbers and exponents %%IncludeFont: Times-Roman /Times-Roman selfont /lfont 20 savefont /sfont 14 savefont %line width, line cap, and joint spec .5 setlinewidth 1 setlinecap 1 setlinejoin end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 080 407 532 756 mathworks begin bpage %%EndPageSetup %%BeginObject: graph 1 bplot 80 407 532 756 bbox portrait csm SO 78.09 77.33 757.00 77.33 757.00 570.67 78.09 570.67 78.09 77.33 M 4 L LF 73.09 71.33 M (10) rsh 78.09 147.81 84.83 147.81 M 1 L 750.27 147.81 757.00 147.81 M 1 L 73.09 141.81 M (20) rsh 78.09 218.28 84.83 218.28 M 1 L 750.27 218.28 757.00 218.28 M 1 L 73.09 212.28 M (30) rsh 78.09 288.76 84.83 288.76 M 1 L 750.27 288.76 757.00 288.76 M 1 L 73.09 282.76 M (40) rsh 78.09 359.24 84.83 359.24 M 1 L 750.27 359.24 757.00 359.24 M 1 L 73.09 353.24 M (50) rsh 78.09 429.72 84.83 429.72 M 1 L 750.27 429.72 757.00 429.72 M 1 L 73.09 423.72 M (60) rsh 78.09 500.19 84.83 500.19 M 1 L 750.27 500.19 757.00 500.19 M 1 L 73.09 494.19 M (70) rsh 73.09 564.67 M (80) rsh 78.09 55.33 M (1) csh 153.53 77.33 153.53 82.53 M 1 L 153.53 565.47 153.53 570.67 M 1 L 153.53 55.33 M (2) csh 228.96 77.33 228.96 82.53 M 1 L 228.96 565.47 228.96 570.67 M 1 L 228.96 55.33 M (3) csh 304.40 77.33 304.40 82.53 M 1 L 304.40 565.47 304.40 570.67 M 1 L 304.40 55.33 M (4) csh 379.83 77.33 379.83 82.53 M 1 L 379.83 565.47 379.83 570.67 M 1 L 379.83 55.33 M (5) csh 455.26 77.33 455.26 82.53 M 1 L 455.26 565.47 455.26 570.67 M 1 L 455.26 55.33 M (6) csh 530.70 77.33 530.70 82.53 M 1 L 530.70 565.47 530.70 570.67 M 1 L 530.70 55.33 M (7) csh 606.13 77.33 606.13 82.53 M 1 L 606.13 565.47 606.13 570.67 M 1 L 606.13 55.33 M (8) csh 681.57 77.33 681.57 82.53 M 1 L 681.57 565.47 681.57 570.67 M 1 L 681.57 55.33 M (9) csh 757.00 55.33 M (10) csh 78.09 127.84 153.53 170.13 228.96 212.41 304.40 254.70 379.83 296.98 455.26 339.27 530.70 381.56 606.13 423.84 681.57 466.13 757.00 508.41 M 9 L DO 78.09 183.05 153.53 183.05 228.96 183.05 304.40 183.05 379.83 183.05 455.26 183.05 530.70 183.05 606.13 183.05 681.57 183.05 757.00 183.05 M 9 L 417.55 14.00 M (k) csh 14.00 324.00 M (coefficient) r90sh eplot %%EndObject graph 1 epage end showpage %%Trailer endTexFig @endspecial 74 1157 p m (Figure) 17 (2:) 23 (V) -3 (ariation) 16 (of) 17 (the) 17 (Co) 1 (e\016cien) 0 (t) 16 (of) ks cmmi10.329 @sf 16 r m (n) s cmr8.300 @sf 919 1142 p m (3) s cmr10.329 @sf 956 1157 p m (in) 18 (w) 0 (ork) 15 (estimate) 16 (mo) 1 (del) 18 (in) 18 (terms) 16 (of) 16 (the) 17 (n) 0 (um) 0 (b) 1 (er) 16 (of) ks 74 1214 p m (steps) s cmmi10.329 @sf 15 r m (k) s cmr10.329 @sf 1 r m (,) 15 (with) ks cmmi10.329 @sf 16 r m (m) s cmr10.329 @sf 12 r m (=) 13 (1,) 15 (and) ks cmmi10.329 @sf 15 r m (p) s cmr10.329 @sf 13 r m (=) 13 (1) 14 (\(see) 16 (expression) 16 (for) 14 (w) 0 (ork\).) ks 74 1526 p @beginspecial @setspecial 18945146 14208860 5262540 26773176 34995896 49731010 startTexFig %!PS-Adobe-2.0 %%Creator: sidani %%Title: MATLAB graph %%CreationDate: 07/26/91 06:28:19 %%Pages: 001 %%BoundingBox: 080 407 532 756 %%DocumentFonts: Times-Roman %%DocumentNeededFonts: Times-Roman %%EndComments % MathWorks dictionary /mathworks 50 dict begin % definition operators /bdef {bind def} bind def /xdef {exch def} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot {gsave} bdef /eplot {grestore} bdef % bounding box in default coordinates /dx 0 def /dy 0 def /sides {/dx urx llx sub def /dy ury lly sub def} bdef /llx 0 def /lly 0 def /urx 0 def /ury 0 def /bbox {/ury xdef /urx xdef /lly xdef /llx xdef sides} bdef % orientation switch /por true def /portrait {/por true def} bdef /landscape {/por false def} bdef % coordinate system mappings /px 8.5 72 mul def /py 11.0 72 mul def /port {dx py div dy px div scale} bdef /land {-90.0 rotate dy neg 0 translate dy py div dx px div scale} bdef /csm {llx lly translate por {port} {land} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [0 4] 0 setdash } bdef /DA { [4] 0 setdash } bdef /DD { [0 4 3 4] 0 setdash } bdef % macros for moveto and polyline /M {moveto} bdef /L {{lineto} repeat stroke} bdef % font control /font_spec () def /lfont currentfont def /sfont currentfont def /selfont {/font_spec xdef} bdef /savefont {font_spec findfont exch scalefont def} bdef /LF {lfont setfont} bdef /SF {sfont setfont} bdef % text display /sh {show} bdef /csh {dup stringwidth pop 2 div neg 0 rmoveto show} bdef /rsh {dup stringwidth pop neg 0 rmoveto show} bdef /r90sh {gsave currentpoint translate 90 rotate csh grestore} bdef currentdict end def %dictionary %%EndProlog %%BeginSetup mathworks begin % fonts for text, standard numbers and exponents %%IncludeFont: Times-Roman /Times-Roman selfont /lfont 20 savefont /sfont 14 savefont %line width, line cap, and joint spec .5 setlinewidth 1 setlinecap 1 setlinejoin end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 080 407 532 756 mathworks begin bpage %%EndPageSetup %%BeginObject: graph 1 bplot 80 407 532 756 bbox portrait csm SO 78.09 77.33 757.00 77.33 757.00 570.67 78.09 570.67 78.09 77.33 M 4 L LF 73.09 71.33 M (29) rsh 78.09 132.15 84.83 132.15 M 1 L 750.27 132.15 757.00 132.15 M 1 L 73.09 126.15 M (29.2) rsh 78.09 186.96 84.83 186.96 M 1 L 750.27 186.96 757.00 186.96 M 1 L 73.09 180.96 M (29.4) rsh 78.09 241.78 84.83 241.78 M 1 L 750.27 241.78 757.00 241.78 M 1 L 73.09 235.78 M (29.6) rsh 78.09 296.59 84.83 296.59 M 1 L 750.27 296.59 757.00 296.59 M 1 L 73.09 290.59 M (29.8) rsh 78.09 351.41 84.83 351.41 M 1 L 750.27 351.41 757.00 351.41 M 1 L 73.09 345.41 M (30) rsh 78.09 406.22 84.83 406.22 M 1 L 750.27 406.22 757.00 406.22 M 1 L 73.09 400.22 M (30.2) rsh 78.09 461.04 84.83 461.04 M 1 L 750.27 461.04 757.00 461.04 M 1 L 73.09 455.04 M (30.4) rsh 78.09 515.85 84.83 515.85 M 1 L 750.27 515.85 757.00 515.85 M 1 L 73.09 509.85 M (30.6) rsh 73.09 564.67 M (30.8) rsh 78.09 55.33 M (1) csh 153.53 77.33 153.53 82.53 M 1 L 153.53 565.47 153.53 570.67 M 1 L 153.53 55.33 M (2) csh 228.96 77.33 228.96 82.53 M 1 L 228.96 565.47 228.96 570.67 M 1 L 228.96 55.33 M (3) csh 304.40 77.33 304.40 82.53 M 1 L 304.40 565.47 304.40 570.67 M 1 L 304.40 55.33 M (4) csh 379.83 77.33 379.83 82.53 M 1 L 379.83 565.47 379.83 570.67 M 1 L 379.83 55.33 M (5) csh 455.26 77.33 455.26 82.53 M 1 L 455.26 565.47 455.26 570.67 M 1 L 455.26 55.33 M (6) csh 530.70 77.33 530.70 82.53 M 1 L 530.70 565.47 530.70 570.67 M 1 L 530.70 55.33 M (7) csh 606.13 77.33 606.13 82.53 M 1 L 606.13 565.47 606.13 570.67 M 1 L 606.13 55.33 M (8) csh 681.57 77.33 681.57 82.53 M 1 L 681.57 565.47 681.57 570.67 M 1 L 681.57 55.33 M (9) csh 757.00 55.33 M (10) csh 78.09 123.01 153.53 431.35 228.96 508.43 304.40 527.70 379.83 532.52 455.26 533.72 530.70 534.03 606.13 534.10 681.57 534.12 757.00 534.12 M 9 L 417.55 14.00 M (m) csh 14.00 324.00 M (coefficient) r90sh eplot %%EndObject graph 1 epage end showpage %%Trailer endTexFig @endspecial 74 2524 p m (Figure) 17 (3:) 23 (V) -3 (ariation) 16 (of) 17 (the) 17 (Co) 1 (e\016cien) 0 (t) 16 (of) ks cmmi10.329 @sf 16 r m (n) s cmr8.300 @sf 919 2509 p m (3) s cmr10.329 @sf 956 2524 p m (in) 18 (w) 0 (ork) 15 (estimate) 16 (mo) 1 (del) 18 (in) 18 (terms) 16 (of) 16 (the) 17 (n) 0 (um) 0 (b) 1 (er) 16 (of) ks 74 2580 p m (splits) s cmmi10.329 @sf 16 r m (m) s cmr10.329 @sf m (,) 15 (with) ks cmmi10.329 @sf 16 r m (k) s cmr10.329 @sf 13 r m (=) 13 (3) 15 (and) ks cmmi10.329 @sf 16 r m (p) s cmr10.329 @sf 12 r m (=) 13 (1) 15 (\(see) 15 (expression) 16 (for) 15 (w) 0 (ork\)) -1 (.) ks @eop 31 @bop0 cmmi8.300 @sf [ 16 20 0 6 18] 112 @dc cmsy10.329 @sf [<0000000400000000020000000002000000000100000000008000000000400000000020FFFFFFFF FCFFFFFFFFFC000000002000000000400000000080000000010000000002000000000200000000 0400> 38 16 -3 -3 45] 33 @dc 31 @bop1 cmr10.329 @sf 1919 -77 p m (31) s 74 67 p m (But) s cmmi10.329 @sf 15 r m (p) s cmsy8.300 @sf 187 52 p m (0) s cmr10.329 @sf 212 67 p m (=) 13 (2) ks cmmi8.300 @sf 283 52 p m (m) s cmr10.329 @sf 331 67 p m (and) 15 (therefore) ks cmmi10.329 @sf 15 r m (p) s cmsy8.300 @sf 633 52 p m (0) s cmr8.300 @sf m (2) s cmr10.329 @sf 675 67 p m (=) 13 (4) ks cmmi8.300 @sf 746 52 p m (m) s cmr10.329 @sf 794 67 p m (and) 15 (hence) ks cmmi10.329 @sf 611 212 p save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmmi8.300 @sf 654 219 p m (p) s cmr10.329 @sf 686 212 p m (=) s cmmi10.329 @sf 739 182 p m (n) s cmr8.300 @sf 766 167 p m (3) s 739 202 p 48 2 ru cmmi10.329 @sf 751 244 p m (p) s cmex10.300 @sf 799 153 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmr10.329 @sf 834 182 p m (16) s 834 202 p 46 2 ru 846 244 p m (3) s 895 212 p m (+) 10 (8) ks cmmi10.329 @sf m (k) s cmr10.329 @sf 11 r m (+) 11 (\(18) ks cmsy10.329 @sf 9 r m (\000) s cmr10.329 @sf 10 r m (8) s cmmi10.329 @sf m (k) s cmr10.329 @sf 1 r m (\)) s 1249 182 p m (1) s 1233 202 p 57 2 ru 1233 244 p m (4) s cmmi8.300 @sf 1256 232 p m (m) s cmex10.300 @sf 1294 153 p save [ 20 99 -1 97 31] 19 @pc restore cmmi10.329 @sf 1332 212 p m (;) s cmr10.329 @sf 1883 212 p m (\(13\)) s 74 358 p m (where) 19 (for) 19 (ease) 19 (of) 19 (reference) 19 (w) 0 (e) 18 (rede\014ne) 21 (the) 19 (v) -2 (arious) 18 (parameters:) ks cmmi10.329 @sf 27 r m (n) s cmr10.329 @sf 19 r m (is) 20 (the) 19 (order) 19 (of) 19 (the) 19 (matrix;) ks cmmi10.329 @sf 74 457 p m (p) s cmr10.329 @sf 17 r m (is) 18 (the) 17 (n) 0 (um) 0 (b) 1 (er) 15 (of) 17 (pro) 1 (cessors;) ks cmmi10.329 @sf 17 r m (k) s cmr10.329 @sf 18 r m (is) 18 (the) 17 (a) 0 (v) -1 (erag) -1 (e) 16 (n) 0 (um) -1 (b) 1 (er) 16 (of) 16 (Newton) 17 (iterations) 17 (needed) 19 (b) 1 (efore) 17 (an) ks 74 557 p m (eigenpair) 17 (is) 15 (accepted;) 16 (and) ks cmmi10.329 @sf 15 r m (m) s cmr10.329 @sf 15 r m (is) 16 (the) 15 (n) 0 (um) 0 (b) 1 (er) 14 (of) 15 (zeros) 15 (in) 0 (tro) 1 (duced) 15 (on) 15 (the) 15 (sub) 1 (diagonal.) ks 124 698 p m (The) 21 (cost) 20 (of) 20 (getting) 20 (the) 21 (eigen) 0 (v) -2 (alues) 20 (and) 21 (eigen) 0 (v) 0 (ectors) 18 (b) 0 (y) 20 (the) 20 (QR) 22 (algorithm) 20 (is) 21 (15) ks cmmi10.329 @sf m (n) s cmr8.300 @sf 1793 683 p m (3) s cmr10.329 @sf 1833 698 p m ([) 0 (8) ks 1869 698 p m (].) 35 (A) ks 74 798 p m (reasonable) 19 (v) -2 (alue) 18 (for) ks cmmi10.329 @sf 18 r m (k) s cmr10.329 @sf 19 r m (is) 19 (3,) 19 (ho) 0 (w) -1 (ev) -1 (er) 16 (there) 19 (are) 17 (cases) 19 (when) ks cmmi10.329 @sf 19 r m (k) s cmr10.329 @sf 19 r m (is) 19 (2) 18 (or) 17 (less.) 30 (There) 19 (are) 18 (also) 18 (cases) ks 74 897 p m (where) s cmmi10.329 @sf 16 r m (k) s cmr10.329 @sf 16 r m (is) 16 (larger) 15 (than) 15 (3,) 14 (mostly) 15 (with) 16 (matrices) 15 (of) 15 (small) 16 (order) 14 (or) 15 (defectiv) 0 (e) 15 (matrices.) ks 124 1039 p m (It) 19 (is) 19 (easy) 18 (to) 18 (v) 0 (erify) 18 (that) 17 (for) ks cmmi10.329 @sf 18 r m (k) s cmr10.329 @sf 20 r m (=) 18 (2) 18 (and) 19 (for) ks cmmi10.329 @sf 18 r m (m) s cmr10.329 @sf 18 r m (=) 18 (1) 19 (\(one) 18 (split\)) 19 (the) 19 (mo) 1 (del) 19 (for) 18 (the) 19 (cost) 18 (of) 18 (the) ks 74 1138 p m (algorithm) 19 (predicts) 20 (that) 18 (a) 18 (sequen) 0 (tial) 19 (implemen) 0 (tation) 19 (of) 18 (our) 19 (algorithm) 19 (is) 19 (faster) 18 (than) 18 (R) 0 (G.) 18 (Our) ks 74 1238 p m (mo) 1 (del) 13 (predicts) 12 (that) 11 (a) 11 (sequen) 0 (tial) 12 (implemen) 0 (tation) 12 (of) 11 (our) 11 (algorithm) 12 (is) 12 (slo) 0 (w) -1 (er) 10 (than) 11 (R) 0 (G) 11 (for) 10 (problems) ks 74 1337 p m (where) s cmmi10.329 @sf 19 r m (k) s cmr10.329 @sf 19 r m (equals) 19 (or) 18 (exceeds) 19 (2) 18 (\(see) 18 (Fig.) 18 (2\).) 28 (Here) 19 (are) 18 (some) 18 (sample) 19 (v) -2 (alues) 18 (of) ks cmmi10.329 @sf 18 r save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmmi8.300 @sf 1629 1344 p m (p) s cmr10.329 @sf 1649 1337 p m (,) 18 (assuming) 19 (that) ks cmmi10.329 @sf 74 1437 p m (k) s cmr10.329 @sf 15 r m (=) 14 (3) 15 (and) ks cmmi10.329 @sf 16 r m (p) s cmr10.329 @sf 14 r m (=) s cmmi10.329 @sf 14 r m (p) s cmsy8.300 @sf 398 1422 p m (0) s cmr10.329 @sf 423 1437 p m (=) 14 (2) ks cmmi8.300 @sf 495 1422 p m (m) s cmr10.329 @sf 528 1437 p m (.) 22 (whic) 0 (h) 15 (means) 16 (that) 15 (the) 16 (original) 17 (problem) 16 (is) 16 (sub) 1 (divi) 1 (ded) 18 (in) 0 (to) 15 (a) 15 (n) 0 (um) 0 (b) 1 (er) 14 (of) ks 74 1537 p m (problems) 16 (equal) 16 (to) 14 (the) 16 (n) 0 (um) 0 (b) 1 (er) 13 (of) 15 (a) 0 (v) -2 (ailable) 15 (pro) 1 (cessors.) ks cmmi10.329 @sf 447 1682 p m (p) s cmr10.329 @sf 13 r m (=) 13 (128) ks cmsy10.329 @sf 11 r m (!) s cmmi10.329 @sf 13 r save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmmi8.300 @sf 712 1689 p m (p) s cmr10.329 @sf 745 1682 p m (=) 13 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf m (2291) s cmmi10.329 @sf m (n) s cmr8.300 @sf 948 1664 p m (3) s cmr10.329 @sf 991 1682 p m (;) s cmmi10.329 @sf 33 r m (p) s cmr10.329 @sf 12 r m (=) 13 (1024) ks cmsy10.329 @sf 12 r m (!) s cmmi10.329 @sf 13 r save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmmi8.300 @sf 1325 1689 p m (p) s cmr10.329 @sf 1357 1682 p m (=) 13 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf m (0286) s cmmi10.329 @sf m (n) s cmr8.300 @sf 1560 1664 p m (3) s cmmi10.329 @sf 1579 1682 p m (:) s cmr10.329 @sf 74 1827 p m (Here) 16 (w) 0 (e) 14 (ha) 0 (v) 0 (e) 13 (assumed) 16 (that) 15 (the) 15 (problem) 16 (is) 16 (large) 16 (enough) 16 (to) 14 (allo) 0 (w) 15 (the) 16 (e\016cien) 0 (t) 15 (use) 16 (of) 15 (that) 15 (man) 0 (y) ks 74 1927 p m (pro) 1 (cessors.) 28 (Note) 18 (that) 17 (the) 18 (ratio) 17 (of) 18 (the) 18 (w) 0 (ork) 16 (estimate) 18 (from) 17 (our) 18 (mo) 1 (del) 18 (to) 18 (the) 18 (w) 0 (ork) 16 (estimate) 18 (of) ks 74 2026 p m (QR) 16 (is) 15 (indep) 1 (e) 1 (nden) 0 (t) 16 (of) ks cmmi10.329 @sf 14 r m (n) s cmr10.329 @sf m (.) 21 (This) 15 (is) 16 (due) 15 (to) 15 (the) 15 (simplifying) 17 (assumption) 15 (on) ks cmmi10.329 @sf 15 r m (k) s cmr10.329 @sf 16 r m (made) 15 (at) 15 (the) 15 (b) 1 (eginning) ks 74 2126 p m (of) 16 (this) 17 (section.) 24 (That) 15 (assumption) 17 (has) 16 (in) 17 (e\013ect) 16 (\\hidden") 18 (the) 16 (dep) 1 (enden) 1 (cy) 18 (on) ks cmmi10.329 @sf 16 r m (n) s cmr10.329 @sf 17 r m (of) 16 (the) 16 (co) 1 (e\016cien) 0 (t) ks 74 2226 p m (of) s cmmi10.329 @sf 16 r m (n) s cmr8.300 @sf 154 2211 p m (3) s cmr10.329 @sf 190 2226 p m (in) 17 (our) 15 (mo) 1 (del.) 23 (Figures) 17 (2,) 15 (3,) 16 (4) 15 (and) 17 (5) 15 (sho) 0 (w) 15 (plots) 16 (of) 15 (the) 17 (w) 0 (ork) 14 (estimate) 15 (for) 16 (v) -2 (arious) 15 (v) -2 (alues) 17 (of) ks 74 2325 p m (the) 15 (parameters) 15 (in) 0 (v) 0 (olv) -1 (ed.) ks 124 2466 p m (W) -3 (e) 11 (note) 11 (lastly) 12 (that) 11 (the) 12 (cost) 11 (of) 11 (our) 12 (algorithm) 11 (will) 14 (increase) 12 (when) 12 (the) 12 (matrix) 11 (or) 11 (the) 12 (subproblems) ks 74 2566 p m (obtained) 13 (in) 14 (the) 12 (divide) 15 (pro) 1 (cess) 12 (are) 13 (ill-condi) 1 (tioned) 15 (\(see) 12 (section) 13 (5) 12 (and) 13 ([) 0 (11) ks 1457 2566 p m (]\).) 18 (F) -3 (urthermore,) 12 (rep) 1 (eated) ks 74 2666 p m (de\015ations) 16 (will) 17 (also) 15 (con) 0 (tribute) 15 (to) 14 (an) 15 (increase) 16 (in) 16 (the) 16 (cost.) ks @eop 30 @bop0 cmmi10.329 @sf [<01E000031800060400060300C601002E00001E00000E00000E00000E00000E00000F00000E8000 0E400007200007200007100007080003880003840003840001820001C20000C10000C100006100 006080003080003080001880000C80000700> 17 32 0 0 19] 96 @dc [<1FC020304008E004F006F00670070007001F01FE03FC07F807800E000606060706030301018200 7C> 16 20 -2 0 21] 115 @dc cmmi8.300 @sf [<03800460081088007800180018001C001A001A000D000C800C400C400620061002100310010801 88008800480030> 13 23 0 0 14] 96 @dc cmmi10.329 @sf [<0E00190038803840384038401C201C001C000E000E00070007008700438043804380238013000E 00000000000000000000000000000000C001E001E000E0> 11 31 -2 0 16] 105 @dc cmr8.300 @sf [ 22 10 -2 -3 27] 61 @dc cmr6.300 @sf [<1F0060808040C060C0600060004000800F000180008000C060C060C021801F00> 11 16 -1 0 15] 51 @dc 1.000000 /cmsy6.300 @newfont cmsy6.300 @sf [ 6 13 -2 -1 9] 48 @dc cmmi8.300 @sf [<70D0C8C8C8C06060606030303030181818180C0C0C0C3E> 7 23 -2 0 11] 108 @dc cmsy10.329 @sf [<70F8F8F870> 5 5 -4 -9 13] 1 @dc 30 @bop1 cmr10.329 @sf 1919 -77 p m (30) s 124 67 p m (The) 22 (cost) 21 (of) 22 (computing) 22 (one) 22 (correction) 22 (at) 22 (the) 22 (lev) 0 (el) ks cmmi10.329 @sf 22 r m (`) s cmr10.329 @sf 22 r m (is) 22 (roughly) 22 (6) ks cmmi10.329 @sf m (s) s cmr8.300 @sf 1490 52 p m (2) s cmmi8.300 @sf 1490 80 p m (`) s cmr10.329 @sf 1510 67 p m (:) 33 (indeed,) 25 (one) 22 (Newton) ks 74 167 p m (iteration) 14 (in) 0 (v) 0 (olv) 0 (es) 12 (the) 14 (solution) 14 (of) 14 (a) 13 (linear) 15 (system) 14 (that) 13 (is) 14 (upp) 1 (er-Hessen) 0 (b) 1 (erg,) 15 (but) 14 (for) 13 (p) 1 (ossible) 16 (non-) ks 74 266 p m (zeros) 16 (in) 18 (the) 16 (last) 17 (ro) 0 (w;) 15 (the) 16 (order) 16 (of) 17 (this) 16 (linear) 18 (system) 16 (is) ks cmmi10.329 @sf 17 r m (s) s cmmi8.300 @sf 1203 273 p m (`) s cmr10.329 @sf 1231 266 p m (+) 11 (1.) 24 (Therefore) 16 (2) 16 (m) 0 (ultipliers) 18 (at) 16 (most) ks 74 366 p m (need) 20 (b) 1 (e) 20 (computed) 19 (p) 1 (er) 19 (column) 20 (and,) 20 (when) 19 (up) 1 (dating) 20 (the) 19 (matrix,) 20 (eac) 0 (h) 18 (of) 18 (these) 19 (will) 21 (b) 1 (e) 20 (used) 19 (in) ks 74 466 p m (2\() s cmmi10.329 @sf m (s) s cmmi8.300 @sf 136 473 p m (`) s cmr10.329 @sf 159 466 p m (+) 7 (1) ks cmsy10.329 @sf 7 r m (\000) s cmmi10.329 @sf 7 r m (i) s cmr10.329 @sf m (\)) 12 (m) 0 (ultiplications) 14 (and) 14 (additions,) 14 (where) ks cmmi10.329 @sf 14 r m (i) s cmr10.329 @sf 13 r m (is) 14 (the) 13 (index) 15 (of) 13 (the) 13 (column.) 21 (The) 13 (factorization) ks 74 565 p m (of) 13 (the) 14 (Jacobian) 14 (requires) 14 (then) 14 (2) ks cmmi10.329 @sf m (s) s cmr8.300 @sf 704 550 p m (2) s cmmi8.300 @sf 704 579 p m (`) s cmr10.329 @sf 737 565 p m (op) 1 (erations) 13 (in) 14 (addition) 15 (to) ks cmmi10.329 @sf 12 r m (O) s cmr10.329 @sf 1 r m (\() s cmmi10.329 @sf m (s) s cmmi8.300 @sf 1313 572 p m (`) s cmr10.329 @sf 1330 565 p m (\)) 13 (op) 1 (erations) 13 (\(includi) 1 (ng) 15 (divisions) ks 74 665 p m (and) 18 (comparisons\).) 29 (The) 18 (forw) 0 (ard) 16 (solv) 0 (e) 17 (is) ks cmmi10.329 @sf 19 r m (O) s cmr10.329 @sf 1 r m (\() s cmmi10.329 @sf m (s) s cmmi8.300 @sf 972 672 p m (`) s cmr10.329 @sf 988 665 p m (\)) 18 (w) 0 (ork) 16 (and) 19 (is) 18 (negligibl) 1 (e.) 31 (The) 18 (bac) 0 (ksolv) 0 (e) 16 (requires) ks cmmi10.329 @sf 74 765 p m (s) s cmr8.300 @sf 95 750 p m (2) s cmmi8.300 @sf 95 778 p m (`) s cmr10.329 @sf 132 765 p m (op) 1 (erations) 18 (and) 17 (computing) 18 (the) 18 (residual) 18 (requires) 18 (another) ks cmmi10.329 @sf 17 r m (s) s cmr8.300 @sf 1288 750 p m (2) s cmmi8.300 @sf 1288 778 p m (`) s cmr10.329 @sf 1326 765 p m (op) 1 (erations.) 26 (Therefore) 17 (for) 17 (a) 17 (real) ks 74 864 p m (curren) 0 (t) 12 (appro) 0 (ximation) 13 (one) 13 (correction) 14 (comes) 13 (at) 13 (the) 13 (cost) 13 (of) 13 (4) ks cmmi10.329 @sf m (s) s cmr8.300 @sf 1272 849 p m (2) s cmmi8.300 @sf 1272 877 p m (`) s cmr10.329 @sf 1292 864 p m (.) 19 (F) -3 (or) 12 (a) 13 (complex) 14 (curren) 0 (t) 12 (eigenpair,) ks 74 964 p m (this) 15 (b) 1 (ecomes) 16 (16) ks cmmi10.329 @sf m (s) s cmr8.300 @sf 410 949 p m (2) s cmmi8.300 @sf 410 977 p m (`) s cmr10.329 @sf 444 964 p m (since) 16 (the) 14 (dominan) 0 (t) 14 (op) 1 (erations) 15 (are) 14 (a) 15 (roughly) 15 (equal) 15 (n) 0 (um) 0 (b) 1 (er) 13 (of) 15 (m) 0 (ultiplications) ks 74 1063 p m (and) 21 (additions.) 36 (Since,) 22 (as) 20 (w) 0 (e) 19 (indicated) 22 (in) 21 (section) 21 (2,) 21 (only) 21 (one) 20 (of) 20 (a) 20 (conjugate) 20 (pair) 20 (of) 20 (complex) ks 74 1163 p m (eigenpairs) 19 (need) 19 (b) 1 (e) 18 (corrected,) 18 (w) 0 (e) 16 (can) 18 (assume) 17 (that) 17 (8) ks cmmi10.329 @sf m (s) s cmr8.300 @sf 1134 1148 p m (2) s cmmi8.300 @sf 1134 1176 p m (`) s cmr10.329 @sf 1172 1163 p m (op) 1 (erations) 18 (are) 17 (required) 19 (for) 17 (correcting) 17 (a) ks 74 1263 p m (complex) 18 (eigenpair.) 25 (Assuming) 18 (again) 16 (that) 16 (the) 17 (matrix) 16 (has) 17 (an) 17 (equal) 17 (n) 0 (um) 0 (b) 1 (er) 15 (of) 16 (real) 17 (and) 17 (complex) ks 74 1362 p m (eigen) 0 (v) -2 (alues,) 16 (our) 16 (estimate) 17 (for) 15 (the) 17 (amoun) 0 (t) 14 (of) 16 (w) 0 (ork) 14 (required) 18 (for) 15 (computing) 17 (one) 17 (correction) 16 (at) 16 (the) ks 74 1462 p m (lev) 0 (el) ks cmmi10.329 @sf 16 r m (`) s cmr10.329 @sf 15 r m (b) 1 (ecomes) 16 (6) ks cmmi10.329 @sf m (s) s cmr8.300 @sf 437 1447 p m (2) s cmmi8.300 @sf 437 1475 p m (`) s cmr10.329 @sf 471 1462 p m (op) 1 (erations.) ks 124 1603 p m (W) -3 (e) 15 (shall) 18 (use) ks cmmi8.300 @sf 396 1586 p m (n) s 396 1593 p 22 2 ru 398 1619 p m (p) s cmr10.329 @sf 438 1603 p m (initial) 19 (guesses) 16 (to) 16 (start) ks cmmi8.300 @sf 901 1586 p m (n) s 901 1593 p 22 2 ru 903 1619 p m (p) s cmr10.329 @sf 944 1603 p m (Newton) 16 (pro) 1 (cesses) 17 (on) 16 (eac) 0 (h) 16 (pro) 1 (cessor.) 23 (W) -3 (e) 16 (no) 0 (w) 14 (ha) 0 (v) 0 (e) ks 74 1703 p m (the) 16 (follo) 0 (wing) 15 (w) 0 (ork) 14 (estimate) 16 (on) 15 (one) 16 (pro) 1 (cessor,) 15 (assuming) 16 (all) 17 (pro) 1 (cessors) 15 (share) 16 (equally) 17 (the) 15 (cost) 16 (of) ks 74 1802 p m (all) 16 (the) 16 (stages) 14 (of) 15 (the) 15 (algorithm) ks cmmi10.329 @sf 508 1934 p save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmmi8.300 @sf 551 1941 p m (p) s cmr10.329 @sf 584 1934 p m (=) s 637 1904 p m (10) s cmmi10.329 @sf m (n) s cmr8.300 @sf 710 1889 p m (3) s 637 1924 p 93 2 ru cmr10.329 @sf 660 1965 p m (3) s cmmi10.329 @sf m (p) s cmr10.329 @sf 744 1934 p m (+) 11 (18) ks cmex10.300 @sf 844 1875 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmmi10.329 @sf 878 1904 p m (p) s cmsy8.300 @sf 901 1889 p m (0) s 878 1924 p 35 2 ru cmmi10.329 @sf 884 1965 p m (p) s cmex10.300 @sf 918 1875 p save [ 20 99 -1 97 31] 19 @pc restore 956 1875 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmmi10.329 @sf 995 1904 p m (n) s 991 1924 p 35 2 ru 991 1965 p m (p) s cmsy8.300 @sf 1014 1953 p m (0) s cmex10.300 @sf 1031 1875 p save [ 20 99 -1 97 31] 19 @pc restore cmr8.300 @sf 1061 1886 p m (3) s cmr10.329 @sf 1091 1934 p m (+) s cmmi8.300 @sf 1137 1881 p m (m) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmex10.300 @sf 1145 1894 p save [ 55 58 -2 58 60] 88 @pc restore cmmi8.300 @sf 1145 1986 p m (`) s cmr8.300 @sf m (=0) s cmr10.329 @sf 1221 1934 p m (6\() s cmmi10.329 @sf 1267 1904 p m (n) s 1267 1924 p 28 2 ru 1269 1965 p m (p) s cmr10.329 @sf 1298 1934 p m (\)) s cmmi10.329 @sf m (k) 1 (s) ks cmr8.300 @sf 1362 1916 p m (2) s cmmi8.300 @sf 1362 1945 p m (`) s cmr10.329 @sf 1392 1934 p m (+) 11 (2) ks cmmi10.329 @sf 1466 1904 p m (n) s cmr8.300 @sf 1493 1889 p m (3) s 1466 1924 p 48 2 ru cmmi10.329 @sf 1477 1965 p m (p) s 1517 1934 p m (;) s cmr10.329 @sf 74 2072 p m (where:) s cmr8.300 @sf 237 2055 p m (10) s cmmi8.300 @sf m (n) s cmr6.300 @sf 294 2044 p m (3) s 237 2062 p 74 2 ru cmr8.300 @sf 256 2088 p m (3) s cmmi8.300 @sf m (p) s cmr10.329 @sf 335 2072 p m (is) 21 (the) 19 (pro) 1 (cessor's) 19 (con) 0 (tribution) 19 (to) 19 (the) 20 (reduction) 20 (of) 20 (the) 19 (original) 21 (matrix) 19 (to) 19 (upp) 1 (er-) ks 74 2172 p m (Hessen) 0 (b) 1 (erg) 13 (form;) 14 (18) ks cmex10.300 @sf 483 2125 p save [<0006000C001800300070006000C001C0018003800300070006000E000C001C001C001800380038 0038003000700070007000700070007000E000E000E000E000E000E000E000E000E000E000E000 E000E000E000E000E000E000E000700070007000700070007000300038003800380018001C001C 000C000E000600070003000380018001C000C00060007000300018000C0006> 15 74 -8 72 25] 16 @pc restore cmmi8.300 @sf 511 2153 p m (p) s cmsy6.300 @sf 529 2142 p m (0) s 511 2163 p 29 2 ru cmmi8.300 @sf 517 2188 p m (p) s cmex10.300 @sf 545 2125 p save [ 15 74 -1 72 25] 17 @pc restore 578 2125 p save [<0006000C001800300070006000C001C0018003800300070006000E000C001C001C001800380038 0038003000700070007000700070007000E000E000E000E000E000E000E000E000E000E000E000 E000E000E000E000E000E000E000700070007000700070007000300038003800380018001C001C 000C000E000600070003000380018001C000C00060007000300018000C0006> 15 74 -8 72 25] 16 @pc restore cmmi8.300 @sf 611 2155 p m (n) s 607 2162 p 29 2 ru 607 2188 p m (p) s cmsy6.300 @sf 625 2180 p m (0) s cmex10.300 @sf 641 2125 p save [ 15 74 -1 72 25] 17 @pc restore cmr8.300 @sf 666 2136 p m (3) s cmr10.329 @sf 700 2172 p m (is) 14 (the) 14 (cost) 13 (of) 13 (applying) 16 (the) 13 (QR) 15 (algrithm) 14 (to) ks cmmi8.300 @sf 1549 2153 p m (p) s cmsy6.300 @sf 1567 2142 p m (0) s 1549 2163 p 29 2 ru cmmi8.300 @sf 1555 2188 p m (p) s cmr10.329 @sf 1597 2172 p m (matrices) 14 (of) 13 (size) ks cmmi8.300 @sf 1921 2155 p m (n) s 1918 2162 p 29 2 ru 1918 2188 p m (p) s cmsy6.300 @sf 1936 2180 p m (0) s cmr10.329 @sf 1951 2172 p m (;) s cmex10.300 @sf 74 2240 p save [ 39 42 -2 42 44] 80 @pc restore cmmi8.300 @sf 118 2253 p m (m) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmmi8.300 @sf 118 2285 p m (`) s cmr8.300 @sf m (=0) s cmr10.329 @sf 204 2271 p m (6\() s cmmi8.300 @sf 250 2254 p m (n) s 250 2261 p 22 2 ru 252 2287 p m (p) s cmr10.329 @sf 276 2271 p m (\)) s cmmi10.329 @sf m (k) 1 (s) ks cmr8.300 @sf 340 2256 p m (2) s cmmi8.300 @sf 340 2285 p m (l) s cmr10.329 @sf 375 2271 p m (is) 15 (the) 15 (cost) 15 (of) 15 (solving) ks cmmi10.329 @sf 16 r m (k) s cmr10.329 @sf 16 r m (linear) 16 (systems) 15 (with) 15 (matrices) 15 (of) 15 (size) ks cmmi10.329 @sf 16 r m (s) s cmmi8.300 @sf 1576 2278 p m (`) s cmr10.329 @sf 1593 2271 p m (,) 14 (rep) 1 (eating) 16 (this) 16 (for) ks cmmi8.300 @sf 79 2354 p m (n) s 79 2361 p 22 2 ru 81 2387 p m (p) s cmr10.329 @sf 119 2371 p m (initial) 15 (guesses) 13 (and) 13 (for) ks cmmi10.329 @sf 13 r m (`) s cmr10.329 @sf 12 r m (=) 13 (0) ks cmmi10.329 @sf m (;) s cmsy10.329 @sf 8 r m (\001) 8 (\001) 8 (\001) ks cmmi10.329 @sf 740 2371 p m (;) 8 (m) ks cmsy10.329 @sf 6 r m (\000) s cmr10.329 @sf 6 r m (1;) 12 (2) ks cmmi8.300 @sf 924 2354 p m (n) s cmr6.300 @sf 945 2343 p m (3) s 924 2361 p 39 2 ru cmmi8.300 @sf 934 2387 p m (p) s cmr10.329 @sf 980 2371 p m (is) 14 (the) 13 (pro) 1 (cessor's) 13 (con) 0 (tribution) 13 (to) 12 (the) 13 (computation) ks 74 2471 p m (of) 17 (the) 18 (eigen) 0 (v) 0 (ectors) 15 (of) 17 (the) 18 (original) 19 (dense) 18 (matrix) ks cmmi10.329 @sf 17 r save [ 30 32 -2 0 34] 65 @pc restore cmr10.329 @sf 52 r m (once) 18 (those) 17 (of) ks cmmi10.329 @sf 17 r m (H) s cmr10.329 @sf 21 r m (ha) 0 (v) -1 (e) 16 (b) 1 (een) 19 (computed.) 27 (The) ks 74 2570 p m (expression) 16 (for) 15 (the) 15 (w) 0 (ork) 13 (can) 16 (b) 1 (e) 16 (rewritten:) ks cmmi10.329 @sf 622 2702 p save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmmi8.300 @sf 665 2709 p m (p) s cmr10.329 @sf 698 2702 p m (=) s cmmi10.329 @sf 751 2672 p m (n) s cmr8.300 @sf 778 2657 p m (3) s 751 2692 p 48 2 ru cmmi10.329 @sf 763 2733 p m (p) s cmex10.300 @sf 810 2643 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmr10.329 @sf 846 2672 p m (16) s 846 2692 p 46 2 ru 857 2733 p m (3) s 906 2702 p m (+) s 960 2672 p m (18) s 957 2692 p 53 2 ru cmmi10.329 @sf 957 2733 p m (p) s cmsy8.300 @sf 980 2721 p m (0) s cmr8.300 @sf m (2) s cmr10.329 @sf 1024 2702 p m (+) s 1075 2672 p m (24) s cmmi10.329 @sf m (k) s 1075 2692 p 71 2 ru cmr10.329 @sf 1098 2733 p m (3) s 1150 2702 p m (\(1) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 10 r m (\() s 1269 2672 p m (1) s 1269 2692 p 23 2 ru 1269 2733 p m (4) s 1296 2702 p m (\)) s cmmi8.300 @sf 1314 2684 p m (m) s cmr10.329 @sf 1347 2702 p m (\)) s cmex10.300 @sf 1365 2643 p save [ 20 99 -1 97 31] 19 @pc restore cmmi10.329 @sf 1403 2702 p m (:) s @eop 29 @bop0 cmmi8.300 @sf [<1FC00300030003000180018039804780C1C080C080C080C0C060C060C06060606070307018D007 10> 12 20 -2 6 16] 113 @dc cmmi6.300 @sf [<0F0008C098005000300018001C001A001A0019000C800C40044006400220034001C0> 11 17 -1 0 13] 96 @dc 29 @bop1 cmr10.329 @sf 1919 -77 p m (29) s 74 67 p m (fact) 14 (that) 14 (it) 14 (is) 15 (the) 14 (structure) 15 (of) 14 (the) 14 (matrix) 14 (that) 14 (caused) 14 (the) 15 (p) 1 (o) 1 (or) 14 (appro) 0 (ximations) 13 (and) 15 (the) 14 (failures,) ks 74 167 p m (and) 16 (not) 14 (some) 15 (inheren) 0 (t) 15 (di\016cult) 0 (y) 16 (with) 15 (the) 16 (sp) 1 (ectrum) 15 (of) 15 (these) 15 (matrices.) ks cmbx10.432 @sf 74 352 p save [<003FC00000FFF00003FFFC0007E07E000FC03F001F803F801F801FC03F001FC03F001FE07F001F E07F001FE07F001FE07F001FE0FF001FE0FF001FE0FF001FE0FF001FC0FF801FC0FF801F80FFC0 3F00FFC03E00FF707C00FF3FF800FF0FC000FF0000007F0000007F0000007F0000003F8000003F 801F001F803F801FC03F800FC03F8007E03F8003F01F8001FC0F0000FFFE00003FFC000007F000> 27 39 -3 0 34] 54 @pc restore 177 352 p save [<00000E00000700000000001F00000F80000000001F00000F80000000001F80001F80000000003F 80001FC0000000003F80001FC0000000003FC0003FC0000000007FC0003FE0000000007FC0003F E000000000FFE0007FF000000000FFE0007FF000000000FFF000FFF000000001FE7000FF380000 0001FE7000FF3800000001FE7801FF3800000003FC3801FE1C00000003FC3801FE1C00000007FC 1C03FC1E00000007F81C03FC0E00000007F81E07FC0E0000000FF00E07F8070000000FF00E07F8 070000001FF00F0FF0078000001FE0070FF0038000001FE0070FF0038000003FE0039FE003C000 003FC0039FE001C000003FC003FFE001C000007F8001FFC000E000007F8001FFC000E00000FF80 00FF8000F00000FF0000FF8000700000FF0000FF8000700001FF0000FF0000780001FE0000FF00 00380001FE0001FF0000380003FC0001FE00001C0003FC0001FE00001C00FFFFE07FFFF007FFF0 FFFFE07FFFF007FFF0FFFFE07FFFF007FFF0> 68 41 -1 0 71] 87 @pc restore 66 r m (or) s save [ 31 42 -2 0 36] 107 @pc restore 59 r save [ 39 41 -3 0 45] 69 @pc restore 45 r m (stim) -1 (ates) ks cmr10.329 @sf 74 538 p m (W) -3 (e) 20 (assume) 21 (in) 21 (this) 21 (section) 21 (that) 20 (w) 0 (e) 20 (are) 20 (giv) 0 (en) 20 (a) 21 (real) 21 (dense) 21 (matrix) ks cmmi10.329 @sf 21 r save [ 30 32 -2 0 34] 65 @pc restore cmr10.329 @sf 34 r m (.) 36 (Then) 21 (the) 21 (\014rst) 20 (task) 20 (in) ks 74 637 p m (our) 16 (algorithm) 17 (is) 17 (to) 15 (reduce) ks cmmi10.329 @sf 18 r save [ 30 32 -2 0 34] 65 @pc restore cmr10.329 @sf 50 r m (to) 16 (an) 16 (upp) 1 (er-Hessen) 0 (b) 1 (erg) 17 (matrix) ks cmmi10.329 @sf 16 r m (H) s cmr10.329 @sf 4 r m (.) 23 (This) 17 (requires) ks cmr8.300 @sf 1663 620 p m (10) s cmmi8.300 @sf m (n) s cmr6.300 @sf 1720 609 p m (3) s 1663 627 p 74 2 ru cmr8.300 @sf 1691 653 p m (3) s cmr10.329 @sf 1758 637 p m (op) 1 (erations) ks 74 737 p m (\(plus) 17 (lo) 0 (w) 0 (er) 13 (order) 16 (terms\)) 15 (if) 17 (elemen) 0 (tary) 15 (transformations) 15 (are) 15 (used,) 17 (since) 17 (these) 16 (matrices) 16 (are) 16 (to) 15 (b) 1 (e) ks 74 837 p m (accum) 0 (ulated.) ks 124 978 p m (The) 16 (dividi) 1 (ng) 18 (pro) 1 (cess) 16 (is) 16 (no) 0 (w) 15 (applied) 18 (to) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 4 r m (.) 22 (Assume) ks cmmi10.329 @sf 16 r m (n) s cmr10.329 @sf 14 r m (=) 15 (2) ks cmmi8.300 @sf 1272 963 p m (m) s cmmi10.329 @sf 1305 978 p m (r) s cmr10.329 @sf 1 r m (,) 15 (for) 15 (some) ks cmmi10.329 @sf 16 r m (m) s cmsy10.329 @sf 14 r save [ 26 36 -4 7 35] 21 @pc restore cmr10.329 @sf 49 r m (1) 16 (where) ks cmmi10.329 @sf 16 r m (r) s cmr10.329 @sf 17 r m (is) 16 (not) ks 74 1077 p m (necessarily) 16 (relativ) 0 (ely) 15 (prime) 16 (to) 14 (2.) 19 (If) 15 (w) 0 (e) 14 (rep) 1 (eat) 15 (the) 14 (dividi) 1 (ng) 17 (pro) 1 (cess) ks cmmi10.329 @sf 15 r m (m) s cmr10.329 @sf 14 r m (times,) 15 (w) 0 (e) 13 (end) 16 (up) 15 (with) 15 (2) ks cmmi8.300 @sf 1931 1062 p m (m) s cmr10.329 @sf 74 1177 p m (matrices) 18 (of) 17 (size) ks cmmi10.329 @sf 18 r m (r) s cmr10.329 @sf 1 r m (,) 18 (eac) 0 (h) 17 (of) 17 (whic) 0 (h) 17 (is) 18 (upp) 1 (er-Hessen) 0 (b) 1 (erg.) 28 (A) 18 (submatrix) 17 (of) 17 (size) ks cmmi8.300 @sf 1608 1160 p m (n) s 1603 1167 p 31 2 ru cmr8.300 @sf 1603 1195 p m (2) s cmmi6.300 @sf 1621 1187 p m (i) s cmr10.329 @sf 1656 1177 p m (obtained) 19 (in) 18 (the) ks 74 1277 p m (dividi) 1 (ng) 16 (pro) 1 (cess) 14 (will) 16 (b) 1 (e) 15 (referred) 14 (to) 14 (as) 14 (a) 14 (matrix) 13 (at) 14 (the) 14 (lev) 0 (el) ks cmmi10.329 @sf 15 r m (i) s cmr10.329 @sf m (.) 19 (The) 14 (matrix) ks cmmi10.329 @sf 14 r m (H) s cmr10.329 @sf 18 r m (itself) 15 (is) 15 (at) 13 (the) 15 (lev) 0 (el) ks 74 1376 p m (0,) 15 (and) 15 (the) ks cmmi10.329 @sf 16 r m (r) s cmr10.329 @sf 16 r m (matrices) 15 (referred) 15 (to) 15 (ab) 1 (o) 0 (v) -1 (e) 14 (are) 15 (at) 14 (the) 16 (lev) 0 (el) ks cmmi10.329 @sf 15 r m (m) s cmr10.329 @sf m (.) 20 (Th) 0 (us,) 14 (w) 0 (e) 14 (ha) 0 (v) -1 (e) ks cmmi10.329 @sf 14 r m (m) s cmr10.329 @sf 10 r m (+) 10 (1) 15 (lev) 0 (els) 16 (in) 16 (total.) ks 74 1476 p m (Let) s cmmi10.329 @sf 16 r m (p) s cmsy8.300 @sf 179 1461 p m (0) s cmr10.329 @sf 204 1476 p m (=) 14 (2) ks cmmi8.300 @sf 276 1461 p m (m) s cmr10.329 @sf 325 1476 p m (b) 1 (e) 16 (the) 16 (n) 0 (um) 0 (b) 1 (er) 14 (of) 16 (submatrices) 16 (at) 15 (the) 16 (lo) 0 (w) -1 (est) 14 (lev) 0 (el,) 16 (and) ks cmmi10.329 @sf 16 r m (p) s cmr10.329 @sf 15 r m (the) 16 (n) 0 (um) 0 (b) 1 (er) 14 (of) 16 (pro) 1 (cessors;) ks 74 1575 p m (w) 0 (e) 14 (will) 17 (assume) 16 (that) ks cmmi10.329 @sf 14 r m (p) s cmr10.329 @sf 13 r m (=) 14 (2) ks cmmi8.300 @sf 591 1560 p m (q) s cmmi10.329 @sf 609 1575 p m (;) s 8 r save [<0FFE0000E00000E0000070000070000070000070000038000038000F380030B800705C00703C00 F01C00F01C00F00E00F00E00F00E00F00E007807007807007807003807003C03801C03800E0380 0705800388C000F040> 18 29 -2 9 20] 113 @pc restore cmsy10.329 @sf 35 r m (\024) s cmmi10.329 @sf 13 r m (m) s cmr10.329 @sf m (.) 20 (The) 16 (cost) 15 (of) 15 (\014nding) 17 (the) 15 (eigenpairs) 17 (of) 15 (a) 15 (\(Hessen) 0 (b) 1 (erg\)) 14 (matrix) ks 74 1675 p m (at) 17 (the) 17 (lo) 0 (w) 0 (est) 15 (lev) 0 (el) 18 (\(b) 0 (y) 16 (the) 17 (QR) 18 (algorithm\)) 17 (is) 18 (roughly) 18 (18) ks cmex10.300 @sf 1203 1628 p save [<0006000C001800300070006000C001C0018003800300070006000E000C001C001C001800380038 0038003000700070007000700070007000E000E000E000E000E000E000E000E000E000E000E000 E000E000E000E000E000E000E000700070007000700070007000300038003800380018001C001C 000C000E000600070003000380018001C000C00060007000300018000C0006> 15 74 -8 72 25] 16 @pc restore cmmi8.300 @sf 1235 1658 p m (n) s 1232 1665 p 29 2 ru 1232 1691 p m (p) s cmsy6.300 @sf 1250 1683 p m (0) s cmex10.300 @sf 1266 1628 p save [ 15 74 -1 72 25] 17 @pc restore cmr8.300 @sf 1290 1639 p m (3) s cmr10.329 @sf 1310 1675 p m (:) 24 (this) 18 (\014gure) 18 (is) 17 (v) 0 (ery) 17 (appro) 0 (ximate) ks 74 1775 p m (and) 19 (assumes) 17 (among) 18 (other) 18 (things) 18 (that) 18 (t) 0 (w) -1 (o) 16 (QR) 19 (steps) 18 (are) 17 (needed) 20 (b) 1 (efore) 18 (a) 18 (real) 19 (or) 17 (t) 0 (w) -1 (o) 16 (complex) ks 74 1874 p m (conjugate) 11 (eigen) 0 (v) -2 (alues) 11 (are) 11 (iden) 0 (ti\014ed) 12 (and) 12 (that) 10 (the) 12 (matrix) 11 (has) 11 (an) 11 (equal) 12 (n) 0 (um) 0 (b) 1 (er) 9 (of) 11 (real) 12 (and) 11 (complex) ks 74 1974 p m (eigen) 0 (v) -2 (alues) 12 ([) 0 (8) ks 342 1974 p m (].) 18 (Let) ks cmmi10.329 @sf 13 r m (s) s cmmi8.300 @sf 486 1981 p m (`) s cmr10.329 @sf 515 1974 p m (=) s cmmi8.300 @sf 574 1957 p m (n) s 568 1964 p 33 2 ru cmr8.300 @sf 568 1992 p m (2) s cmmi6.300 @sf 586 1984 p m (`) s cmr10.329 @sf 618 1974 p m (b) 1 (e) 13 (the) 12 (size) 13 (of) 12 (one) 12 (matrix) 12 (at) 12 (the) 12 (lev) 0 (el) ks cmmi10.329 @sf 13 r m (`) s cmr10.329 @sf m (.) 19 (Let) ks cmmi10.329 @sf 12 r m (k) s cmmi8.300 @sf 1491 1981 p m (`) s cmr10.329 @sf 1519 1974 p m (b) 1 (e) 13 (the) 13 (a) 0 (v) -1 (erag) -1 (e) 11 (n) 0 (um) 0 (b) 1 (er) ks 74 2074 p m (of) 17 (iterations) 18 (needed) 18 (to) 17 (get) 17 (one) 17 (eigenpair) 19 (of) 17 (a) 17 (matrix) 17 (at) 17 (the) 17 (lev) 0 (el) ks cmmi10.329 @sf 18 r m (`) s cmr10.329 @sf m (.) s cmmi10.329 @sf 26 r m (k) s cmmi8.300 @sf 1474 2081 p m (`) s cmr10.329 @sf 1508 2074 p m (dep) 1 (ends) 19 (on) 17 (the) 17 (matrix) ks 74 2173 p m (and) 17 (on) 16 (its) 17 (size) 17 (of) 16 (course.) 23 (W) -3 (e) 16 (will) 18 (mak) 0 (e) 15 (the) 16 (follo) 0 (wing) 16 (simplifyi) 1 (ng) 18 (assumption) 16 (ho) 0 (w) 0 (ev) -1 (er:) ks cmmi10.329 @sf 20 r m (k) s cmmi8.300 @sf 1846 2180 p m (`) s cmr10.329 @sf 1876 2173 p m (=) s cmmi10.329 @sf 15 r m (k) s cmr10.329 @sf 1 r m (,) s cmmi10.329 @sf 74 2273 p m (`) s cmr10.329 @sf 16 r m (=) 15 (0) ks cmmi10.329 @sf m (;) s cmsy10.329 @sf 8 r m (\001) 8 (\001) 8 (\001) ks cmmi10.329 @sf 263 2273 p m (;) 8 (m) ks cmr10.329 @sf m (,) 16 (i.e.,) 17 (w) 0 (e) 15 (assume) 17 (that) 16 (the) 17 (a) 0 (v) -1 (erage) 15 (n) 0 (um) 0 (b) 1 (er) 15 (of) 17 (steps) 16 (required) 18 (for) 17 (con) 0 (v) -1 (ergence) 16 (is) 17 (the) ks 74 2372 p m (same) 13 (at) 12 (all) 15 (lev) 0 (els.) 19 (Our) 13 (exp) 1 (erience) 16 (with) 13 (the) 13 (algorithm) 14 (suggests) 12 (that) 12 (this) 14 (is) 14 (a) 12 (realistic) 15 (assumption) ks 74 2472 p m (as) 18 (long) 19 (as) 18 (the) 18 (size) 19 (of) 18 (the) 19 (submatrices) 18 (remains) 19 (mo) 1 (derate.) 29 (If) 19 (the) 18 (n) 0 (um) 0 (b) 1 (er) 17 (of) 18 (lev) 0 (els) 18 (is) 19 (increased) ks 74 2572 p m (to) 15 (the) 16 (p) 1 (oin) 0 (t) 15 (where) 16 (w) 0 (e) 14 (are) 16 (left) 16 (with) 16 (small) 16 (submatrices) 16 (\(less) 16 (than) 16 (20) ks cmsy10.329 @sf 9 r m (\002) s cmr10.329 @sf 11 r m (20) 15 (sa) 0 (y\),) 14 (then) ks cmmi10.329 @sf 16 r m (k) s cmmi8.300 @sf 1767 2579 p m (`) s cmr10.329 @sf 1798 2572 p m (b) 1 (ecomes) ks 74 2671 p m (signi\014can) 0 (tly) 13 (larger) 12 (as) ks cmmi10.329 @sf 12 r m (`) s cmr10.329 @sf 12 r m (increases) 13 (\(for) 11 (v) 0 (ery) 11 (small) 13 (matrices) 12 (it) 13 (can) 12 (b) 1 (e) 13 (more) 12 (than) 12 (10) 12 (on) 12 (the) 12 (a) 0 (v) -1 (erage\)) -1 (.) ks @eop 28 @bop0 cmex10.300 @sf [ 5 27 -12 26 36] 66 @dc [ 5 27 -18 26 36] 67 @dc 28 @bop1 cmr10.329 @sf 1919 -77 p m (28) s cmmi10.329 @sf 74 67 p m (H) s cmr10.329 @sf 4 r m (,) 14 (namely:) ks 761 204 p m (\() s cmex10.300 @sf 779 83 p m (0) s 779 156 p m (B) s 779 181 p m (B) s 779 206 p m (B) s 779 233 p m (@) s cmr10.329 @sf 836 120 p m (0) s 836 176 p m (1) s 836 233 p m (0) s 836 289 p m (0) s cmex10.300 @sf 879 83 p m (1) s 879 156 p m (C) s 879 181 p m (C) s 879 206 p m (C) s 879 233 p m (A) s cmmi10.329 @sf 923 204 p m (;) s cmr10.329 @sf 8 r m (0\)) s cmmi10.329 @sf m (;) s cmr10.329 @sf 44 r m (\() s cmex10.300 @sf 1060 83 p m (0) s 1060 156 p m (B) s 1060 181 p m (B) s 1060 206 p m (B) s 1060 233 p m (@) s cmr10.329 @sf 1117 120 p m (0) s 1117 176 p m (0) s 1117 233 p m (0) s 1117 289 p m (1) s cmex10.300 @sf 1160 83 p m (1) s 1160 156 p m (C) s 1160 181 p m (C) s 1160 206 p m (C) s 1160 233 p m (A) s cmmi10.329 @sf 1204 204 p m (;) s cmr10.329 @sf 8 r m (0\)) s cmmi10.329 @sf m (;) s cmr10.329 @sf 74 371 p m (if) 16 (the) 15 (zero) 15 (is) 16 (in) 0 (tro) 1 (duced) 15 (in) 16 (the) 16 (\(3) ks cmmi10.329 @sf m (;) s cmr10.329 @sf 8 r m (2\)) 13 (p) 1 (osition.) ks 124 512 p m (F) -3 (urthermore,) 13 (the) 14 (Jacobian) 16 (is) 15 (exactly) 15 (singular) 15 (at) 14 (eac) 0 (h) 14 (of) 14 (these) 14 (initial) 17 (appro) 0 (ximations.) 19 (Indeed) ks 74 650 p m (the) 15 (Jacobian) 16 (at) 15 (\() ks cmex10.300 @sf 416 528 p m (0) s 416 601 p m (B) s 416 626 p m (B) s 416 651 p m (B) s 416 678 p m (@) s cmr10.329 @sf 473 565 p m (0) s 473 621 p m (1) s 473 678 p m (0) s 473 734 p m (0) s cmex10.300 @sf 516 528 p m (1) s 516 601 p m (C) s 516 626 p m (C) s 516 651 p m (C) s 516 678 p m (A) s cmmi10.329 @sf 560 650 p m (;) s cmr10.329 @sf 8 r m (0\)) 14 (is) ks cmex10.300 @sf 805 761 p m (0) s 805 834 p m (B) s 805 859 p m (B) s 805 884 p m (B) s 805 909 p m (B) s 805 934 p m (B) s 805 961 p m (@) s cmr10.329 @sf 862 795 p m (0) s 926 795 p m (0) s 990 795 p m (0) s 1054 795 p m (0) s 1136 795 p m (0) s 862 851 p m (1) s 926 851 p m (0) s 990 851 p m (0) s 1054 851 p m (0) s cmsy10.329 @sf 1119 851 p m (\000) s cmr10.329 @sf m (1) s 862 908 p m (0) s 926 908 p m (1) s 990 908 p m (0) s 1054 908 p m (0) s 1136 908 p m (0) s 862 964 p m (0) s 926 964 p m (0) s 990 964 p m (1) s 1054 964 p m (0) s 1136 964 p m (0) s 862 1021 p m (0) s 926 1021 p m (1) s 990 1021 p m (0) s 1054 1021 p m (0) s 1136 1021 p m (0) s cmex10.300 @sf 1197 761 p m (1) s 1197 834 p m (C) s 1197 859 p m (C) s 1197 884 p m (C) s 1197 909 p m (C) s 1197 934 p m (C) s 1197 961 p m (A) s cmr10.329 @sf 74 1100 p m (whic) 0 (h) 13 (is) 13 (clearly) 14 (of) 12 (rank) 13 (three) 13 (since) 14 (the) 13 (\014rst) 12 (and) 13 (the) 13 (last) 13 (columns) 13 (are) 13 (linearly) 15 (dep) 1 (enden) 0 (t,) 13 (and) 13 (the) ks 74 1238 p m (fourth) 14 (column) 15 (is) 15 (zero.) 19 (Similarly) 16 (it) 15 (can) 14 (b) 1 (e) 15 (seen) 15 (that) 13 (the) 14 (Jacobian) 15 (at) 14 (\() ks cmex10.300 @sf 1441 1116 p m (0) s 1441 1189 p m (B) s 1441 1214 p m (B) s 1441 1239 p m (B) s 1441 1266 p m (@) s cmr10.329 @sf 1498 1153 p m (0) s 1498 1209 p m (0) s 1498 1266 p m (0) s 1498 1322 p m (1) s cmex10.300 @sf 1541 1116 p m (1) s 1541 1189 p m (C) s 1541 1214 p m (C) s 1541 1239 p m (C) s 1541 1266 p m (A) s cmmi10.329 @sf 1585 1238 p m (;) s cmr10.329 @sf 8 r m (0\)) 13 (is) 14 (also) 15 (singular.) ks 74 1375 p m (A) 13 (remedy) 13 (to) 12 (this) 14 (situation) 13 (is) 13 (to) 12 (p) 1 (erturb) 14 (the) 13 (initial) 15 (guess) 12 (zero) 13 (b) 0 (y) 12 (a) 12 (small) 14 (amoun) 0 (t) 11 (thereb) 0 (y) 12 (making) ks 74 1474 p m (the) 20 (Jacobian) 22 (non) 20 (singular,) 22 (and) 20 (indeed) 22 (this) 21 (has) 20 (b) 1 (een) 22 (successful) 21 (in) 21 (practice.) 36 (The) 20 (problem) 21 (in) ks 74 1574 p m (this) 16 (case,) 15 (as) 15 (in) 17 (most) 14 (other) 15 (similar) 17 (cases,) 15 (results) 16 (from) 15 (the) 15 (particular) 16 (structure) 16 (of) 15 (the) 15 (matrix.) 20 (In) ks 74 1674 p m (order) 16 (to) 15 (obtain) 16 (further) 16 (eigen) 0 (v) -2 (alues,) 15 (w) 0 (e) 15 (need) 16 (to) 15 (de\015ate) 16 (the) 16 (matrix) 16 (eac) 0 (h) 15 (time) 16 (a) 15 (new) 16 (eigenpair) 18 (is) ks 74 1773 p m (computed) 16 (whic) 0 (h) 15 (mak) 0 (es) 13 (the) 16 (algorithm) 15 (almost) 15 (serial.) ks cmbx12.300 @sf 74 1937 p save [<03F8000FFF001C1F803007C07007E0FC03F0FC03F0FE03F8FE03F87C03F83803F80003F80003F8 0003F00003F01803E01807E01E0FC01FFF0019FC001800001800001800001800001BC0001FF800 1FFE001FFF001FFF801FFFC01E01E0100020> 21 32 -3 0 28] 53 @pc restore 28 r m (.) s save [<01FE000FFFC01E07F07801F87E01FCFF00FCFF00FEFF00FEFF00FE7E00FE3C00FE0000FC0000FC 0001F80001F00007C001FF0001FE00001F800007C00003E00003F01F03F01F03F83F81F83F81F8 3F81F83F03F01E03F00F07E007FFC000FE00> 23 32 -2 0 28] 51 @pc restore 202 1937 p save [ 38 34 -2 0 44] 75 @pc restore 44 r m (no) s -1 r save [<001800C000003800E000003C01E000007C01F000007E03F000007E03F00000FE03D80000FB07D8 0001FB079C0001F38F8C0001F18F0C0003E18F060003E0DF060007E0DE070007C0DE030007C07E 03000F807C01800F807C01800F807801801F007800C0FFE7FF07F8FFE7FF07F8> 37 22 -1 0 40] 119 @pc restore 40 r m (n) s 19 r save [<7FF8007FF8000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F8000 0F80000F80000F80000F80000F80000F80000F8000FFFC00FFFC000F80000F80000F80000F8000 0F80000F80000F83C00F87E007C7E003C7E001E3E000FFC0003F80> 19 35 -1 0 17] 102 @pc restore 17 r m (ailures) s cmr10.329 @sf 74 2107 p m (Some) 17 (matrices) 16 (of) 16 (the) 17 (structure) 16 (men) 0 (tioned) 16 (at) 16 (the) 16 (end) 17 (of) 16 (section) 17 (5.2) 16 (\(companion-lik) 0 (e) 17 (matrices\),) ks 74 2207 p m (pro) 0 (vided) 13 (us) 14 (with) 13 (the) 14 (only) 14 (cases) 13 (where) 14 (the) 13 (algorithm) 13 (failed) 15 (in) 14 (practice) 14 (to) 13 (con) 0 (v) 0 (erg) -1 (e) 12 (to) 12 (the) 14 (desired) ks 74 2306 p m (eigenpairs,) 12 (i.e.,) 11 (failed) 12 (to) 9 (pro) 1 (duce) 12 (eigenpairs) 11 (with) 11 (small) 11 (residuals) 11 (after) 10 (a) 10 (\014xed) 11 (n) 0 (um) 0 (b) 1 (er) 8 (of) 10 (iterations.) ks 74 2406 p m (When) 17 (these) 16 (matrices) 17 (w) 0 (ere) 15 (sub) 3 (jected) 16 (to) 16 (random) 16 (orthogonal) 15 (similarit) 0 (y) 17 (transformations) 15 (ho) 0 (w) -1 (ev) -1 (er) ks 74 2505 p m (and) 17 (then) 16 (reduced) 17 (bac) 0 (k) 15 (to) 16 (upp) 1 (er-Hessen) 0 (b) 1 (erg) 17 (form,) 15 (the) 16 (dividi) 1 (ng) 18 (pro) 1 (cess) 16 (pro) 0 (vided) 16 (us) 17 (with) 16 (m) 0 (uc) 0 (h) ks 74 2605 p m (b) 1 (etter) 13 (initial) 16 (appro) 0 (ximations) 12 (and) 13 (indeed,) 15 (the) 13 (algorithm) 14 (con) 0 (v) -1 (erged) 12 (for) 12 (all) 14 (initial) 16 (appro) 0 (ximations.) ks 74 2705 p m (W) -3 (e) 16 (are) 17 (certainly) 18 (not) 17 (adv) 0 (o) 1 (cating) 16 (this) 18 (as) 17 (a) 16 (general) 18 (viable) 19 (sc) 0 (heme:) 23 (w) 0 (e) 16 (w) 0 (an) -1 (ted) 15 (to) 17 (emphasize) 18 (the) ks @eop 27 @bop0 27 @bop1 cmr10.329 @sf 1919 -77 p m (27) s 74 67 p m (unc) 0 (hanged) 13 (after) 13 (a) 13 (zero) 14 (has) 13 (b) 1 (een) 14 (in) 0 (tro) 1 (duced) 14 (in) 14 (the) 14 (sub) 1 (diagonal.) 21 (An) 13 (example,) 15 (is) 13 (the) 14 (2) ks cmsy10.329 @sf 7 r m (\002) s cmr10.329 @sf 7 r m (2) 12 (matrix) ks cmex10.300 @sf 912 140 p save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pc restore cmr10.329 @sf 966 185 p m (1) s 1030 185 p m (0) s 966 241 p m (1) s 1030 241 p m (1) s cmex10.300 @sf 1073 140 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1114 212 p m (:) s cmr10.329 @sf 74 358 p m (After) 15 (the) 15 (dividi) 1 (ng) 17 (pro) 1 (cess) 15 (w) 0 (e) 14 (ha) 0 (v) 0 (e) ks cmex10.300 @sf 912 385 p save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pc restore cmr10.329 @sf 966 430 p m (1) s 1030 430 p m (0) s 966 486 p m (0) s 1030 486 p m (1) s cmex10.300 @sf 1073 385 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1114 457 p m (:) s cmr10.329 @sf 74 613 p m (The) 13 (starting) 11 (eigenpairs) 14 (are) 12 (then) 13 (\() ks cmex10.300 @sf 733 541 p save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pc restore cmr10.329 @sf 786 586 p m (1) s 786 641 p m (0) s cmex10.300 @sf 829 541 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 870 613 p m (;) s cmr10.329 @sf 8 r m (1\)) 11 (and) 12 (\() ks cmex10.300 @sf 1046 541 p save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pc restore cmr10.329 @sf 1100 586 p m (0) s 1100 641 p m (1) s cmex10.300 @sf 1143 541 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1184 613 p m (;) s cmr10.329 @sf 8 r m (1\).) 17 (The) 13 (second) 12 (of) 12 (these) 13 (is) 13 (of) 12 (course) 12 (the) ks 74 713 p m (exact) 12 (eigenpair.) 21 (No) 0 (w,) 11 (ev) 0 (en) 11 (though) 13 (the) 12 (\014rst) 12 (starting) 12 (eigen) 0 (v) 0 (ector) 11 (is) 13 (orthogonal) 11 (to) 12 (the) 13 (desired) 13 (one,) ks 74 812 p m (the) 16 (equations) 17 (arising) 16 (during) 17 (the) 17 (\014rst) 15 (of) 16 (Newton's) 15 (iterations) 17 (can) 16 (b) 1 (e) 17 (solv) 0 (ed) 15 (in) 17 (a) 16 (w) 0 (a) -1 (y) 14 (to) 15 (pro) 1 (duce) ks 74 912 p m (the) 14 (desired) 15 (eigen) 0 (v) 0 (ector) 12 (from) 14 (the) 14 (\014rst) 13 (step:) 20 (zero) 13 (piv) 0 (ots) 13 (need) 15 (to) 13 (b) 1 (e) 15 (replaced) 15 (b) 0 (y) 13 (small) 15 (n) 0 (um) 0 (b) 1 (ers) 12 (on) ks 74 1012 p m (the) 15 (order) 15 (of) 15 (the) 15 (mac) 0 (hine) 15 (unit) 16 (roundo\013) 15 (\(as) 15 (is) 15 (done) 16 (in) 16 (in) 0 (v) 0 (erse) 14 (iteration,) 15 (INVIT) 16 ([) 0 (15) ks 1692 1012 p m (]\).) s 124 1153 p m (Finally) -3 (,) 24 (w) 0 (e) 20 (men) 0 (tion) 22 (that) 21 (the) 22 (de\015ation) 22 (pro) 1 (cess) 22 (can) 23 (con) 0 (tribute) 21 (to) 21 (the) 22 (impro) 0 (v) 0 (emen) -1 (t) 20 (of) 21 (the) ks 74 1252 p m (condition) 15 (of) 13 (the) 14 (eigen) 0 (v) -2 (alues.) 19 (Indeed,) 15 (if) ks cmmi10.329 @sf 14 r m (\025) s cmr10.329 @sf 13 r m (and) s cmmi10.329 @sf 13 r m (\025) s cmsy8.300 @sf 1003 1237 p m (0) s cmr10.329 @sf 1028 1252 p m (are) 13 (pathologically) 15 (close) 14 (\(and) 13 (fairly) 15 (distan) 0 (t) 12 (from) ks 74 1352 p m (the) 17 (rest) 17 (of) 17 (the) 17 (eigen) 0 (v) -2 (alues\),) 17 (then) 17 (b) 0 (y) 16 (de\015ating) ks cmmi10.329 @sf 18 r m (\025) s cmr10.329 @sf m (,) s cmmi10.329 @sf 17 r m (\025) s cmsy8.300 @sf 1090 1337 p m (0) s cmr10.329 @sf 1118 1352 p m (will) 19 (ha) 0 (v) -1 (e) 16 (a) 16 (b) 1 (etter) 18 (condition) 18 (n) 0 (um) 0 (b) 1 (er) 15 (as) 17 (an) ks 74 1452 p m (eigen) 0 (v) -2 (alue) 15 (of) 15 (the) 15 (resulting) 17 (matrix.) 19 (Indeed,) ks cmmi10.329 @sf 16 r m (\025) s cmsy8.300 @sf 961 1437 p m (0) s cmr10.329 @sf 988 1452 p m (is) 16 (no) 15 (longer) 15 (part) 15 (of) 15 (a) 14 (cluster.) ks cmbx12.300 @sf 74 1615 p save [<03F8000FFF001C1F803007C07007E0FC03F0FC03F0FE03F8FE03F87C03F83803F80003F80003F8 0003F00003F01803E01807E01E0FC01FFF0019FC001800001800001800001800001BC0001FF800 1FFE001FFF001FFF801FFFC01E01E0100020> 21 32 -3 0 28] 53 @pc restore 28 r m (.2) s 202 1615 p save [<0003FE0000001FFFC00000FF00F00001F800380003F0000C0007C00006000F800003001F800003 003F000003803F000001807F000001807E000001807E00000000FE00000000FE00000000FE0000 0000FE00000000FE00000000FE00000000FE00000000FE000000007E000001807E000001807F00 0001803F000003803F000003801F800007800F8000078007C0000F8003E0001F8001F8003F8000 FF01E380001FFF81800003FE0080> 33 34 -3 0 40] 67 @pc restore 40 r m (ase) s 19 r save [<001800C000003800E000003C01E000007C01F000007E03F000007E03F00000FE03D80000FB07D8 0001FB079C0001F38F8C0001F18F0C0003E18F060003E0DF060007E0DE070007C0DE030007C07E 03000F807C01800F807C01800F807801801F007800C0FFE7FF07F8FFE7FF07F8> 37 22 -1 0 40] 119 @pc restore 40 r m (hen) s 19 r save [ 40 34 -2 0 40] 72 @pc restore cmr8.300 @sf 523 1622 p m (0) s cmbx12.300 @sf 562 1615 p m (is) 18 (de) ks save [<7FF8007FF8000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F8000 0F80000F80000F80000F80000F80000F80000F8000FFFC00FFFC000F80000F80000F80000F8000 0F80000F80000F83C00F87E007C7E003C7E001E3E000FFC0003F80> 19 35 -1 0 17] 102 @pc restore 17 r m (ecti) s save [<000E0000000E0000001F0000001F0000003F8000003F8000007FC000007CC000007CC00000F860 0000F8600001F0300001F0300003E0180003E0180007E01C0007C00C000FC00E000F8006000F80 0600FFE01FE0FFE01FE0> 27 22 -1 0 30] 118 @pc restore 29 r m (e) s cmr10.329 @sf 74 1785 p m (It) 18 (can) 19 (happ) 1 (en) 19 (in) 19 (this) 18 (case) 19 (\(e.g.,) 17 (if) ks cmmi10.329 @sf 19 r m (H) s cmr10.329 @sf 21 r m (is) 19 (non-defectiv) 0 (e\)) 18 (that) 17 (the) 19 (initial) 20 (dividing) 20 (pro) 1 (cess) 19 (w) 0 (ould) ks 74 1885 p m (lea) 0 (v) 0 (e) 21 (us) 22 (with) 23 (a) 21 (n) 0 (um) 0 (b) 1 (er) 21 (of) 22 (initial) 24 (appro) 0 (ximations) 21 (that) 22 (is) 23 (smaller) 23 (than) ks cmmi10.329 @sf 22 r m (n) s cmr10.329 @sf m (.) 41 (This) 23 (will) 24 (inhibit) ks 74 1985 p m (the) 16 (parallelism) 18 (of) 15 (the) 16 (algorithm) 16 (in) 16 (that) 15 (few) 0 (er) 15 (Newton) 15 (pro) 1 (cesses) 16 (can) 16 (b) 1 (e) 17 (started) 15 (sim) 0 (ultaneously) -3 (.) ks 74 2084 p m (F) -3 (urthermore,) 12 (whatev) 0 (er) 12 (eigenpairs) 15 (w) 0 (e) 12 (ha) 0 (v) -1 (e) 12 (can) 14 (b) 1 (e) 14 (extremely) 14 (p) 1 (o) 1 (or) 13 (appro) 0 (ximations) 12 (to) 13 (the) 14 (desired) ks 74 2184 p m (ones.) 20 (An) 16 (extreme) 15 (situation) 15 (is) 16 (illustrated) 17 (b) 0 (y) 14 (the) 15 (matrix) ks cmmi10.329 @sf 793 2367 p m (H) s cmr10.329 @sf 16 r m (=) s cmex10.300 @sf 895 2245 p m (0) s 895 2318 p m (B) s 895 2343 p m (B) s 895 2368 p m (B) s 895 2395 p m (@) s cmr10.329 @sf 952 2282 p m (0) s 1017 2282 p m (0) s 1081 2282 p m (0) s 1145 2282 p m (1) s 952 2338 p m (1) s 1017 2338 p m (0) s 1081 2338 p m (0) s 1145 2338 p m (0) s 952 2395 p m (0) s 1017 2395 p m (1) s 1081 2395 p m (0) s 1145 2395 p m (0) s 952 2451 p m (0) s 1017 2451 p m (0) s 1081 2451 p m (1) s 1145 2451 p m (0) s cmex10.300 @sf 1189 2245 p m (1) s 1189 2318 p m (C) s 1189 2343 p m (C) s 1189 2368 p m (C) s 1189 2395 p m (A) s cmmi10.329 @sf 1232 2367 p m (:) s cmr10.329 @sf 124 2591 p m (No) 15 (matter) 14 (where) 15 (the) 15 (zero) 15 (is) 16 (in) 0 (tro) 1 (duced) 15 (on) 15 (the) 15 (sub) 1 (diagonal,) 16 (the) 16 (resulting) 16 (matrix) 14 (has) 15 (0) 15 (as) 15 (its) ks 74 2691 p m (only) 17 (eigen) 0 (v) -2 (alue,) 17 (and) 17 (w) 0 (e) 15 (only) 17 (ha) 0 (v) 0 (e) 14 (t) 0 (w) -1 (o) 15 (initial) 18 (appro) 0 (ximations) 16 (to) 16 (the) 17 (four) 16 (distinct) 18 (eigenpairs) 18 (of) ks @eop 26 @bop0 cmti10.329 @sf [<8000400020002000100008000800040004003C003C003C003C001C000000000000000000000000 000000000000000000038007C007C003C001C0> 10 29 -3 9 14] 59 @dc [ 8 14 -9 -18 14] 39 @dc 26 @bop1 cmr10.329 @sf 1919 -77 p m (26) s 74 26 p @beginspecial @setspecial 18945146 14208860 5262540 26773176 34995896 49731010 startTexFig 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(.) sh 300.31 326.48 M (.) sh 176.59 397.77 M (.) sh 189.21 393.28 M (.) sh 204.16 387.27 M (.) sh 219.21 380.75 M (.) sh 233.46 374.36 M (.) sh 246.51 368.47 M (.) sh 258.22 363.25 M (.) sh 268.50 358.73 M (.) sh 277.35 354.84 M (.) sh 284.87 351.42 M (.) sh 291.27 348.34 M (.) sh 296.81 345.57 M (.) sh 301.83 343.16 M (.) sh 307.90 341.69 M (.) sh 305.98 345.21 M (.) sh 307.70 344.46 M (.) sh 307.87 344.66 M (.) sh 307.87 344.66 M (.) sh 307.86 344.65 M (.) sh 307.87 344.66 M (.) sh 307.88 344.65 M (.) sh 307.87 344.66 M (.) sh 307.87 344.65 M (.) sh 307.87 344.65 M (.) sh 307.87 344.66 M (.) sh 307.85 344.65 M (.) sh 307.87 344.65 M (.) sh 307.87 344.66 M (.) sh 307.87 344.66 M (.) sh 307.87 344.65 M (.) sh 307.87 344.65 M (.) sh 307.87 344.65 M (.) sh 307.86 344.65 M (.) sh 307.87 344.65 M (.) sh 307.87 344.66 M (.) sh 307.86 344.66 M (.) sh 307.87 344.65 M (.) sh 307.87 344.64 M (.) sh 307.87 344.65 M (.) sh 307.87 344.65 M (.) sh 176.59 247.53 M (.) sh 189.21 252.02 M (.) sh 204.16 258.03 M (.) sh 219.21 264.55 M (.) sh 233.46 270.94 M (.) sh 246.51 276.83 M (.) sh 258.22 282.05 M (.) sh 268.50 286.57 M (.) sh 277.35 290.46 M (.) sh 284.87 293.88 M (.) sh 291.27 296.96 M (.) sh 296.81 299.73 M (.) sh 301.83 302.14 M (.) sh 307.90 303.61 M (.) sh 305.98 300.09 M (.) sh 307.70 300.84 M (.) sh 307.87 300.64 M (.) sh 307.87 300.64 M (.) sh 307.86 300.65 M (.) sh 307.87 300.64 M (.) sh 307.88 300.65 M (.) sh 307.87 300.64 M (.) sh 307.87 300.65 M (.) sh 307.87 300.65 M (.) sh 307.87 300.64 M (.) sh 307.85 300.65 M (.) sh 307.87 300.65 M (.) sh 307.87 300.64 M (.) sh 307.87 300.64 M (.) sh 307.87 300.65 M (.) sh 307.87 300.65 M (.) sh 307.87 300.65 M (.) sh 307.86 300.65 M (.) sh 307.87 300.65 M (.) sh 307.87 300.64 M (.) sh 307.86 300.64 M (.) sh 307.87 300.65 M (.) sh 307.87 300.66 M (.) sh 307.87 300.65 M (.) sh 307.87 300.65 M (.) sh 437.53 457.79 M (.) sh 453.01 443.02 M (.) sh 443.82 435.85 M (.) sh 430.42 425.48 M (.) sh 417.10 415.00 M (.) sh 405.11 405.33 M (.) sh 394.91 396.70 M (.) sh 386.53 389.01 M (.) sh 379.73 382.08 M (.) sh 374.19 375.79 M (.) sh 369.62 370.07 M (.) sh 365.81 364.89 M (.) sh 362.60 360.20 M (.) sh 359.85 355.98 M (.) sh 357.17 352.03 M (.) sh 349.50 347.07 M (.) sh 352.93 350.58 M (.) sh 351.04 353.42 M (.) sh 351.04 352.55 M (.) sh 350.97 352.52 M (.) sh 350.97 352.52 M (.) sh 350.96 352.52 M (.) sh 350.96 352.52 M (.) sh 350.97 352.52 M (.) sh 350.97 352.52 M (.) sh 350.96 352.51 M (.) sh 350.97 352.52 M (.) sh 350.97 352.52 M (.) sh 350.97 352.52 M (.) sh 350.97 352.52 M (.) sh 350.96 352.52 M (.) sh 350.96 352.51 M (.) sh 350.97 352.52 M (.) sh 350.97 352.52 M (.) sh 350.97 352.52 M (.) sh 350.97 352.52 M (.) sh 350.97 352.52 M (.) sh 350.96 352.52 M (.) sh 350.96 352.52 M (.) sh 350.96 352.52 M (.) sh 437.53 187.51 M (.) sh 453.01 202.28 M (.) sh 443.82 209.45 M (.) sh 430.42 219.82 M (.) sh 417.10 230.30 M (.) sh 405.11 239.97 M (.) sh 394.91 248.60 M (.) sh 386.53 256.29 M (.) sh 379.73 263.22 M (.) sh 374.19 269.51 M (.) sh 369.62 275.23 M (.) sh 365.81 280.41 M (.) sh 362.60 285.10 M (.) sh 359.85 289.32 M (.) sh 357.17 293.27 M (.) sh 349.50 298.23 M (.) sh 352.93 294.72 M (.) sh 351.04 291.88 M (.) sh 351.04 292.75 M (.) sh 350.97 292.78 M (.) sh 350.97 292.78 M (.) sh 350.96 292.78 M (.) sh 350.96 292.78 M (.) sh 350.97 292.78 M (.) sh 350.97 292.78 M (.) sh 350.96 292.79 M (.) sh 350.97 292.78 M (.) sh 350.97 292.78 M (.) sh 350.97 292.78 M (.) sh 350.97 292.78 M (.) sh 350.96 292.78 M (.) sh 350.96 292.79 M (.) sh 350.97 292.78 M (.) sh 350.97 292.78 M (.) sh 350.97 292.78 M (.) sh 350.97 292.78 M (.) sh 350.97 292.78 M (.) sh 350.96 292.78 M (.) sh 350.96 292.78 M (.) sh 350.96 292.78 M (.) sh 446.24 322.65 M (.) sh 441.82 322.65 M (.) sh 432.08 322.65 M (.) sh 416.54 322.65 M (.) sh 417.07 322.65 M (.) sh 414.38 322.65 M (.) sh 413.07 322.65 M (.) sh 412.91 322.65 M (.) sh 412.91 322.65 M (.) sh 412.91 322.65 M (.) sh 421.84 355.09 M (.) sh 421.72 355.29 M (.) sh 416.15 354.14 M (.) sh 409.64 352.52 M (.) sh 403.03 350.62 M (.) sh 396.69 348.59 M (.) sh 390.78 346.54 M (.) sh 385.42 344.54 M (.) sh 380.62 342.61 M (.) sh 376.38 340.84 M (.) sh 372.99 339.73 M (.) sh 371.95 339.99 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.02 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.02 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.03 339.98 M (.) sh 372.04 339.98 M (.) sh 372.03 339.98 M (.) sh 372.02 339.98 M (.) sh 421.84 290.21 M (.) sh 421.72 290.01 M (.) sh 416.15 291.16 M (.) sh 409.64 292.78 M (.) sh 403.03 294.68 M (.) sh 396.69 296.71 M (.) sh 390.78 298.76 M (.) sh 385.42 300.76 M (.) sh 380.62 302.69 M (.) sh 376.38 304.46 M (.) sh 372.99 305.57 M (.) sh 371.95 305.31 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.02 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.02 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.03 305.32 M (.) sh 372.04 305.32 M (.) sh 372.03 305.32 M (.) sh 372.02 305.32 M (.) sh 336.92 346.84 M (.) sh 336.92 298.46 M (.) sh 422.97 322.65 M (.) sh 422.43 322.65 M (.) sh 419.24 322.65 M (.) sh 415.82 322.65 M (.) sh 413.56 322.65 M (.) sh 412.93 322.65 M (.) sh 412.91 322.65 M (.) sh 412.91 322.65 M (.) sh 361.51 322.65 M (.) sh 397.58 322.65 M (.) sh 397.66 322.65 M (.) sh 394.54 322.65 M (.) sh 390.77 322.65 M (.) sh 386.75 322.65 M (.) sh 382.77 322.65 M (.) sh 379.39 322.65 M (.) sh 378.00 322.65 M (.) sh 378.03 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.03 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.01 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.02 322.65 M (.) sh 378.03 322.65 M (.) sh 270.11 322.65 M (.) sh 270.41 322.65 M (.) sh 274.31 322.65 M (.) sh 279.15 322.65 M (.) sh 284.27 322.65 M (.) sh 289.34 322.65 M (.) sh 294.19 322.65 M (.) sh 298.94 322.65 M (.) sh 311.09 323.92 M (.) sh 304.64 323.41 M (.) sh 299.64 323.53 M (.) sh 304.61 329.58 M (.) sh 301.92 327.00 M (.) sh 300.53 326.39 M (.) sh 300.31 326.48 M (.) sh 300.31 326.48 M (.) sh 300.30 326.49 M (.) sh 300.33 326.47 M (.) sh 300.28 326.50 M (.) sh 300.29 326.50 M (.) sh 300.29 326.50 M (.) sh 300.33 326.47 M (.) sh 300.30 326.49 M (.) sh 300.32 326.48 M (.) sh 300.27 326.51 M (.) sh 300.31 326.49 M (.) sh 300.29 326.49 M (.) sh 300.31 326.49 M (.) sh 300.32 326.48 M (.) sh 300.30 326.49 M (.) sh 300.32 326.49 M (.) sh 300.30 326.49 M (.) sh 300.31 326.49 M (.) sh 300.29 326.50 M (.) sh 300.31 326.49 M (.) sh 300.32 326.48 M (.) sh 300.30 326.49 M (.) sh 300.31 326.48 M (.) sh 300.30 326.50 M (.) sh 300.29 326.50 M (.) sh 319.91 322.65 M (.) sh 314.83 322.65 M (.) sh 314.83 322.65 M (.) sh 314.83 322.65 M (.) sh 314.83 322.65 M (.) sh 314.83 322.65 M (.) sh 314.83 322.65 M (.) sh 314.83 322.65 M (.) sh 314.83 322.65 M (.) sh 314.83 322.65 M (.) sh 299.01 316.74 M (o) sh 299.04 316.76 M (o) sh 362.16 295.70 M (o) sh 362.16 345.50 M (o) sh 680.15 320.60 M (o) sh 318.23 292.04 M (o) sh 318.23 349.16 M (o) sh 333.85 289.92 M (o) sh 333.85 351.28 M (o) sh 299.06 316.77 M (o) sh 306.62 298.60 M (o) sh 306.62 342.60 M (o) sh 349.71 290.73 M (o) sh 349.71 350.47 M (o) sh 411.66 320.60 M (o) sh 370.77 303.27 M (o) sh 370.77 337.93 M (o) sh 335.67 296.41 M (o) sh 335.67 344.79 M (o) sh 411.66 320.60 M (o) sh 360.26 320.60 M (o) sh 376.78 320.60 M (o) sh 299.04 316.75 M (o) sh 318.66 320.60 M (o) sh 313.58 320.60 M (o) sh LF 417.55 14.00 M (real part) csh 14.00 324.00 M (imag part) r90sh eplot %%EndObject graph 1 epage end showpage %%Trailer endTexFig @endspecial 74 1024 p m (Figure) 21 (1:) ks cmti10.329 @sf 29 r m (The) 20 (b) -1 (ehavior) 20 (of) 21 (the) 22 (algorithm) 21 (for) 21 (an) 21 (almost) 20 (defe) -1 (ctive) ks 20 r save [<80780080FC0041FE0047FF007E0300200180100080100040080040040000030000008000006000 001800000C000007000003800703C00881E00840E00820F00820F00820F0041070042070022070 0200700100E00080E0006180001F00> 20 31 -4 1 23] 50 @pc restore 23 r save [<1F000061C000406000803000803800801C00E01E00F00E00F00F00700F00000F00000780000780 0007800007800807000C0700060600058C00047800040000020000020000020000020000010000 01000001FE0001FF8000FFC000C060> 19 31 -5 1 23] 53 @pc restore cmsy10.329 @sf 23 r m (\002) s cmti10.329 @sf save [<80780080FC0041FE0047FF007E0300200180100080100040080040040000030000008000006000 001800000C000007000003800703C00881E00840E00820F00820F00820F0041070042070022070 0200700100E00080E0006180001F00> 20 31 -4 1 23] 50 @pc restore 23 r save [<1F000061C000406000803000803800801C00E01E00F00E00F00F00700F00000F00000780000780 0007800007800807000C0700060600058C00047800040000020000020000020000020000010000 01000001FE0001FF8000FFC000C060> 19 31 -5 1 23] 53 @pc restore 45 r m (matrix.) 35 (The) 20 (cr) -1 (osses) ks 74 1080 p m (ar) -1 (e) 18 (the) 19 (eigenvalues) 18 (of) 19 (the) 19 (original) 19 (matrix;) 20 (the) 20 (stars) 18 (ar) -1 (e) 18 (the) 19 (initial) 18 (guesses;) 19 (the) 19 (cir) -1 (cles) 17 (ar) -1 (e) 18 (the) ks 74 1137 p m (eigenvalues) 15 (c) -1 (ompute) -1 (d) 15 (by) 16 (our) 17 (algorithm;) 17 (the) 17 (dots) 16 (ar) -1 (e) 15 (the) 17 (iter) -1 (ates) 15 (arising) 15 (in) 16 (Newton) -4 ('s) 15 (iter) -1 (ations.) ks cmr10.329 @sf 74 1266 p m (to) s cmmi10.329 @sf 19 r m (\025) s cmr10.329 @sf 19 r m (can) 20 (b) 1 (e) 20 (exp) 1 (ected) 21 (to) 19 (con) 0 (v) 0 (erge) 17 (to) 19 (the) 20 (space) 20 (generated) 20 (b) 0 (y) ks cmmi10.329 @sf 18 r m (x) s cmr8.300 @sf 1352 1273 p m (1) s cmmi10.329 @sf 1372 1266 p m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 1453 1266 p m (;) 8 (x) ks cmmi8.300 @sf 1500 1273 p m (`) s cmr10.329 @sf 1515 1266 p m (.) 34 (As) 19 (the) 20 (eigen) 0 (v) -2 (alue) ks cmmi10.329 @sf 20 r m (\025) s cmr10.329 @sf 74 1366 p m (approac) 0 (hes) 14 (the) 15 (cluster) 15 (ho) 0 (w) -1 (ev) -1 (er,) 13 (con) 0 (tin) 0 (ued) 14 (corrections) 15 (to) 14 (the) 15 (eigen) 0 (v) 0 (ector) 13 (cannot) 14 (b) 1 (e) 16 (exp) 1 (ected) 16 (to) ks 74 1466 p m (re\014ne) 16 (it.) 20 (W) -3 (e) 14 (refer) 14 (the) 15 (reader) 15 (to) 14 (the) 15 (particularly) 16 (lucid) 17 (accoun) 0 (t) 14 (in) 15 ([) 0 (14) ks 1429 1466 p m (]) 14 (for) 14 (a) 15 (justi\014cation) 15 (of) 15 (these) ks 74 1565 p m (claims.) 25 (Solving) 17 (as) 16 (in) 18 (in) 0 (v) 0 (erse) 15 (iteration) 16 (\(see) 17 (INVIT) 17 ([) 0 (15) ks 1146 1565 p m (]\)) 16 (is) 17 (a) 16 (p) 1 (ossible) 18 (w) 0 (a) -1 (y) 14 (around) 17 (this) 17 (problem.) ks 74 1665 p m (Computing) 13 (the) 13 (residual) 15 (with) 13 (extended) 14 (precision) 14 (arithmetic) 14 (is) 13 (also) 13 (an) 13 (ob) 0 (vious) 12 (approac) 0 (h,) 12 (and) 13 (has) ks 74 1765 p m (b) 1 (een) 16 (successful) 17 (in) 16 (practice.) ks 124 1906 p m (When) 13 (approac) 0 (hing) 13 (a) 12 (singular) 14 (solution,) 14 (Newton's) 13 (metho) 1 (d) 13 (loses) 13 (its) 14 (quadratic) 13 (con) 0 (v) -1 (ergence) 12 (rate.) ks 74 2005 p m (W) -3 (e) 20 (ha) 0 (v) 0 (e) 19 (pro) 0 (v) -1 (ed) 20 (earlier) 22 (\(Thm.) 21 (4.1\)) 19 (that) 21 (the) 21 (Jacobian) 22 (is) 22 (singular) 22 (at) 20 (m) 0 (ultiple) 22 (eigenpairs) 23 (and) ks 74 2105 p m (therefore) 15 (w) 0 (e) 14 (can) 15 (exp) 1 (ect) 16 (slo) 0 (w) 0 (er) 13 (con) 0 (v) 0 (erg) -1 (ence) 14 (when) 16 (these) 15 (are) 15 (the) 16 (target) 14 (\(see) 15 (Fig.) 15 (1\).) ks 124 2246 p m (Recall) 17 (the) 15 (rate) 15 (of) 15 (c) 0 (hange) 14 (of) ks cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf 14 r m (that) 15 (w) 0 (e) 14 (deriv) 0 (ed) 15 (in) 16 (section) 16 (2:) ks cmsy10.329 @sf 796 2386 p m (j) s cmmi10.329 @sf m (\025) s cmsy8.300 @sf 836 2368 p m (0) s cmr10.329 @sf 847 2386 p m (\(0\)) s cmsy10.329 @sf m (j) s cmr10.329 @sf 11 r m (=) s cmsy10.329 @sf 983 2356 p m (j) s cmmi10.329 @sf m (\013) s cmsy10.329 @sf m (jj) s cmmi10.329 @sf m (y) s cmmi8.300 @sf 1073 2363 p m (k) s cmr8.300 @sf 1 r m (+1) s cmsy10.329 @sf 1139 2356 p m (jj) s cmmi10.329 @sf m (x) s cmmi8.300 @sf 1191 2363 p m (k) s cmsy10.329 @sf 1212 2356 p m (j) s 983 2376 p 242 2 ru 1049 2417 p m (j) s cmmi10.329 @sf m (y) s cmmi8.300 @sf 1086 2405 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 1120 2417 p m (x) s cmsy10.329 @sf m (j) s cmmi10.329 @sf 1229 2386 p m (:) s cmr10.329 @sf 74 2526 p m (W) -3 (e) 18 (wish) 20 (to) 18 (caution) 20 (from) 18 (hastily) 20 (dra) 0 (wing) 18 (conclusions) 20 (ab) 1 (out) 19 (the) 19 (sensitivit) 0 (y) 19 (of) 19 (the) 19 (eigen) 0 (v) -2 (alues) ks 74 2626 p m (of) 17 (a) 16 (defectiv) 0 (e) 17 (matrix) 16 (to) 16 (our) 17 (dividing) 19 (pro) 1 (cess) 17 (from) 16 (this) 17 (expression.) 26 (Indeed,) 18 (as) 17 (an) 16 (extreme) 17 (case) ks 74 2726 p m (whic) 0 (h) 17 (will) 19 (help) 18 (illu) 1 (strate) 18 (our) 17 (p) 1 (oin) 0 (t,) 16 (the) 17 (eigen) 0 (v) -2 (alues) 18 (of) 16 (a) 17 (defectiv) 0 (e) 17 (matrix) 17 (can) 17 (remain) 18 (virtually) ks @eop 25 @bop0 cmr8.300 @sf [<87807FC03C20> 11 3 -3 -19 18] 126 @dc cmmi8.300 @sf [<78F000C50800E70400C3020003020003000001800001800001800041800020C30020C38011A180 0F1F00> 17 14 -1 0 20] 120 @dc cmmi6.300 @sf [<7C008300C000808001801F003E002000218010800F00> 9 11 -3 0 15] 115 @dc 25 @bop1 cmr10.329 @sf 1919 -77 p m (25) s 74 99 p m (Therefore,) 15 (letting) ks cmmi10.329 @sf 16 r save [<1F0031C060E06070E038E03CE01CE01EE01EE01E700F700F700F700F380F380F3C0E3A0E1D0C1C F01C001C000E000E000E000E0007000700070007003F800780> 16 32 -2 0 20] 98 @pc restore cmr10.329 @sf 32 r m (=) s cmex10.300 @sf 517 27 p save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pc restore cmmi10.329 @sf 571 72 p m (r) s cmr10.329 @sf 571 127 p m (0) s cmex10.300 @sf 614 27 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 647 99 p m (,) 15 (w) 0 (e) 14 (ha) 0 (v) -1 (e,) ks cmex10.300 @sf 487 200 p save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pc restore cmmi10.329 @sf 542 245 p m (y) s 541 300 p m (\026) s cmex10.300 @sf 589 200 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 634 272 p m (=) s cmmi10.329 @sf 13 r save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 711 254 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 759 272 p save [<1F0031C060E06070E038E03CE01CE01EE01EE01E700F700F700F700F380F380F3C0E3A0E1D0C1C F01C001C000E000E000E000E0007000700070007003F800780> 16 32 -2 0 20] 98 @pc restore cmr10.329 @sf 32 r m (=) s cmmi10.329 @sf 13 r save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 868 254 p m (\000) s cmr8.300 @sf m (1) s 864 284 p m (0) s cmmi10.329 @sf 916 272 p save [<1F0031C060E06070E038E03CE01CE01EE01EE01E700F700F700F700F380F380F3C0E3A0E1D0C1C F01C001C000E000E000E000E0007000700070007003F800780> 16 32 -2 0 20] 98 @pc restore cmsy10.329 @sf 29 r m (\000) s cmmi10.329 @sf 1070 242 p m (v) s cmmi8.300 @sf 1094 227 p m (T) s cmmi10.329 @sf 1121 242 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 1150 224 p m (\000) s cmr8.300 @sf m (1) s 1146 254 p m (0) s cmmi10.329 @sf 1198 242 p save [<1F0031C060E06070E038E03CE01CE01EE01EE01E700F700F700F700F380F380F3C0E3A0E1D0C1C F01C001C000E000E000E000E0007000700070007003F800780> 16 32 -2 0 20] 98 @pc restore 996 262 p 296 2 ru cmr10.329 @sf 996 307 p m (1) 10 (+) ks cmmi10.329 @sf 10 r m (v) s cmmi8.300 @sf 1098 295 p m (T) s cmmi10.329 @sf 1125 307 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 1154 289 p m (\000) s cmr8.300 @sf m (1) s 1150 319 p m (0) s cmmi10.329 @sf 1202 307 p m (e) s cmmi8.300 @sf 1223 314 p m (n) s cmr8.300 @sf m (+1) s cmmi10.329 @sf 1297 272 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 1326 254 p m (\000) s cmr8.300 @sf m (1) s 1322 284 p m (0) s cmmi10.329 @sf 1373 272 p m (e) s cmmi8.300 @sf 1394 279 p m (n) s cmr8.300 @sf m (+1) s cmmi10.329 @sf 1463 272 p m (:) s cmr10.329 @sf 1883 272 p m (\(11\)) s 74 416 p m (It) 15 (can) 16 (b) 1 (e) 16 (easily) 16 (c) 0 (hec) 0 (k) -1 (ed) 14 (that) ks cmmi10.329 @sf 856 515 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 885 497 p m (\000) s cmr8.300 @sf m (1) s 881 528 p m (0) s cmmi10.329 @sf 933 515 p save [<1F0031C060E06070E038E03CE01CE01EE01EE01E700F700F700F700F380F380F3C0E3A0E1D0C1C F01C001C000E000E000E000E0007000700070007003F800780> 16 32 -2 0 20] 98 @pc restore cmr10.329 @sf 32 r m (=) s cmex10.300 @sf 1013 444 p save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pc restore cmsy10.329 @sf 1067 488 p m (\000) s cmmi10.329 @sf m (x) s cmr10.329 @sf 1086 544 p m (0) s cmex10.300 @sf 1149 444 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 74 641 p m (and) 16 (that) ks cmmi10.329 @sf 839 741 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 868 723 p m (\000) s cmr8.300 @sf m (1) s 864 753 p m (0) s cmmi10.329 @sf 916 741 p m (e) s cmmi8.300 @sf 937 748 p m (n) s cmr8.300 @sf m (+1) s cmr10.329 @sf 1018 741 p m (=) s cmex10.300 @sf 1066 669 p save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pc restore cmr10.329 @sf 1123 714 p m (~) s cmmi10.329 @sf 1120 714 p m (x) s cmr10.329 @sf 1121 769 p m (1) s cmex10.300 @sf 1166 669 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 74 867 p m (where) 17 (\() ks cmmi10.329 @sf m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 11 r m (\025I) s cmr10.329 @sf 4 r m (\)) 3 (~) ks cmmi10.329 @sf 392 867 p m (x) s cmr10.329 @sf 431 867 p m (=) s cmmi10.329 @sf 15 r m (x) s cmr10.329 @sf m (.) 24 (No) 0 (w) 14 (if) 17 (w) 0 (e) 15 (let) 17 (\() ks cmmi10.329 @sf m (x) s cmr8.300 @sf 870 874 p m (1) s cmmi10.329 @sf 889 867 p m (;) 8 (\025) ks cmr8.300 @sf 937 874 p m (1) s cmr10.329 @sf 956 867 p m (\)) 16 (b) 1 (e) 17 (the) 16 (next) 17 (eigenpair) 18 (w) 0 (e) 15 (ha) 0 (v) -1 (e) 15 (from) 15 (\(11\)) 15 (and) 17 (the) ks 74 966 p m (subsequen) 0 (t) 15 (equalities,) ks cmex10.300 @sf 280 1038 p save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pc restore cmmi10.329 @sf 334 1083 p m (x) s cmr8.300 @sf 360 1090 p m (1) s cmmi10.329 @sf 333 1138 p m (\025) s cmr8.300 @sf 360 1145 p m (1) s cmex10.300 @sf 400 1038 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 446 1110 p m (=) s cmex10.300 @sf 494 1038 p save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pc restore cmmi10.329 @sf 548 1083 p m (x) s 547 1138 p m (\025) s cmex10.300 @sf 595 1038 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 638 1110 p m (+) s cmex10.300 @sf 683 1038 p save [<0000180000300000600000E00000C0000180000380000700000600000E00000C00001C00003800 00380000700000700000E00000E00001E00001C00001C000038000038000038000078000070000 0700000F00000E00000E00001E00001E00001E00001C00001C00003C00003C00003C00003C0000 380000780000780000780000780000780000780000780000780000700000F00000F00000F00000 F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000 F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000700000780000780000 7800007800007800007800007800007800003800003C00003C00003C00003C00001C00001C0000 1E00001E00001E00000E00000E00000F000007000007000007800003800003800003800001C000 01C00001E00000E00000E000007000007000003800003800001C00000C00000E00000600000700 0003800001800000C00000E0000060000030000018> 21 124 -10 122 33] 32 @pc restore cmmi10.329 @sf 738 1083 p m (y) s 737 1138 p m (\026) s cmex10.300 @sf 785 1038 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 830 1110 p m (=) s cmex10.300 @sf 878 1038 p save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pc restore cmmi10.329 @sf 932 1083 p m (x) s 932 1138 p m (\025) s cmex10.300 @sf 979 1038 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1022 1110 p m (+) s cmex10.300 @sf 1068 1038 p save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pc restore cmsy10.329 @sf 1121 1083 p m (\000) s cmmi10.329 @sf m (x) s cmr10.329 @sf 1141 1138 p m (0) s cmex10.300 @sf 1203 1038 p save [ 21 124 -1 122 33] 33 @pc restore cmsy10.329 @sf 1246 1110 p m (\000) s cmmi10.329 @sf 1371 1080 p m (v) s cmmi8.300 @sf 1395 1065 p m (T) s cmmi10.329 @sf 1422 1080 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 1451 1062 p m (\000) s cmr8.300 @sf m (1) s 1447 1092 p m (0) s cmmi10.329 @sf 1499 1080 p save [<1F0031C060E06070E038E03CE01CE01EE01EE01E700F700F700F700F380F380F3C0E3A0E1D0C1C F01C001C000E000E000E000E0007000700070007003F800780> 16 32 -2 0 20] 98 @pc restore 1297 1100 p 296 2 ru cmr10.329 @sf 1297 1145 p m (1) 10 (+) ks cmmi10.329 @sf 10 r m (v) s cmmi8.300 @sf 1399 1133 p m (T) s cmmi10.329 @sf 1426 1145 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 1455 1127 p m (\000) s cmr8.300 @sf m (1) s 1451 1157 p m (0) s cmmi10.329 @sf 1503 1145 p m (e) s cmmi8.300 @sf 1524 1152 p m (n) s cmr8.300 @sf m (+1) s cmex10.300 @sf 1605 1038 p save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pc restore cmr10.329 @sf 1662 1083 p m (~) s cmmi10.329 @sf 1659 1083 p m (x) s cmr10.329 @sf 1660 1138 p m (1) s cmex10.300 @sf 1706 1038 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1746 1110 p m (:) s cmr10.329 @sf 74 1254 p m (F) -3 (urthermore,) ks cmmi10.329 @sf 881 1324 p m (v) s cmmi8.300 @sf 905 1308 p m (T) s cmmi10.329 @sf 932 1324 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 961 1306 p m (\000) s cmr8.300 @sf m (1) s 957 1335 p m (0) s cmmi10.329 @sf 1009 1324 p save [<1F0031C060E06070E038E03CE01CE01EE01EE01E700F700F700F700F380F380F3C0E3A0E1D0C1C F01C001C000E000E000E000E0007000700070007003F800780> 16 32 -2 0 20] 98 @pc restore 807 1344 p 296 2 ru cmr10.329 @sf 807 1388 p m (1) 10 (+) ks cmmi10.329 @sf 10 r m (v) s cmmi8.300 @sf 909 1376 p m (T) s cmmi10.329 @sf 936 1388 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 965 1370 p m (\000) s cmr8.300 @sf m (1) s 961 1401 p m (0) s cmmi10.329 @sf 1013 1388 p m (e) s cmmi8.300 @sf 1034 1395 p m (n) s cmr8.300 @sf m (+1) s cmr10.329 @sf 1120 1354 p m (=) s cmsy10.329 @sf 1173 1324 p m (\000) s cmr10.329 @sf m (1) s 1173 1344 p 59 2 ru 1183 1385 p m (~) s cmmi10.329 @sf 1180 1385 p m (x) s cmmi8.300 @sf 1206 1392 p m (s) s cmr10.329 @sf 74 1479 p m (and) 17 (so) 16 (\014nally) 18 (w) 0 (e) 15 (see) 17 (that) 16 (our) 16 (sc) 0 (heme) 16 (reduces) 17 (to) 16 (the) 17 (follo) 0 (wing:) 22 (Giv) 0 (en) 16 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 15 (compute) 16 (the) 17 (next) ks 74 1579 p m (iterate) 15 (\() ks cmmi10.329 @sf m (x) s cmr8.300 @sf 262 1586 p m (1) s cmmi10.329 @sf 282 1579 p m (;) 8 (\025) ks cmr8.300 @sf 330 1586 p m (1) s cmr10.329 @sf 348 1579 p m (\)) 15 (via) ks 830 1678 p m (\() s cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (\025I) s cmr10.329 @sf 4 r m (\)) 3 (~) ks cmmi10.329 @sf 1014 1678 p m (x) s cmr10.329 @sf 1051 1678 p m (=) s cmmi10.329 @sf 13 r m (x) s 888 1735 p m (x) s cmr8.300 @sf 914 1742 p m (1) s cmr10.329 @sf 947 1735 p m (=) s cmr8.300 @sf 1009 1718 p m (1) s 1000 1725 p 37 2 ru 1002 1751 p m (~) s cmmi8.300 @sf 1000 1751 p m (x) s cmmi6.300 @sf 1020 1755 p m (s) s cmr10.329 @sf 1044 1735 p m (~) s cmmi10.329 @sf 1041 1735 p m (x) s 854 1794 p m (\025) s cmr8.300 @sf 881 1801 p m (1) s cmr10.329 @sf 912 1794 p m (=) s cmmi10.329 @sf 13 r m (\025) s cmr10.329 @sf 10 r m (+) s cmr8.300 @sf 1057 1777 p m (1) s 1048 1784 p 37 2 ru 1050 1810 p m (~) s cmmi8.300 @sf 1048 1810 p m (x) s cmmi6.300 @sf 1068 1814 p m (s) s cmmi10.329 @sf 1089 1794 p m (:) s cmr10.329 @sf 1883 1738 p m (\(12\)) s cmbx12.300 @sf 74 1957 p save [<03F8000FFF001C1F803007C07007E0FC03F0FC03F0FE03F8FE03F87C03F83803F80003F80003F8 0003F00003F01803E01807E01E0FC01FFF0019FC001800001800001800001800001BC0001FF800 1FFE001FFF001FFF801FFFC01E01E0100020> 21 32 -3 0 28] 53 @pc restore 28 r m (.1) s 202 1957 p save [<0003FE0000001FFFC00000FF00F00001F800380003F0000C0007C00006000F800003001F800003 003F000003803F000001807F000001807E000001807E00000000FE00000000FE00000000FE0000 0000FE00000000FE00000000FE00000000FE00000000FE000000007E000001807E000001807F00 0001803F000003803F000003801F800007800F8000078007C0000F8003E0001F8001F8003F8000 FF01E380001FFF81800003FE0080> 33 34 -3 0 40] 67 @pc restore 40 r m (ase) s 19 r save [<001800C000003800E000003C01E000007C01F000007E03F000007E03F00000FE03D80000FB07D8 0001FB079C0001F38F8C0001F18F0C0003E18F060003E0DF060007E0DE070007C0DE030007C07E 03000F807C01800F807C01800F807801801F007800C0FFE7FF07F8FFE7FF07F8> 37 22 -1 0 40] 119 @pc restore 40 r m (hen) s 19 r save [ 40 34 -2 0 40] 72 @pc restore cmbx12.300 @sf 63 r m (is) 18 (de) ks save [<7FF8007FF8000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F8000 0F80000F80000F80000F80000F80000F80000F8000FFFC00FFFC000F80000F80000F80000F8000 0F80000F80000F83C00F87E007C7E003C7E001E3E000FFC0003F80> 19 35 -1 0 17] 102 @pc restore 17 r m (ecti) s save [<000E0000000E0000001F0000001F0000003F8000003F8000007FC000007CC000007CC00000F860 0000F8600001F0300001F0300003E0180003E0180007E01C0007C00C000FC00E000F8006000F80 0600FFE01FE0FFE01FE0> 27 22 -1 0 30] 118 @pc restore 29 r m (e) s cmr10.329 @sf 74 2128 p m (When) 15 (the) 15 (algorithm) 15 (is) 15 (expressed) 16 (as) 14 (in) 15 (\(12\)) 14 (w) 0 (e) 13 (can) 15 (readily) 16 (see) 15 (some) 15 (of) 14 (the) 15 (di\016culties) 17 (that) 14 (arise) ks 74 2227 p m (when) 13 (the) 13 (matrix) ks cmmi10.329 @sf 13 r m (H) s cmr10.329 @sf 16 r m (is) 13 (defectiv) 0 (e) 13 (or) 12 (almost) 13 (defectiv) 0 (e,) 12 (whic) 0 (h) 13 (is) 13 (more) 13 (lik) 0 (ely) 13 (in) 14 (general) 13 (due) 14 (to) 12 (round-) ks 74 2327 p m (o\013) 11 (errors.) 19 (These) 12 (problems) 13 (are) 12 (similar) 13 (to) 11 (the) 13 (kind) 13 (of) 12 (problems) 12 (that) 12 (face) 12 (the) 12 (application) 14 (of) 12 (in) 0 (v) 0 (erse) ks 74 2427 p m (iteration.) 20 (More) 12 (precisely) -3 (,) 15 (assume) 13 (that) ks cmmi10.329 @sf 13 r m (H) s cmr10.329 @sf 17 r m (is) 14 (almost) 12 (defectiv) 0 (e) 14 (with) ks cmmi10.329 @sf 14 r m (x) s cmr8.300 @sf 1395 2434 p m (1) s cmmi10.329 @sf 1414 2427 p m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 1495 2427 p m (;) 8 (x) ks cmmi8.300 @sf 1542 2434 p m (n) s cmr10.329 @sf 1578 2427 p m (as) 13 (a) 13 (complete) 14 (set) 14 (of) ks 74 2526 p m (eigen) 0 (v) 0 (ectors.) 17 (Let) ks cmmi10.329 @sf 14 r m (\025) s cmr8.300 @sf 452 2533 p m (1) s cmmi10.329 @sf 471 2526 p m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 552 2526 p m (;) 8 (\025) ks cmmi8.300 @sf 600 2533 p m (`) s cmr10.329 @sf 628 2526 p m (b) 1 (e) 14 (a) 13 (cluster) 13 (of) 13 (eigen) 0 (v) -2 (alues) 13 (of) ks cmmi10.329 @sf 13 r m (H) s cmr10.329 @sf 16 r m (and) 14 (supp) 1 (ose) 14 (that) 12 (the) 13 (initial) 15 (appro) 0 (x-) ks 74 2626 p m (imate) 19 (eigen) 0 (v) -2 (alue) ks cmmi10.329 @sf 18 r m (\025) s cmr10.329 @sf 18 r m (corresp) 1 (onds) 19 (to) 18 (one) 18 (of) 18 (these.) 30 (The) 19 (eigen) 0 (v) 0 (ectors) ks cmmi10.329 @sf 17 r m (x) s cmr8.300 @sf 1447 2633 p m (1) s cmmi10.329 @sf 1466 2626 p m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 1547 2626 p m (;) 8 (x) ks cmmi8.300 @sf 1594 2633 p m (`) s cmr10.329 @sf 1628 2626 p m (corresp) 1 (onding) 20 (to) ks 74 2726 p m (these) 15 (eigen) 0 (v) -2 (alues) 15 (are) 14 (then) 15 (almost) 14 (linearly) 16 (dep) 1 (enden) 1 (t.) 20 (In) 15 (general,) 15 (the) 14 (eigen) 0 (v) 0 (ector) 13 (corresp) 1 (onding) ks @eop 24 @bop0 24 @bop1 cmr10.329 @sf 1919 -77 p m (24) s 74 67 p m (this) 18 (section) 17 (with) 18 (a) 17 (particular) 17 (emphasis) 18 (on) 17 (the) 18 (case) 17 (when) 17 (either) 18 (the) 17 (matrix) ks cmmi10.329 @sf 17 r m (H) s cmr10.329 @sf 21 r m (or) 16 (the) 18 (mo) 1 (di\014ed) ks 74 167 p m (matrix) s cmmi10.329 @sf 17 r m (H) s cmr8.300 @sf 262 174 p m (0) s cmr10.329 @sf 298 167 p m (is) 18 (defectiv) 0 (e,) 16 (i.e.,) 18 (when) 17 (either) 18 (one) 17 (of) 16 (these) 17 (matrices) 17 (do) 1 (es) 17 (not) 17 (ha) 0 (v) -1 (e) 16 (a) 16 (complete) 18 (set) 17 (of) ks 74 266 p m (eigen) 0 (v) 0 (ectors.) 17 (As) 13 (w) 0 (e) 12 (remark) 0 (ed) 11 (earlier,) 14 (an) 13 (eigen) 0 (v) -2 (alue) 12 (of) ks cmmi10.329 @sf 13 r m (H) s cmr10.329 @sf 16 r m (\(with) 13 (no) 13 (zeros) 12 (on) 13 (the) 13 (sub) 1 (diagonal\)) 14 (can) ks 74 366 p m (only) 19 (ha) 0 (v) -1 (e) 17 (geometric) 18 (m) 0 (ultiplicit) 0 (y) 18 (one,) 19 (and) 18 (therefore) ks cmmi10.329 @sf 18 r m (H) s cmr10.329 @sf 22 r m (is) 18 (defectiv) 0 (e) 18 (whenev) 0 (er) 18 (it) 18 (has) 18 (a) 18 (m) 0 (ultiple) ks 74 466 p m (eigen) 0 (v) -2 (alue.) 20 (An) 15 (eigen) 0 (v) -2 (alue) 14 (of) ks cmmi10.329 @sf 14 r m (H) s cmr8.300 @sf 688 473 p m (0) s cmr10.329 @sf 722 466 p m (on) 15 (the) 15 (other) 14 (hand,) 15 (can) 14 (ha) 0 (v) 0 (e) 12 (geometric) 15 (m) 0 (ultiplicit) 0 (y) 15 (one) 15 (or) 14 (t) 0 (w) -1 (o) -1 (.) ks 74 565 p m (In) 16 (what) 15 (follo) 0 (ws) ks cmmi10.329 @sf 14 r m (n) s cmr10.329 @sf 15 r m (is) 16 (the) 15 (order) 15 (of) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 4 r m (.) s 124 706 p m (The) 11 (connection) 13 (b) 1 (et) 0 (w) -1 (een) 10 (Newton's) 10 (metho) 1 (d) 12 (and) 11 (in) 0 (v) 0 (erse) 10 (iteration) 11 (is) 12 (w) 0 (ell) 11 (kno) 0 (wn) 10 ([) 0 (14) ks 1703 706 p m (].) 18 (W) -3 (e) 10 (presen) 0 (t) ks 74 806 p m (a) 18 (pro) 1 (of) 18 (whic) 0 (h) 18 (motiv) -2 (ates) 17 (the) 19 (subsequen) 0 (t) 18 (analysis:) 26 (w) 0 (e) 17 (let) ks cmmi10.329 @sf 19 r save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmr10.329 @sf 48 r m (b) 1 (e) 19 (the) 18 (Jacobian) 20 (of) 17 (the) 19 (map) ks cmmi10.329 @sf 18 r save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 1887 813 p m (s) s cmr10.329 @sf 1924 806 p m (at) s 74 906 p m (\() s cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 13 (de\014ned) 17 (in) 16 (section) 16 (2,) ks cmmi10.329 @sf 785 1005 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmr10.329 @sf 43 r m (=) s cmex10.300 @sf 876 933 p save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pc restore cmmi10.329 @sf 929 978 p m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmsy10.329 @sf 1118 978 p m (\000) s cmmi10.329 @sf m (x) s 978 1033 p m (e) s cmmi8.300 @sf 999 1018 p m (T) s 999 1045 p m (s) s cmr10.329 @sf 1137 1033 p m (0) s cmex10.300 @sf 1200 933 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1240 1005 p m (;) s cmr10.329 @sf 74 1132 p m (and) 16 (w) 0 (e) 13 (assume) 16 (that) ks cmmi10.329 @sf 14 r m (x) s cmmi8.300 @sf 511 1139 p m (s) s cmr10.329 @sf 542 1132 p m (=) 13 (1.) 20 (The) 15 (order) 15 (of) 15 (the) 15 (Jacobian) 16 (is) ks cmmi10.329 @sf 16 r m (n) s cmr10.329 @sf 10 r m (+) 11 (1.) 19 (Then,) ks cmmi10.329 @sf 853 1277 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmr10.329 @sf 43 r m (=) s cmmi10.329 @sf 13 r save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmr8.300 @sf 969 1284 p m (0) s cmr10.329 @sf 999 1277 p m (+) s cmmi10.329 @sf 10 r m (e) s cmmi8.300 @sf 1065 1284 p m (n) s cmr8.300 @sf m (+1) s cmmi10.329 @sf 1134 1277 p m (v) s cmmi8.300 @sf 1158 1259 p m (T) s cmr10.329 @sf 74 1422 p m (with) s cmmi10.329 @sf 788 1522 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmr8.300 @sf 813 1529 p m (0) s cmr10.329 @sf 845 1522 p m (=) s cmex10.300 @sf 893 1450 p save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pc restore cmmi10.329 @sf 947 1495 p m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmsy10.329 @sf 1136 1495 p m (\000) s cmmi10.329 @sf m (x) s cmr10.329 @sf 1009 1550 p m (0) s 1155 1550 p m (1) s cmex10.300 @sf 1218 1450 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 74 1649 p m (and,) s cmmi10.329 @sf 758 1836 p m (v) s cmr10.329 @sf 14 r m (=) s cmmi10.329 @sf 13 r m (e) s cmmi8.300 @sf 863 1843 p m (s) s cmsy10.329 @sf 892 1836 p m (\000) s cmmi10.329 @sf 10 r m (e) s cmmi8.300 @sf 958 1843 p m (n) s cmr8.300 @sf m (+1) s cmr10.329 @sf 1040 1836 p m (=) s cmex10.300 @sf 1088 1664 p m (0) s 1088 1737 p m (B) s 1088 1762 p m (B) s 1088 1787 p m (B) s 1088 1812 p m (B) s 1088 1837 p m (B) s 1088 1862 p m (B) s 1088 1887 p m (B) s 1088 1914 p m (@) s cmr10.329 @sf 1163 1701 p m (0) s 1168 1724 p m (.) s 1168 1741 p m (.) s 1168 1758 p m (.) s 1163 1796 p m (0) s 1163 1836 p m (1) s 1163 1876 p m (0) s 1168 1899 p m (.) s 1168 1916 p m (.) s 1168 1933 p m (.) s cmsy10.329 @sf 1145 1970 p m (\000) s cmr10.329 @sf m (1) s cmex10.300 @sf 1224 1664 p m (1) s 1224 1737 p m (C) s 1224 1762 p m (C) s 1224 1787 p m (C) s 1224 1812 p m (C) s 1224 1837 p m (C) s 1224 1862 p m (C) s 1224 1887 p m (C) s 1224 1914 p m (A) s cmmi10.329 @sf 1268 1836 p m (:) s cmr10.329 @sf 74 2050 p m (Assume) s cmmi10.329 @sf 15 r save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmr8.300 @sf 267 2057 p m (0) s cmr10.329 @sf 302 2050 p m (it) 15 (is) 16 (not) 14 (singular;) 16 (this) 15 (is) 15 (true) 15 (if) 15 (and) 15 (only) 16 (if) ks cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf 14 r m (is) 16 (not) 14 (an) 15 (eigen) 0 (v) -2 (alue.) 20 (Assume) 15 (also) 15 (that) ks cmmi10.329 @sf 74 2150 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmr10.329 @sf 45 r m (is) 16 (not) 14 (singular.) 21 (The) 16 (correction) 15 (to) 15 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 13 (is) 15 (computed) 16 (in) 16 (the) 15 (follo) 0 (wing) 15 (manner:) ks cmex10.300 @sf 804 2223 p save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pc restore cmmi10.329 @sf 860 2268 p m (y) s 858 2323 p m (\026) s cmex10.300 @sf 906 2223 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 952 2295 p m (=) s cmmi10.329 @sf 13 r save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 1029 2277 p m (\000) s cmr8.300 @sf m (1) s cmex10.300 @sf 1084 2223 p save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pc restore cmmi10.329 @sf 1138 2268 p m (r) s cmr10.329 @sf 1137 2323 p m (0) s cmex10.300 @sf 1181 2223 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1221 2295 p m (;) s cmr10.329 @sf 74 2440 p m (where) s cmmi10.329 @sf 16 r m (r) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (\025x) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (H) 4 (x) ks cmr10.329 @sf m (.) 19 (Using) 16 (the) 15 (Sherman-Morrison-W) -3 (o) 1 (o) 1 (dbury) 15 (form) 0 (ula) 14 ([) 0 (8) ks 1511 2440 p m (]) 15 (w) 0 (e) 14 (can) 15 (write) ks cmmi10.329 @sf 16 r save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 1835 2425 p m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 1897 2440 p m (as,) s cmmi10.329 @sf 386 2586 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 415 2568 p m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 475 2586 p m (=) 13 (\() ks cmmi10.329 @sf save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmr8.300 @sf 566 2593 p m (0) s cmr10.329 @sf 596 2586 p m (+) s cmmi10.329 @sf 10 r m (e) s cmmi8.300 @sf 662 2593 p m (n) s cmr8.300 @sf m (+1) s cmmi10.329 @sf 731 2586 p m (v) s cmmi8.300 @sf 755 2568 p m (T) s cmr10.329 @sf 782 2586 p m (\)) s cmsy8.300 @sf 800 2568 p m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 859 2586 p m (=) s cmmi10.329 @sf 13 r save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 936 2568 p m (\000) s cmr8.300 @sf m (1) s 932 2598 p m (0) s cmsy10.329 @sf 994 2586 p m (\000) s cmr10.329 @sf 1181 2556 p m (1) s 1045 2576 p 296 2 ru 1045 2621 p m (1) 10 (+) ks cmmi10.329 @sf 10 r m (v) s cmmi8.300 @sf 1147 2609 p m (T) s cmmi10.329 @sf 1174 2621 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 1203 2603 p m (\000) s cmr8.300 @sf m (1) s 1199 2633 p m (0) s cmmi10.329 @sf 1251 2621 p m (e) s cmmi8.300 @sf 1272 2628 p m (n) s cmr8.300 @sf m (+1) s cmmi10.329 @sf 1346 2586 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 1375 2568 p m (\000) s cmr8.300 @sf m (1) s 1371 2598 p m (0) s cmmi10.329 @sf 1422 2586 p m (e) s cmmi8.300 @sf 1443 2593 p m (n) s cmr8.300 @sf m (+1) s cmmi10.329 @sf 1512 2586 p m (v) s cmmi8.300 @sf 1536 2568 p m (T) s cmmi10.329 @sf 1563 2586 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmsy8.300 @sf 1592 2568 p m (\000) s cmr8.300 @sf m (1) s 1588 2598 p m (0) s cmmi10.329 @sf 1640 2586 p m (:) s @eop 23 @bop0 cmex10.300 @sf [ 2 27 -6 26 14] 12 @dc 1.000000 /cmbx10.329 @newfont cmbx10.329 @sf [<387CFEFEFE7C38> 7 7 -4 0 15] 46 @dc cmti10.329 @sf [<8040202010080804043C3C3C3C1C> 6 14 -3 9 14] 44 @dc 23 @bop1 cmr10.329 @sf 1919 -77 p m (23) s 74 67 p m (direction) 17 (since) 17 (then) 16 (the) 16 (eigen) 0 (v) -2 (alue) 16 (w) 0 (ould) 15 (b) 1 (e) 17 (acting) 16 (lik) 0 (e) 16 (an) 16 (eigen) 0 (v) -2 (alue) 15 (of) 16 (geometric) 16 (m) 0 (ultiplicit) 0 (y) ks 74 167 p m (more) 15 (than) 15 (one,) 15 (whic) 0 (h) 15 (is) 16 (imp) 1 (ossible) 17 (since) 17 (the) 15 (matrix) 15 (is) 15 (unreduced) 17 (\(recall) 16 (that) ks cmmi10.329 @sf 15 r m (x) s cmmi8.300 @sf 1654 174 p m (s) s cmr10.329 @sf 1685 167 p m (=) 13 (1\).) ks 124 308 p m (The) 15 (second) 16 (deriv) -2 (ativ) 0 (e) 15 (of) ks cmmi10.329 @sf 14 r save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 653 315 p m (s) s cmr10.329 @sf 687 308 p m (is) 16 (a) 15 (constan) 0 (t) 13 (biline) 1 (ar) 16 (op) 1 (erator) 15 (with) 15 (norm) 15 (equal) 16 (to) 14 (2.) 20 (In) 16 (fact,) ks cmmi10.329 @sf 717 450 p save [ 32 31 -2 0 29] 70 @pc restore cmsy8.300 @sf 752 432 p m (00) s cmmi8.300 @sf 746 461 p m (s) s cmr10.329 @sf 774 450 p m (\() s cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 11 (=) ks cmex10.300 @sf 943 378 p save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pc restore cmr10.329 @sf 1001 423 p m (0) s 1065 423 p m (-I) s 1001 478 p m (0) s 1070 478 p m (0) s cmex10.300 @sf 1118 376 p m (\014) s 1118 401 p m (\014) s 1118 426 p m (\014) s 1118 451 p m (\014) s 1118 476 p m (\014) s cmr10.329 @sf 1152 423 p m (-I) s 1225 423 p m (0) s 1156 478 p m (0) s 1225 478 p m (0) s cmex10.300 @sf 1268 378 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1309 450 p m (:) s cmr10.329 @sf 74 592 p m (Supp) 1 (ose) 20 (no) 0 (w) 16 (that) 18 (our) 18 (pro) 1 (cedure) 19 (is) 19 (started) 18 (with) 18 (initial) 21 (guess) 18 (\() ks cmmi10.329 @sf m (x) s cmr8.300 @sf 1367 599 p m (0) s cmmi10.329 @sf 1386 592 p m (;) 8 (\025) ks cmr8.300 @sf 1434 599 p m (0) s cmr10.329 @sf 1453 592 p m (\).) 29 (W) -3 (e) 17 (no) 0 (w) 17 (giv) 0 (e) 17 (su\016cien) 0 (t) ks 74 691 p m (conditions) 15 (for) 13 (the) 13 (con) 0 (v) 0 (ergence) 12 (of) 13 (our) 14 (pro) 1 (cedure) 14 (with) 14 (the) 14 (giv) 0 (en) 13 (initial) 15 (guess.) 20 (This) 14 (is) 14 (pro) 0 (vided) 13 (b) 0 (y) ks 74 791 p m (the) 15 (classical) 17 (Kan) 0 (toro) -1 (vic) -1 (h) 14 (theorem) 15 ([) 0 (5) ks 797 791 p m (].) 20 (Let) 15 (us) 15 (\014rst) 15 (in) 0 (tro) 1 (duce) ks cmmi10.329 @sf 824 933 p save [ 37 31 -2 0 39] 75 @pc restore cmr10.329 @sf 55 r m (=) s cmsy10.329 @sf 13 r m (k) s cmmi10.329 @sf save [ 32 31 -2 0 29] 70 @pc restore cmsy8.300 @sf 985 915 p m (0) s 997 910 p m (\000) s cmr8.300 @sf m (1) s cmmi8.300 @sf 997 944 p m (s) s cmr10.329 @sf 1044 933 p m (\() s cmmi10.329 @sf m (x) s cmr8.300 @sf 1088 940 p m (0) s cmmi10.329 @sf 1107 933 p m (;) 8 (\025) ks cmr8.300 @sf 1155 940 p m (0) s cmr10.329 @sf 1174 933 p m (\)) s cmsy10.329 @sf m (k) s cmr10.329 @sf 74 1075 p m (and) s cmmi10.329 @sf 765 1174 p m (c) s cmr8.300 @sf 785 1181 p m (1) s cmr10.329 @sf 817 1174 p m (=) s cmsy10.329 @sf 13 r m (k) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (x) s cmr8.300 @sf 932 1181 p m (1) s cmmi10.329 @sf 951 1174 p m (;) 8 (\025) ks cmr8.300 @sf 999 1181 p m (1) s cmr10.329 @sf 1017 1174 p m (\)) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 11 r m (\() s cmmi10.329 @sf m (x) s cmr8.300 @sf 1135 1181 p m (0) s cmmi10.329 @sf 1154 1174 p m (;) 8 (\025) ks cmr8.300 @sf 1202 1181 p m (0) s cmr10.329 @sf 1220 1174 p m (\)) s cmsy10.329 @sf m (k) s cmmi10.329 @sf m (;) s cmr10.329 @sf 74 1299 p m (where) 16 (\() ks cmmi10.329 @sf m (x) s cmr8.300 @sf 250 1306 p m (1) s cmmi10.329 @sf 269 1299 p m (;) 8 (\025) ks cmr8.300 @sf 317 1306 p m (1) s cmr10.329 @sf 335 1299 p m (\)) 15 (is) 16 (the) 15 (\014rst) 15 (iterate,) 15 (i.e.,) ks 561 1441 p m (\() s cmmi10.329 @sf m (x) s cmr8.300 @sf 605 1448 p m (1) s cmmi10.329 @sf 625 1441 p m (;) 8 (\025) ks cmr8.300 @sf 673 1448 p m (1) s cmr10.329 @sf 691 1441 p m (\)) s cmmi8.300 @sf 709 1423 p m (T) s cmr10.329 @sf 749 1441 p m (=) 13 (\() ks cmmi10.329 @sf m (x) s cmr8.300 @sf 841 1448 p m (0) s cmmi10.329 @sf 860 1441 p m (;) 8 (\025) ks cmr8.300 @sf 908 1448 p m (0) s cmr10.329 @sf 927 1441 p m (\)) s cmmi8.300 @sf 945 1423 p m (T) s cmsy10.329 @sf 982 1441 p m (\000) s cmmi10.329 @sf 10 r save [ 32 31 -2 0 29] 70 @pc restore cmsy8.300 @sf 1062 1423 p m (0) s 1075 1418 p m (\000) s cmr8.300 @sf m (1) s cmmi8.300 @sf 1075 1452 p m (s) s cmr10.329 @sf 1122 1441 p m (\() s cmmi10.329 @sf m (x) s cmr8.300 @sf 1166 1448 p m (0) s cmmi10.329 @sf 1185 1441 p m (;) 8 (\025) ks cmr8.300 @sf 1233 1448 p m (0) s cmr10.329 @sf 1252 1441 p m (\)) s cmmi10.329 @sf save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 1299 1448 p m (s) s cmr10.329 @sf 1317 1441 p m (\() s cmmi10.329 @sf m (x) s cmr8.300 @sf 1361 1448 p m (0) s cmmi10.329 @sf 1380 1441 p m (;) 8 (\025) ks cmr8.300 @sf 1428 1448 p m (0) s cmr10.329 @sf 1447 1441 p m (\)) s cmmi10.329 @sf m (:) s cmr10.329 @sf 74 1583 p m (W) -3 (e) 14 (call) 17 (\() ks cmmi10.329 @sf m (x) s cmr8.300 @sf 280 1590 p m (0) s cmmi10.329 @sf 299 1583 p m (;) 8 (\025) ks cmr8.300 @sf 347 1590 p m (0) s cmr10.329 @sf 366 1583 p m (\),) 14 (.) 8 (.) 8 (.) ks 472 1583 p m (,\() s cmmi10.329 @sf m (x) s cmmi8.300 @sf 529 1590 p m (k) s cmmi10.329 @sf 549 1583 p m (;) 8 (\025) ks cmmi8.300 @sf 597 1590 p m (k) s cmr10.329 @sf 617 1583 p m (\)) 15 (the) 15 (sequence) 17 (of) 15 (iterates) 15 (pro) 1 (duced) 16 (b) 0 (y) 14 (the) 15 (algorithm.) ks cmbx10.329 @sf 74 1770 p save [<03FFFFC003FFFFC00007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0 000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E000C007 E006C007E006C007E006C007E006E007E00E6007E00C6007E00C7007E01C7C07E07C7FFFFFFC7F FFFFFC> 31 30 -2 0 36] 84 @pc restore 36 r save [ 24 32 -3 0 29] 104 @pc restore 29 r save [<00FF8007FFE00F80701E00183E00187C00007C0000FC0000FC0000FC0000FFFFF8FFFFF8FC00F8 7C00F87C00F03E00F01E01E00F83C007FF8001FE00> 21 20 -1 0 24] 101 @pc restore 24 r save [<01FF0007FFC01F83F03E00F83E00F87C007C7C007CFC007EFC007EFC007EFC007EFC007EFC007E 7C007C7C007C3E00F83E00F81F83F007FFC001FF00> 23 20 -1 0 26] 111 @pc restore 26 r save [ 18 20 -2 0 22] 114 @pc restore 22 r save [<00FF8007FFE00F80701E00183E00187C00007C0000FC0000FC0000FC0000FFFFF8FFFFF8FC00F8 7C00F87C00F03E00F01E01E00F83C007FF8001FE00> 21 20 -1 0 24] 101 @pc restore 24 r save [ 39 20 -3 0 46] 109 @pc restore 61 r save [<00FFFE00FFFE0007C00007C00007C00007C00007C00007C0FFFFFEFFFFFEE003C07003C03803C0 1803C00C03C00E03C00703C00383C00183C000C3C00063C00073C0003BC0001FC0000FC00007C0 0007C00003C00001C0> 23 29 -1 0 26] 52 @pc restore 26 r m (.) s save [<03FC001FFF803C0FC07807E0FC03F0FE03F0FE03F8FE03F87C03F83803F80003F80003F00003E0 0007C0000F8001FC0001FC00001F00000F80000FC01E0FC03F07E03F07E03F07E03F07E01E0FC0 0E0F8007FF0001FC00> 21 29 -2 0 26] 51 @pc restore cmti10.329 @sf 386 1770 p m (If) s cmmi10.329 @sf 18 r save [<800000800000800000400000400000400000400000200000200000207C002187001201C01400E0 1400F018007008007808003C08003C08003C04001E04001E04001E04001E02001E02001C02001C 0207D80104700107F801000C01000E008006008007004007004007002003001003000803000406 0003060000F8> 24 41 -1 9 26] 12 @pc restore cmr8.300 @sf 462 1777 p m (0) s cmr10.329 @sf 498 1770 p m (=) s cmmi10.329 @sf 17 r save [ 37 31 -2 0 39] 75 @pc restore 42 r m (c) s cmr8.300 @sf 612 1777 p m (1) s cmmi10.329 @sf 648 1770 p save [<000001C00000078000001E00000078000001E00000078000000E00000038000000F0000003C000 000F0000003C000000F0000000F00000003C0000000F00000003C0000000F0000000380000000E 0000000780000001E0000000780000001E0000000780000001C0> 26 26 -4 2 35] 60 @pc restore cmr10.329 @sf 52 r m (1) s cmmi10.329 @sf m (=) s cmr10.329 @sf m (4) s cmti10.329 @sf m (,) 18 (then) 19 (the) 18 (se) ks -1 r save [<0FFE0000E00000E0000070000070000070000070000038000038000F380030B800705C00703C00 F01C00F01C00F00E00F00E00F00E00F00E007807007807007807003807003C03801C03800E0380 0705800388C000F040> 18 29 -4 9 21] 113 @pc restore 21 r m (uenc) -2 (e) ks cmr10.329 @sf 16 r m (\() s cmmi10.329 @sf m (x) s cmmi8.300 @sf 1213 1777 p m (k) s cmmi10.329 @sf 1234 1770 p m (;) 8 (\025) ks cmmi8.300 @sf 1282 1777 p m (k) s cmr10.329 @sf 1302 1770 p m (\)) s cmti10.329 @sf 19 r m (c) -1 (onver) -2 (ges) ks 16 r save [<0FFE0000E00000E0000070000070000070000070000038000038000F380030B800705C00703C00 F01C00F01C00F00E00F00E00F00E00F00E007807007807007807003807003C03801C03800E0380 0705800388C000F040> 18 29 -4 9 21] 113 @pc restore 21 r m (uadr) -1 (atic) -1 (al) 2 (ly) 17 (starting) ks 74 1869 p m (fr) -1 (om) ks cmr10.329 @sf 16 r m (\() s cmmi10.329 @sf m (x) s cmr8.300 @sf 226 1876 p m (0) s cmmi10.329 @sf 245 1869 p m (;) 8 (\025) ks cmr8.300 @sf 293 1876 p m (0) s cmr10.329 @sf 311 1869 p m (\)) s cmti10.329 @sf m (.) s cmr10.329 @sf 124 2056 p m (The) 14 (pro) 1 (cess) 14 (can) 14 (b) 1 (e) 15 (regarded) 13 (as) 14 (starting) 13 (from) 13 (an) 0 (y) 13 (of) 13 (the) 14 (iterates) 14 (\() ks cmmi10.329 @sf m (x) s cmmi8.300 @sf 1447 2063 p m (i) s cmmi10.329 @sf 1461 2056 p m (;) 8 (\025) ks cmmi8.300 @sf 1509 2063 p m (i) s cmr10.329 @sf 1521 2056 p m (\)) 14 (and) 14 (in) 15 (fact) 13 (will) 15 (often) ks 74 2156 p m (con) 0 (v) 0 (erge) 11 (ev) 0 (en) 13 (when) 14 (the) 14 (conditions) 15 (of) 13 (the) 13 (theorem) 14 (are) 13 (not) 13 (satis\014ed) 14 (at) 13 (\() ks cmmi10.329 @sf m (x) s cmr8.300 @sf 1496 2163 p m (0) s cmmi10.329 @sf 1516 2156 p m (;) 8 (\025) ks cmr8.300 @sf 1564 2163 p m (0) s cmr10.329 @sf 1582 2156 p m (\).) 19 (These) 14 (conditions) ks 74 2256 p m (will) 17 (then) 16 (b) 1 (e) 15 (met) 15 (for) 15 (some) 15 (\() ks cmmi10.329 @sf m (x) s cmmi8.300 @sf 644 2263 p m (k) s cmmi10.329 @sf 665 2256 p m (;) 8 (\025) ks cmmi8.300 @sf 713 2263 p m (k) s cmr10.329 @sf 733 2256 p m (\)) 15 (at) 14 (whic) 0 (h) 15 (stage) 15 (con) 0 (v) -1 (ergence) 14 (b) 1 (ecomes) 16 (quadratic.) ks cmbx10.432 @sf 74 2440 p save [<00FF800003FFF0000FFFF8001F01FE003C007F0078003F8078003F80FC001FC0FE001FC0FE001F E0FE001FE0FE001FE07C001FE018001FE000001FE000001FE000001FC000001FC000001F800C00 3F000E003E000F80FC000FFFF8000E7FC0000E0000000E0000000E0000000E0000000E0000000E 0000000FFE00000FFFC0000FFFE0000FFFF0000FFFF8000FFFFC000FFFFE000F803F000C000300> 27 39 -3 0 34] 53 @pc restore 177 2440 p m (Defecti) -1 (v) -1 (e) ks 20 r save [<00003FF800000003FFFF0000000FFFFFC000003FF007E00000FF8000F80001FE00003C0003FC00 001E0007F000000E000FF0000007001FE0000007001FE0000003803FC0000003803FC000000380 7FC0000003807F80000000007F8000000000FF8000000000FF8000000000FF8000000000FF8000 000000FF8000000000FF8000000000FF8000000000FF8000000000FF80000000007F8000000000 7F80000003807FC0000003803FC0000003803FC0000007801FE0000007801FE0000007800FF000 000F8007F000001F8003FC00003F8001FE00007F8000FF8001FF80003FF007DF80000FFFFF8780 0003FFFE038000003FF00180> 41 41 -4 0 50] 67 @pc restore 50 r m (ase) s cmr10.329 @sf 74 2626 p m (Ours) 16 (b) 1 (eing) 17 (a) 15 (non-stationary) 15 (iteration) 16 (\(the) 15 (iterating) 16 (map) 15 (is) 16 (not) 16 (\014xed\),) 15 (it) 16 (is) 16 (not) 15 (easy) 15 (to) 15 (analyze) ks 74 2726 p m (the) 22 (b) 1 (eha) 0 (vior) 21 (of) 22 (the) 21 (successiv) 0 (e) 22 (appro) 0 (ximations.) 39 (W) -3 (e) 21 (try) 21 (ho) 0 (w) -1 (ev) -1 (er) 20 (to) 21 (address) 22 (this) 22 (problem) 22 (in) ks @eop 22 @bop0 cmbx10.329 @sf [<387CFEFEFE7C38000000000000387CFEFEFE7C38> 7 20 -4 0 15] 58 @dc 22 @bop1 cmr10.329 @sf 1919 -77 p m (22) s cmbx10.329 @sf 74 99 p save [<03FFFFC003FFFFC00007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0 000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E000C007 E006C007E006C007E006C007E006E007E00E6007E00C6007E00C7007E01C7C07E07C7FFFFFFC7F FFFFFC> 31 30 -2 0 36] 84 @pc restore 36 r save [ 24 32 -3 0 29] 104 @pc restore 29 r save [<00FF8007FFE00F80701E00183E00187C00007C0000FC0000FC0000FC0000FFFFF8FFFFF8FC00F8 7C00F87C00F03E00F01E01E00F83C007FF8001FE00> 21 20 -1 0 24] 101 @pc restore 24 r save [<01FF0007FFC01F83F03E00F83E00F87C007C7C007CFC007EFC007EFC007EFC007EFC007EFC007E 7C007C7C007C3E00F83E00F81F83F007FFC001FF00> 23 20 -1 0 26] 111 @pc restore 26 r save [ 18 20 -2 0 22] 114 @pc restore 22 r save [<00FF8007FFE00F80701E00183E00187C00007C0000FC0000FC0000FC0000FFFFF8FFFFF8FC00F8 7C00F87C00F03E00F01E01E00F83C007FF8001FE00> 21 20 -1 0 24] 101 @pc restore 24 r save [ 39 20 -3 0 46] 109 @pc restore 61 r save [<00FFFE00FFFE0007C00007C00007C00007C00007C00007C0FFFFFEFFFFFEE003C07003C03803C0 1803C00C03C00E03C00703C00383C00183C000C3C00063C00073C0003BC0001FC0000FC00007C0 0007C00003C00001C0> 23 29 -1 0 26] 52 @pc restore 26 r m (.) s save [ 19 29 -3 0 26] 50 @pc restore cmti10.329 @sf 386 99 p m (Assume) s cmr10.329 @sf 15 r m (\() s cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) s cmti10.329 @sf 14 r m (is) 16 (not) 16 (an) 16 (exact) ks 17 r save [<80E00041F80063FC003E0C00100200080200040100020000010000008000004000002000001000 0008000004000802000C1F0007F18003E08001C040> 18 20 -3 0 19] 122 @pc restore 19 r m (er) -1 (o) 14 (of) ks cmmi10.329 @sf 17 r save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 1169 106 p m (s) s cmti10.329 @sf 1187 99 p m (.) 21 (Then) ks cmex10.300 @sf 1341 27 p save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pc restore cmmi10.329 @sf 1394 72 p m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmsy10.329 @sf 1583 72 p m (\000) s cmmi10.329 @sf m (x) s 1443 127 p m (e) s cmmi8.300 @sf 1464 112 p m (T) s 1464 139 p m (s) s cmr10.329 @sf 1602 127 p m (0) s cmex10.300 @sf 1665 27 p save [ 21 124 -1 122 33] 33 @pc restore cmti10.329 @sf 1714 99 p m (is) 16 (singular) 15 (if) ks 74 199 p m (and) 16 (only) 16 (if) 16 (at) 17 (le) -1 (ast) 14 (one) 16 (of) 17 (the) 16 (fol) 2 (lowing) 16 (is) 16 (true:) ks 124 340 p save [ 15 30 -5 0 23] 49 @pc restore 23 r save [<8000006000003000001800000C000006000003000001000001800000C00000E000006000007000 003000003800001800001C00000C00000C00000E00000600000600000700000700000300000300 000300000380000380000380000180000180000180000180000180000180000180000100000300 000300000300000200000600000400000800001000> 17 46 0 12 19] 41 @pc restore cmmi10.329 @sf 35 r m (\025) s cmti10.329 @sf 16 r m (is) 16 (an) 16 (eigenvalue) 15 (of) ks cmmi10.329 @sf 17 r m (H) s cmti10.329 @sf 19 r m (and) 17 (has) 16 (an) 16 (eigenve) -1 (ctor) 14 (whose) ks cmmi10.329 @sf 17 r m (s) s cmmi8.300 @sf 1294 325 p save [<1E003100310030803080300018001800180018000C000C000C00FFC00600060006000600030003 00> 10 20 -1 0 13] 116 @pc restore 13 r save [ 16 23 -2 0 20] 104 @pc restore cmti10.329 @sf 1346 340 p m (c) -1 (omp) -2 (onent) 14 (is) ks 16 r save [<80E00041F80063FC003E0C00100200080200040100020000010000008000004000002000001000 0008000004000802000C1F0007F18003E08001C040> 18 20 -3 0 19] 122 @pc restore 19 r m (er) -1 (o.) ks 124 481 p save [<80780080FC0041FE0047FF007E0300200180100080100040080040040000030000008000006000 001800000C000007000003800703C00881E00840E00820F00820F00820F0041070042070022070 0200700100E00080E0006180001F00> 20 31 -4 1 23] 50 @pc restore 23 r save [<8000006000003000001800000C000006000003000001000001800000C00000E000006000007000 003000003800001800001C00000C00000C00000E00000600000600000700000700000300000300 000300000380000380000380000180000180000180000180000180000180000180000100000300 000300000300000200000600000400000800001000> 17 46 0 12 19] 41 @pc restore cmmi10.329 @sf 37 r m (x) s cmti10.329 @sf 18 r m (b) -1 (elongs) 16 (to) 18 (the) 19 (sp) -1 (ac) -2 (e) 16 (gener) -1 (ate) -2 (d) 17 (by) ks cmr10.329 @sf 18 r m (\() s cmmi10.329 @sf m (c) s cmr8.300 @sf 943 488 p m (1) s cmmi10.329 @sf 962 481 p m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 1043 481 p m (;) 8 (c) ks cmmi8.300 @sf 1084 488 p m (s) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1146 481 p m (;) 8 (c) ks cmmi8.300 @sf 1187 488 p m (s) s cmr8.300 @sf m (+1) s cmmi10.329 @sf 1250 481 p m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 7 (.) ks cmmi10.329 @sf 1330 481 p m (;) 8 (c) ks cmmi8.300 @sf 1371 488 p m (n) s cmr10.329 @sf 1394 481 p m (\)) s cmti10.329 @sf m (,) 18 (wher) -1 (e) ks cmmi10.329 @sf 17 r m (c) s cmmi8.300 @sf 1594 488 p m (i) s cmti10.329 @sf 1626 481 p m (is) 18 (the) ks cmmi10.329 @sf 19 r m (i) s cmmi8.300 @sf 1771 466 p save [<1E003100310030803080300018001800180018000C000C000C00FFC00600060006000600030003 00> 10 20 -1 0 13] 116 @pc restore 13 r save [ 16 23 -2 0 20] 104 @pc restore cmti10.329 @sf 1824 481 p m (c) -1 (olumn) ks 74 581 p m (of) s cmmi10.329 @sf 17 r m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (\025I) s cmti10.329 @sf 19 r save [<0800100010002000600060004000C000C000C000C000C000C000C000C000C000C000C000C000C0 00E000E000600060007000700030003800380018001C000C000E000600070003000180018000C0 0060002000100008000400020001> 16 46 -7 12 19] 40 @pc restore cmmi10.329 @sf 19 r m (\025) s cmti10.329 @sf 15 r m (may) 17 (or) 17 (may) 16 (not) 17 (b) -1 (e) 14 (an) 16 (eigenvalue) ks save [<8000006000003000001800000C000006000003000001000001800000C00000E000006000007000 003000003800001800001C00000C00000C00000E00000600000600000700000700000300000300 000300000380000380000380000180000180000180000180000180000180000180000100000300 000300000300000200000600000400000800001000> 17 46 0 12 19] 41 @pc restore 19 r m (.) s cmbx10.329 @sf 74 772 p save [ 30 31 -2 0 36] 80 @pc restore 36 r save [ 18 20 -2 0 22] 114 @pc restore 22 r save [<01FF0007FFC01F83F03E00F83E00F87C007C7C007CFC007EFC007EFC007EFC007EFC007EFC007E 7C007C7C007C3E00F83E00F81F83F007FFC001FF00> 23 20 -1 0 26] 111 @pc restore 27 r save [<01FF0007FFC01F83F03E00F83E00F87C007C7C007CFC007EFC007EFC007EFC007EFC007EFC007E 7C007C7C007C3E00F83E00F81F83F007FFC001FF00> 23 20 -1 0 26] 111 @pc restore 26 r save [<3FFC003FFC0007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C000 07C00007C00007C00007C00007C000FFFC00FFFC0007C00007C00007C00007C00007C00007C3C0 07C7E003C7E003E7E001F3E000FFC0001F80> 19 32 -1 0 16] 102 @pc restore 16 r m (.) s cmr10.329 @sf 21 r m (Assume) 15 (\014rst) 15 (that) 15 (1\)) 15 (is) 16 (true) 15 (and) 16 (let) ks cmmi10.329 @sf 15 r m (y) s cmr10.329 @sf 18 r m (b) 1 (e) 16 (an) 15 (eigen) 0 (v) 0 (ector,) ks cmmi10.329 @sf 13 r m (y) s cmmi8.300 @sf 1386 779 p m (s) s cmr10.329 @sf 1418 772 p m (=) 13 (0.) 21 (Then) ks cmex10.300 @sf 1641 700 p save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pc restore cmmi10.329 @sf 1695 745 p m (y) s cmr10.329 @sf 1696 800 p m (0) s cmex10.300 @sf 1740 700 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1788 772 p m (is) 16 (clearly) ks 74 900 p m (in) 17 (the) 17 (n) 0 (ull) 17 (space) 16 (of) 16 (the) 17 (Jacobian.) 24 (If) 17 (2\)) 16 (holds,) 17 (and) ks cmmi10.329 @sf 16 r m (x) s cmr10.329 @sf 15 r m (=) 15 (\() ks cmmi10.329 @sf m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 11 r m (\025I) s cmr10.329 @sf 4 r m (\)) s cmmi10.329 @sf m (y) s cmr10.329 @sf 2 r m (,) 15 (with) ks cmmi10.329 @sf 17 r m (y) s cmmi8.300 @sf 1546 907 p m (s) s cmr10.329 @sf 1579 900 p m (=) 15 (0,) 16 (then) ks cmex10.300 @sf 1786 828 p save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pc restore cmmi10.329 @sf 1840 873 p m (y) s cmr10.329 @sf 1840 929 p m (1) s cmex10.300 @sf 1884 828 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1934 900 p m (is) s 74 1000 p m (in) 16 (the) 15 (n) 0 (ull) 16 (space) 16 (of) 14 (the) 16 (Jacobian.) ks 124 1141 p m (Con) 0 (v) -1 (ersely) -3 (,) 13 (if) 16 (the) 15 (Jacobian) 16 (is) 16 (singular) 16 (then) 15 (there) 16 (exists) 15 (a) 15 (v) 0 (ector) ks cmex10.300 @sf 1410 1069 p save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pc restore cmmi10.329 @sf 1466 1114 p m (y) s 1464 1169 p m (\026) s cmex10.300 @sf 1512 1069 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1560 1141 p m (suc) 0 (h) 15 (that,) ks cmex10.300 @sf 721 1244 p save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pc restore cmmi10.329 @sf 775 1289 p m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmsy10.329 @sf 964 1289 p m (\000) s cmmi10.329 @sf m (x) s 824 1344 p m (e) s cmmi8.300 @sf 845 1329 p m (T) s 845 1355 p m (s) s cmr10.329 @sf 983 1344 p m (0) s cmex10.300 @sf 1046 1244 p save [ 21 124 -1 122 33] 33 @pc restore 1086 1244 p save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pc restore cmmi10.329 @sf 1142 1289 p m (y) s 1140 1344 p m (\026) s cmex10.300 @sf 1188 1244 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1233 1316 p m (=) 13 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf 74 1461 p m (This) 16 (implies) 17 (that) ks cmex10.300 @sf 819 1488 p save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pc restore cmr10.329 @sf 873 1533 p m (\() s cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (\025I) s cmr10.329 @sf 4 r m (\)) s cmmi10.329 @sf m (y) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (\026x) s 955 1589 p m (e) s cmmi8.300 @sf 976 1574 p m (T) s 976 1600 p m (s) s cmmi10.329 @sf 1004 1589 p m (y) s cmr10.329 @sf 15 r m (=) 13 (0) ks 74 1687 p m (and) 18 (clearly) ks cmmi10.329 @sf 18 r m (y) s cmmi8.300 @sf 334 1694 p m (s) s cmr10.329 @sf 370 1687 p m (=) 16 (0.) 27 (W) -3 (e) 16 (no) 0 (w) 16 (consider) 19 (t) 0 (w) -1 (o) 15 (cases) 17 (according) 18 (to) 17 (whether) ks cmmi10.329 @sf 18 r m (\026) s cmr10.329 @sf 17 r m (is) 18 (zero) 18 (or) 17 (not.) 26 (If) ks cmmi10.329 @sf 18 r m (\026) s cmr10.329 @sf 18 r m (is) s 74 1787 p m (zero,) 15 (then) ks cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf 15 r m (is) 15 (an) 15 (eigen) 0 (v) -2 (alue) 15 (with) 15 (corresp) 1 (onding) 16 (eigen) 0 (v) 0 (ector) ks cmmi10.329 @sf 14 r m (y) s cmr10.329 @sf 2 r m (,) 14 (therefore) 15 (w) 0 (e) 14 (are) 14 (in) 16 (case) 15 (1\).) 19 (If) ks cmmi10.329 @sf 16 r m (\026) s cmr10.329 @sf 74 1886 p m (is) 16 (not) 15 (zero) 15 (then) ks cmmi10.329 @sf 16 r m (\026x) s cmr10.329 @sf 15 r m (and) 16 (hence) ks cmmi10.329 @sf 16 r m (x) s cmr10.329 @sf 15 r m (is) 16 (in) 16 (the) 15 (range) 15 (of) ks cmmi10.329 @sf 15 r m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmr10.329 @sf 19 r m (and) 15 (therefore) 15 (w) 0 (e) 14 (are) 15 (in) 16 (case) 15 (2\)) 15 (since) ks cmmi10.329 @sf 74 1986 p m (y) s cmmi8.300 @sf 96 1993 p m (s) s cmr10.329 @sf 115 1986 p m (=0.) 20 (Note) 15 (that) ks cmmi10.329 @sf 14 r m (\025) s cmr10.329 @sf 15 r m (ma) 0 (y) 13 (or) 15 (ma) 0 (y) 13 (not) 15 (b) 1 (e) 16 (an) 15 (eigen) 0 (v) -2 (alue) 15 (in) 16 (this) 16 (last) 15 (case.) ks 477 r save [<7FFFFF80FFFFFF80C0000180C0000180C0000180C0000180C0000180C0000180C0000180C00001 80C0000180C0000180C0000180C0000180C0000180C0000180C0000180C0000180C0000180C000 0180C0000180C0000180C0000180FFFFFF807FFFFF80> 25 25 -4 -3 34] 50 @pc restore cmbx10.329 @sf 124 2127 p save [ 36 31 -2 0 39] 82 @pc restore 39 r save [<00FF8007FFE00F80701E00183E00187C00007C0000FC0000FC0000FC0000FFFFF8FFFFF8FC00F8 7C00F87C00F03E00F01E01E00F83C007FF8001FE00> 21 20 -1 0 24] 101 @pc restore 24 r save [ 39 20 -3 0 46] 109 @pc restore 46 r save [<0FE07E3FF8FE7E0DE0FC05E0F803E0F803E0F803E07C03E03C03E01F03E007FBE0007FE00003E0 0C03E03F03E03F03E03F07C03F0F801FFF0007FC00> 23 20 -1 0 25] 97 @pc restore 25 r save [ 18 20 -2 0 22] 114 @pc restore 22 r save [ 24 32 -2 0 28] 107 @pc restore 27 r save [ 16 20 -2 0 21] 115 @pc restore 21 r m (:) s cmr10.329 @sf 16 r m (The) 11 (theorem) 11 (tells) 13 (us) 12 (that) 10 (more) 11 (often) 11 (than) 12 (not,) 11 (a) 11 (singular) 13 (Jacobian) 12 (is) 12 (an) 11 (indication) ks 74 2227 p m (that) 17 (w) 0 (e) 16 (already) 17 (ha) 0 (v) 0 (e) 15 (an) 17 (eigen) 0 (v) -2 (alue,) 17 (and) 18 (this) 17 (has) 17 (b) 1 (een) 19 (our) 17 (exp) 1 (erience) 19 (indeed.) 28 (The) 17 (singularit) 0 (y) ks 74 2326 p m (of) 14 (the) 14 (Jacobian) 15 (is) 14 (also) 14 (an) 15 (indication) 16 (of) 13 (an) 14 (ill-cond) 1 (iti) 1 (oned) 16 (eigensystem.) 20 (In) 15 (fact,) 13 (if) 15 (w) 0 (e) 12 (accept) 15 (that) ks 74 2426 p m (the) 14 (curren) 0 (t) 14 (eigen) 0 (v) 0 (ector) 12 (w) 0 (as) 12 (mo) 0 (ving) 13 (in) 15 (the) 15 (\\righ) 0 (t") 12 (direction) 16 (then) 14 (if) 15 (it) 14 (satis\014es) 15 (condition) 15 (2) 14 (of) 14 (the) ks 74 2526 p m (theorem,) 19 (w) 0 (e) 17 (can) 19 (sa) 0 (y) 17 (that) 18 (the) 19 (eigen) 0 (v) -2 (alue) 19 (is) 19 (acting) 19 (lik) 0 (e) 19 (a) 18 (m) 0 (ultiple) 19 (one) 19 (since) 20 (the) 19 (eigen) 0 (v) 0 (ector) 17 (is) ks 74 2625 p m (also) 15 (in) 16 (the) 15 (range) 15 (of) 15 (\() ks cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmr10.329 @sf 4 r m (\).) 19 (In) 15 (practice) 16 (w) 0 (e) 14 (ha) 0 (v) -1 (e) 14 (not) 14 (encoun) 0 (tered) 15 (a) 15 (situation) 15 (where) 16 (condition) ks 74 2725 p m (1) 15 (applied:) 23 (this) 16 (is) 16 (understandable) 17 (again) 16 (if) 16 (w) 0 (e) 14 (accept) 16 (that) 15 (the) 16 (eigen) 0 (v) 0 (ector) 13 (is) 17 (mo) 0 (ving) 14 (in) 17 (the) 15 (righ) 0 (t) ks @eop 21 @bop0 21 @bop1 cmr10.329 @sf 1919 -77 p m (21) s cmbx10.329 @sf 74 67 p save [<03FFFFC003FFFFC00007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0 000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E000C007 E006C007E006C007E006C007E006E007E00E6007E00C6007E00C7007E01C7C07E07C7FFFFFFC7F FFFFFC> 31 30 -2 0 36] 84 @pc restore 36 r save [ 24 32 -3 0 29] 104 @pc restore 29 r save [<00FF8007FFE00F80701E00183E00187C00007C0000FC0000FC0000FC0000FFFFF8FFFFF8FC00F8 7C00F87C00F03E00F01E01E00F83C007FF8001FE00> 21 20 -1 0 24] 101 @pc restore 24 r save [<01FF0007FFC01F83F03E00F83E00F87C007C7C007CFC007EFC007EFC007EFC007EFC007EFC007E 7C007C7C007C3E00F83E00F81F83F007FFC001FF00> 23 20 -1 0 26] 111 @pc restore 26 r save [ 18 20 -2 0 22] 114 @pc restore 22 r save [<00FF8007FFE00F80701E00183E00187C00007C0000FC0000FC0000FC0000FFFFF8FFFFF8FC00F8 7C00F87C00F03E00F01E01E00F83C007FF8001FE00> 21 20 -1 0 24] 101 @pc restore 24 r save [ 39 20 -3 0 46] 109 @pc restore 61 r save [<00FFFE00FFFE0007C00007C00007C00007C00007C00007C0FFFFFEFFFFFEE003C07003C03803C0 1803C00C03C00E03C00703C00383C00183C000C3C00063C00073C0003BC0001FC0000FC00007C0 0007C00003C00001C0> 23 29 -1 0 26] 52 @pc restore 26 r m (.) s save [ 17 29 -4 0 26] 49 @pc restore 43 r save [<0018007000E001C00380038007000E000E001E001C003C003C007800780078007800F800F000F0 00F000F000F000F000F000F000F000F80078007800780078003C003C001C001E000E000E000700 0380038001C000E000700018> 13 45 -3 11 20] 40 @pc restore 20 r save [<00018000300000000380003800000003C0007800000007C0007C00000007C0007C00000007E000 FC0000000FE000FE0000000FF001FE0000000FF001FE0000001FB001FB0000001F9803F3000000 3F9803F38000003F1803F18000003F0C07E18000007E0C07E0C000007E0E0FE0C000007E060FC0 C00000FC060FC0600000FC031F80600001FC031F80700001F8031F80300001F801BF00300003F0 01BF00180003F001FF00180003F000FE00180007E000FE000C0007E000FE000C000FE000FC000E 000FC000FC000E00FFFE0FFFC0FFE0FFFE0FFFC0FFE0> 51 31 -1 0 54] 87 @pc restore 54 r save [ 11 33 -2 0 14] 105 @pc restore 14 r save [ 11 32 -2 0 14] 108 @pc restore 14 r save [ 24 32 -2 0 28] 107 @pc restore 28 r save [ 11 33 -2 0 14] 105 @pc restore 14 r save [ 24 20 -3 0 29] 110 @pc restore 29 r save [ 16 20 -2 0 21] 115 @pc restore 21 r save [<01FF0007FFC01F83F03E00F83E00F87C007C7C007CFC007EFC007EFC007EFC007EFC007EFC007E 7C007C7C007C3E00F83E00F81F83F007FFC001FF00> 23 20 -1 0 26] 111 @pc restore 26 r save [ 24 20 -3 0 29] 110 @pc restore 29 r save [ 13 45 -3 11 20] 41 @pc restore cmti10.329 @sf 674 67 p m (Assume) s cmr10.329 @sf 15 r m (\() s cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) s cmti10.329 @sf 15 r m (is) 16 (an) 16 (exact) ks 16 r save [<80E00041F80063FC003E0C00100200080200040100020000010000008000004000002000001000 0008000004000802000C1F0007F18003E08001C040> 18 20 -3 0 19] 122 @pc restore 19 r m (er) -1 (o) 15 (of) ks cmmi10.329 @sf 16 r save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 1377 74 p m (s) s cmti10.329 @sf 1396 67 p m (.) 21 (Then) ks cmex10.300 @sf 841 123 p save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pc restore cmmi10.329 @sf 894 168 p m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmsy10.329 @sf 1083 168 p m (\000) s cmmi10.329 @sf m (x) s 943 223 p m (e) s cmmi8.300 @sf 964 208 p m (T) s 964 234 p m (s) s cmr10.329 @sf 1102 223 p m (0) s cmex10.300 @sf 1165 123 p save [ 21 124 -1 122 33] 33 @pc restore cmti10.329 @sf 74 322 p m (is) 16 (singular) 16 (if) 16 (and) 16 (only) 16 (if) ks cmmi10.329 @sf 16 r m (\025) s cmti10.329 @sf 16 r m (is) 15 (multiple.) ks cmbx10.329 @sf 74 493 p save [ 30 31 -2 0 36] 80 @pc restore 36 r save [ 18 20 -2 0 22] 114 @pc restore 22 r save [<01FF0007FFC01F83F03E00F83E00F87C007C7C007CFC007EFC007EFC007EFC007EFC007EFC007E 7C007C7C007C3E00F83E00F81F83F007FFC001FF00> 23 20 -1 0 26] 111 @pc restore 27 r save [<01FF0007FFC01F83F03E00F83E00F87C007C7C007CFC007EFC007EFC007EFC007EFC007EFC007E 7C007C7C007C3E00F83E00F81F83F007FFC001FF00> 23 20 -1 0 26] 111 @pc restore 26 r save [<3FFC003FFC0007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C000 07C00007C00007C00007C00007C000FFFC00FFFC0007C00007C00007C00007C00007C00007C3C0 07C7E003C7E003E7E001F3E000FFC0001F80> 19 32 -1 0 16] 102 @pc restore 16 r m (.) s cmr10.329 @sf 19 r m (Let) 15 (us) 14 (assume) 14 (\014rst) 14 (that) ks cmmi10.329 @sf 13 r m (\025) s cmr10.329 @sf 14 r m (is) 14 (a) 14 (m) 0 (ultiple) 15 (eigen) 0 (v) -2 (alue) 14 (of) ks cmmi10.329 @sf 14 r m (H) s cmr10.329 @sf 18 r m (and) 14 (that) ks cmmi10.329 @sf 13 r m (x) s cmr10.329 @sf 14 r m (is) 15 (the) 14 (corresp) 1 (onding) ks 74 592 p m (\(exact\)) 14 (eigen) 0 (v) 0 (ector,) 13 (then) 16 (there) 15 (exists) 16 (a) 15 (nonzero) 15 (v) 0 (ector) ks cmmi10.329 @sf 13 r m (y) s cmr10.329 @sf 17 r m (suc) 0 (h) 15 (that) ks cmmi10.329 @sf 716 720 p m (y) s cmmi8.300 @sf 740 702 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 774 720 p m (\() s cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmr10.329 @sf 4 r m (\)) 12 (=) 13 (0) 14 (and) ks cmmi10.329 @sf 1143 720 p m (y) s cmmi8.300 @sf 1167 702 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 1200 720 p m (x) s cmr10.329 @sf 13 r m (=) 13 (0;) ks cmmi10.329 @sf 74 848 p m (y) s cmr10.329 @sf 17 r m (is) 16 (simply) 16 (a) 15 (left) 16 (eigen) 0 (v) 0 (ector) 13 (of) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 18 r m (corresp) 1 (onding) 17 (to) ks cmmi10.329 @sf 14 r m (\025) s cmr10.329 @sf m (.) 19 (Th) 0 (us,) 14 (\() ks cmmi10.329 @sf m (y) s cmmi8.300 @sf 1343 833 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 1389 848 p m (0\)) 15 (is) 15 (a) 15 (nonzero) 16 (v) 0 (ector) 13 (and) ks 725 975 p m (\() s cmmi10.329 @sf m (y) s cmmi8.300 @sf 767 957 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 813 975 p m (0\)) s cmex10.300 @sf 862 903 p save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pc restore cmmi10.329 @sf 914 948 p m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmsy10.329 @sf 1103 948 p m (\000) s cmmi10.329 @sf m (x) s 963 1004 p m (e) s cmmi8.300 @sf 984 989 p m (T) s 984 1015 p m (s) s cmr10.329 @sf 1122 1004 p m (0) s cmex10.300 @sf 1185 903 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1230 975 p m (=) 13 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf 74 1103 p m (This) 16 (pro) 0 (v) -1 (es) 13 (that) 15 (the) 15 (Jacobian) 16 (is) 16 (singular.) ks 124 1244 p m (No) 0 (w) 18 (con) 0 (v) 0 (ersely) -3 (,) 18 (if) ks cmex10.300 @sf 510 1172 p save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pc restore cmmi10.329 @sf 564 1217 p m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (\025I) s cmsy10.329 @sf 752 1217 p m (\000) s cmmi10.329 @sf m (x) s 613 1272 p m (e) s cmmi8.300 @sf 634 1257 p m (T) s 634 1284 p m (s) s cmr10.329 @sf 772 1272 p m (0) s cmex10.300 @sf 834 1172 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 887 1244 p m (is) 20 (singular) 21 (then) 20 (there) 19 (exists) 20 (a) 20 (nonzero) 20 (v) 0 (ector) ks cmex10.300 @sf 1829 1172 p save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pc restore cmmi10.329 @sf 1885 1217 p m (v) s 1883 1272 p m (\026) s cmex10.300 @sf 1931 1172 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 74 1344 p m (suc) 0 (h) 15 (that) ks cmex10.300 @sf 721 1371 p save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pc restore cmmi10.329 @sf 775 1416 p m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmsy10.329 @sf 964 1416 p m (\000) s cmmi10.329 @sf m (x) s 824 1472 p m (e) s cmmi8.300 @sf 845 1457 p m (T) s 845 1483 p m (s) s cmr10.329 @sf 983 1472 p m (0) s cmex10.300 @sf 1046 1371 p save [ 21 124 -1 122 33] 33 @pc restore 1086 1371 p save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pc restore cmmi10.329 @sf 1142 1416 p m (v) s 1140 1472 p m (\026) s cmex10.300 @sf 1188 1371 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1233 1443 p m (=) 13 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf 74 1590 p m (But) 16 (then) ks cmmi10.329 @sf 15 r m (v) s cmmi8.300 @sf 290 1597 p m (s) s cmr10.329 @sf 321 1590 p m (=) 14 (0) 15 (and) 15 (\() ks cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (\025I) s cmr10.329 @sf 4 r m (\)) s cmmi10.329 @sf m (v) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (\026x) s cmr10.329 @sf m (.) 21 (If) ks cmmi10.329 @sf 16 r m (\026) s cmr10.329 @sf 13 r m (=) 13 (0,) 15 (then) ks cmmi10.329 @sf 15 r m (v) s cmr10.329 @sf 17 r m (is) 16 (nonzero) 15 (since) ks cmex10.300 @sf 1504 1518 p save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pc restore cmmi10.329 @sf 1559 1563 p m (v) s 1558 1618 p m (\026) s cmex10.300 @sf 1606 1518 p save [ 21 124 -1 122 33] 33 @pc restore cmsy10.329 @sf 1651 1590 p m (6) s cmr10.329 @sf m (=) 14 (0,) 14 (and) 16 (so) ks cmmi10.329 @sf 15 r m (v) s cmr10.329 @sf 17 r m (is) s 74 1690 p m (an) 15 (eigen) 0 (v) 0 (ector) 13 (that) 15 (is) 15 (linearly) 17 (indep) 1 (end) 1 (en) 0 (t) 15 (of) ks cmmi10.329 @sf 15 r m (x) s cmr10.329 @sf m (,) 15 (since) ks cmmi10.329 @sf 16 r m (x) s cmmi8.300 @sf 1180 1697 p m (s) s cmr10.329 @sf 1211 1690 p m (=) 13 (1) 15 (and) ks cmmi10.329 @sf 15 r m (v) s cmmi8.300 @sf 1407 1697 p m (s) s cmr10.329 @sf 1438 1690 p m (=) 13 (0.) 19 (Hence) ks cmmi10.329 @sf 16 r m (\025) s cmr10.329 @sf 15 r m (is) 16 (a) 14 (m) 0 (ultiple) ks 74 1790 p m (eigen) 0 (v) -2 (alue) 15 (in) 16 (this) 16 (case.) 20 (If) ks cmmi10.329 @sf 15 r m (\026) s cmsy10.329 @sf 13 r m (6) s cmr10.329 @sf m (=) 13 (0,) 15 (then) ks cmmi10.329 @sf 15 r m (v) s cmr10.329 @sf 17 r m (is) 16 (also) 15 (nonzero;) 15 (if) 16 (it) 15 (w) 0 (ere) 14 (then) 16 (w) 0 (e) 13 (w) 0 (ould) 15 (ha) 0 (v) -1 (e) ks cmmi10.329 @sf 685 1917 p m (\026x) s cmr10.329 @sf 13 r m (=) 13 (\() ks cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmr10.329 @sf 4 r m (\)) s cmmi10.329 @sf m (v) s cmr10.329 @sf 13 r m (=) 13 (\() ks cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (\025I) s cmr10.329 @sf 4 r m (\)0) 11 (=) 13 (0) ks 74 2045 p m (and) 16 (hence) ks cmmi10.329 @sf 18 r m (x) s cmr10.329 @sf 14 r m (=) 14 (0,) 16 (con) 0 (tradicting) 15 (our) 16 (assumption) 16 (on) ks cmmi10.329 @sf 16 r m (x) s cmr10.329 @sf m (.) 22 (But) 17 (\() ks cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (\025I) s cmr10.329 @sf 4 r m (\)) s cmr8.300 @sf 1433 2030 p m (2) s cmmi10.329 @sf 1452 2045 p m (v) s cmr10.329 @sf 16 r m (=) s cmmi10.329 @sf 14 r m (\026) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 11 r m (\025I) s cmr10.329 @sf 4 r m (\)) s cmmi10.329 @sf m (x) s cmr10.329 @sf 13 r m (=) 14 (0,) 16 (and) ks 74 2144 p m (th) 0 (us) ks cmmi10.329 @sf 14 r m (v) s cmr10.329 @sf 17 r m (is) 16 (a) 15 (nonzero) 15 (v) 0 (ector) 13 (that) 15 (has) 15 (grade) 15 (2.) 19 (Therefore) ks cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf 15 r m (is) 16 (m) 0 (ultiple) 16 (in) 16 (this) 15 (case) 16 (as) 14 (w) 0 (ell.) ks 114 r save [<7FFFFF80FFFFFF80C0000180C0000180C0000180C0000180C0000180C0000180C0000180C00001 80C0000180C0000180C0000180C0000180C0000180C0000180C0000180C0000180C0000180C000 0180C0000180C0000180C0000180FFFFFF807FFFFF80> 25 25 -4 -3 34] 50 @pc restore cmbx10.329 @sf 124 2286 p save [ 36 31 -2 0 39] 82 @pc restore 39 r save [<00FF8007FFE00F80701E00183E00187C00007C0000FC0000FC0000FC0000FFFFF8FFFFF8FC00F8 7C00F87C00F03E00F01E01E00F83C007FF8001FE00> 21 20 -1 0 24] 101 @pc restore 24 r save [ 39 20 -3 0 46] 109 @pc restore 46 r save [<0FE07E3FF8FE7E0DE0FC05E0F803E0F803E0F803E07C03E03C03E01F03E007FBE0007FE00003E0 0C03E03F03E03F03E03F07C03F0F801FFF0007FC00> 23 20 -1 0 25] 97 @pc restore 25 r save [ 18 20 -2 0 22] 114 @pc restore 22 r save [ 24 32 -2 0 28] 107 @pc restore 27 r m (:) s cmr10.329 @sf 20 r m (Since) 17 (w) 0 (e) 15 (are) 16 (assuming) 16 (that) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 20 r m (is) 17 (upp) 1 (er-Hessen) 0 (b) 1 (erg) 16 (and) 17 (unreduced,) 17 (an) 16 (eigen) 0 (v) -2 (alue) ks 74 2385 p m (can) 15 (only) 16 (b) 1 (e) 16 (non-derogatory) -3 (,) 13 (i.e.,) 15 (the) 15 (asso) 1 (ciated) 16 (eigenspace) 16 (has) 15 (dimension) 17 (one.) ks 124 2526 p m (The) 14 (previous) 15 (result) 14 (applies) 16 (to) 13 (the) 14 (Jacobian) 15 (at) 13 (a) 14 (zero) 14 (of) ks cmmi10.329 @sf 13 r save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 1257 2533 p m (s) s cmr10.329 @sf 1276 2526 p m (.) 19 (W) -3 (e) 13 (wish) 15 (to) 13 (kno) 0 (w) 13 (more) 13 (ab) 1 (out) 14 (the) ks 74 2626 p m (Jacobian) 18 (at) 17 (those) 17 (appro) 0 (ximations) 16 (arising) 18 (during) 19 (Newton's) 16 (iteration) 18 (and) 17 (b) 1 (efore) 18 (con) 0 (v) 0 (erg) -1 (ence) 17 (is) ks 74 2726 p m (declared.) s @eop 20 @bop0 cmmi8.300 @sf [<40402020101070F0F060> 4 10 -3 6 10] 59 @dc 20 @bop1 cmr10.329 @sf 1919 -77 p m (20) s 74 67 p m (task:) 25 (in) 18 (particular,) 19 (they) 18 (will) 20 (not) 17 (b) 1 (e) 19 (detected) 19 (if) 18 (their) 18 (di\013erence) 19 (is) 19 (compared) 18 (to) ks cmmi10.329 @sf 17 r save [<0F00188038403820382038201C101C001C001C000E000E000E000E0007000700070007000380FF F80380038001C001C001C001C000E000C0> 13 28 -1 0 16] 116 @pc restore 16 r m (o) s save [<38006400E200E200E200E200710070007000700038003800380038001C001C001C001C000E000E 000E000E00070007000700070003800380038003801FC003C0> 10 32 -2 0 14] 108 @pc restore cmr10.329 @sf 33 r m (in) 0 (tro) 1 (duced) ks 74 167 p m (earlier.) 20 (Con) 0 (v) -1 (ersely) -3 (,) 11 (it) 13 (can) 13 (happ) 1 (en) 14 (that) 12 (under) 13 (certain) 14 (conditions) 14 (the) 12 (tolerated) 13 (size) 14 (of) 12 (the) 13 (residual) ks 74 266 p m (b) 1 (e) 12 (m) 0 (uc) -1 (h) 9 (larger) 11 (than) 11 (the) 11 (distance) 11 (b) 1 (et) 0 (w) 0 (een) 9 (certain) 12 (exact) 10 (eigen) 0 (v) -2 (alues) 11 (and) 11 (therefore) 11 (b) 1 (et) 0 (w) -1 (een) 10 (certain) ks 74 366 p m (computed) 16 (eigen) 0 (v) -2 (alues.) 21 (In) 16 (this) 16 (case,) 16 (it) 16 (could) 16 (happ) 1 (en) 17 (that) 15 (distinct) 17 (computed) 16 (eigen) 0 (v) -2 (alues) 15 (will) 17 (b) 1 (e) ks 74 466 p m (declared) 17 (as) 14 (duplic) 1 (ates) 16 (if) 16 (their) 16 (di\013erence) 16 (is) 16 (compared) 15 (to) ks cmmi10.329 @sf 15 r save [<0F00188038403820382038201C101C001C001C000E000E000E000E0007000700070007000380FF F80380038001C001C001C001C000E000C0> 13 28 -1 0 16] 116 @pc restore 16 r m (o) s save [<38006400E200E200E200E200710070007000700038003800380038001C001C001C001C000E000E 000E000E00070007000700070003800380038003801FC003C0> 10 32 -2 0 14] 108 @pc restore cmr10.329 @sf 15 r m (.) s cmbx10.329 @sf 74 644 p save [ 30 31 -2 0 34] 69 @pc restore 34 r save [ 25 20 -1 0 28] 120 @pc restore 28 r save [<0FE07E3FF8FE7E0DE0FC05E0F803E0F803E0F803E07C03E03C03E01F03E007FBE0007FE00003E0 0C03E03F03E03F03E03F07C03F0F801FFF0007FC00> 23 20 -1 0 25] 97 @pc restore 25 r save [ 39 20 -3 0 46] 109 @pc restore 46 r save [ 24 29 -2 9 29] 112 @pc restore 29 r save [ 11 32 -2 0 14] 108 @pc restore 14 r save [<00FF8007FFE00F80701E00183E00187C00007C0000FC0000FC0000FC0000FFFFF8FFFFF8FC00F8 7C00F87C00F03E00F01E01E00F83C007FF8001FE00> 21 20 -1 0 24] 101 @pc restore 40 r save [<03FC001FFF803C0FC07807E0FC03F0FE03F0FE03F8FE03F87C03F83803F80003F80003F00003E0 0007C0000F8001FC0001FC00001F00000F80000FC01E0FC03F07E03F07E03F07E03F07E01E0FC0 0E0F8007FF0001FC00> 21 29 -2 0 26] 51 @pc restore 26 r m (.) s save [ 19 29 -3 0 26] 50 @pc restore cmti10.329 @sf 380 644 p save [<04000800000006000800000006000C00000007001E00000007001E00000007801F00000007801F 0000000FC01E8000000F601E8000000F201E4000000F101E4000000F101E2000000F081E200000 0F081E1000000F041E0800000F041E0800000F021E0400000F021E0400000F011E0200000F009E 0200000F009E0100000F005E0100000F005E0080000F003E00C0000F003E0040000F003C002000 0F003C0020000F003C0010000F003C0010001F003C0018001F003E001C00FFF1FFC0FF80> 41 32 -9 1 45] 87 @pc restore 45 r m (e) 16 (il) 2 (lustr) -1 (ate) 15 (this) 16 (last) 16 (c) -1 (ase) 14 (with) 17 (the) 17 (fol) 2 (lowing) 16 (matrix) ks cmmi10.329 @sf 698 801 p m (H) s cmr10.329 @sf 16 r m (=) s cmex10.300 @sf 800 704 p m (0) s 800 778 p m (B) s 800 805 p m (@) s cmr10.329 @sf 857 745 p m (2) s cmsy10.329 @sf 10 r m (\001) s cmr10.329 @sf 9 r m (10) s cmsy8.300 @sf 958 730 p m (\000) s cmr8.300 @sf save [<04000E000E000E000E000E0006000600020003000100010000800080004080208010C0087FF87F FC7FFE4000> 15 22 -2 0 18] 55 @pc restore cmr10.329 @sf 1081 745 p m (0) s 1211 745 p m (0) s 919 801 p m (2) s 1046 801 p m (10) s cmsy8.300 @sf 1092 786 p m (\000) s cmr8.300 @sf save [<04000E000E000E000E000E0006000600020003000100010000800080004080208010C0087FF87F FC7FFE4000> 15 22 -2 0 18] 55 @pc restore cmr10.329 @sf 1211 801 p m (0) s 919 858 p m (0) s 1081 858 p m (2) s 1181 858 p m (10) s cmr8.300 @sf 1227 843 p m (10) s cmex10.300 @sf 1284 704 p m (1) s 1284 778 p m (C) s 1284 805 p m (A) s cmmi10.329 @sf 1328 801 p m (:) s cmti10.329 @sf 74 961 p m (The) 18 (toler) -1 (ate) -1 (d) 16 (si) ks save [<80E00041F80063FC003E0C00100200080200040100020000010000008000004000002000001000 0008000004000802000C1F0007F18003E08001C040> 18 20 -3 0 19] 122 @pc restore 19 r m (e) 17 (of) 18 (the) 19 (r) -1 (esiduals) 16 (for) 18 (this) 18 (matrix) 19 (as) 18 (chosen) 18 (in) 17 (our) 19 (algorithm) 19 (is) ks cmmi10.329 @sf 17 r save [<0F00188038403820382038201C101C001C001C000E000E000E000E0007000700070007000380FF F80380038001C001C001C001C000E000C0> 13 28 -1 0 16] 116 @pc restore 16 r m (o) s save [<38006400E200E200E200E200710070007000700038003800380038001C001C001C001C000E000E 000E000E00070007000700070003800380038003801FC003C0> 10 32 -2 0 14] 108 @pc restore cmsy10.329 @sf 31 r m (\031) 16 (k) ks cmmi10.329 @sf m (H) s cmsy10.329 @sf 4 r m (k) s cmmi10.329 @sf m (\017) 16 (>) ks cmr10.329 @sf 74 1061 p m (10) s cmsy8.300 @sf 120 1046 p m (\000) s cmr8.300 @sf save [<07C018303018300C600E600EE00EE00EE00EF00CF018EC30E3E0E00060007000301C181C080C06 0801F0> 15 21 -1 0 18] 54 @pc restore cmti10.329 @sf 167 1061 p m (.) 25 (Ther) -1 (efor) -2 (e) 16 (if) 18 (we) 18 (de) -1 (cide) 16 (to) 18 (de) -1 (clar) -1 (e) 15 (as) 18 (duplic) -1 (ates) 16 (those) 18 (eigenvalues) 17 (whose) 18 (di) ks save [<3C07C00000620C600000F31E100000798F18000031860C000001C00E000001C00E000000C00600 0000E007000000E007000000E007000000E0070000006003800000700380000070038000007003 80000070038000007001C000003801C000003801C000003801C000003801C000003800E000001C 00E000001C00E000001C00E000001C00E000001C00700000FFFFFF80000E007000000E00700000 0E007000000E00380000070038000007003800000700380000030318600003879CF00001878CF0 0000C3867000003F03E0> 36 41 2 9 28] 11 @pc restore 28 r m (er) -1 (enc) -2 (e) 15 (is) 17 (less) ks 74 1160 p m (than) s cmmi10.329 @sf 17 r save [<0F00188038403820382038201C101C001C001C000E000E000E000E0007000700070007000380FF F80380038001C001C001C001C000E000C0> 13 28 -1 0 16] 116 @pc restore 16 r m (o) s save [<38006400E200E200E200E200710070007000700038003800380038001C001C001C001C000E000E 000E000E00070007000700070003800380038003801FC003C0> 10 32 -2 0 14] 108 @pc restore cmti10.329 @sf 31 r m (then) 16 (the) ks 16 r save [<3C00000062000000F3000000798000003180000001C0000001C0000000C0000000E0000000E003 8000E0064000E00E2000700E2000700E2000700E20007007100070070000380700003807000038 03800038038000380380001C0380001C01C0001C01C0001C01C0001C01C0000E00E000FFFFE000 0E0000000E0000000E000000070000000700000007000000070030000300780003807800018038 0000E01000003FE0> 29 41 2 9 26] 12 @pc restore 26 r m (rst) 16 (two) 17 (distinct) 15 (eigenvalues) 15 (of) ks cmmi10.329 @sf 17 r m (H) s cmti10.329 @sf 20 r m (wil) 2 (l) 16 (b) -1 (e) 14 (de) -1 (clar) -1 (e) -3 (d) 15 (as) 16 (duplic) -1 (ates.) ks cmr10.329 @sf 124 1339 p m (The) 15 (problems) 15 (w) 0 (e) 14 (ha) 0 (v) -1 (e) 13 (just) 14 (raised) 15 (do) 15 (not) 14 (ha) 0 (v) 0 (e) 12 (easy) 15 (solutions) 15 ([) 0 (9) ks 1374 1339 p m (],) 14 (and) 14 (indeed) 17 (more) 14 (researc) 0 (h) 14 (is) ks 74 1438 p m (needed) 17 (here.) ks cmbx10.432 @sf 74 1623 p save [<007FFFF8007FFFF8007FFFF80000FE000000FE000000FE000000FE000000FE000000FE000000FE 000000FE00FFFFFFF8FFFFFFF8FFFFFFF8E0007E0070007E0038007E001C007E000E007E000E00 7E0007007E0003807E0001C07E0000E07E0000E07E0000707E0000387E00001C7E00000E7E0000 0E7E0000077E000003FE000001FE000000FE000000FE0000007E0000003E0000001E0000000E00> 29 39 -2 0 34] 52 @pc restore 177 1623 p save [<00003FF800000003FFFF0000000FFFFFC000003FF007E00000FF8000F80001FE00003C0003FC00 001E0007F000000E000FF0000007001FE0000007001FE0000003803FC0000003803FC000000380 7FC0000003807F80000000007F8000000000FF8000000000FF8000000000FF8000000000FF8000 000000FF8000000000FF8000000000FF8000000000FF8000000000FF80000000007F8000000000 7F80000003807FC0000003803FC0000003803FC0000007801FE0000007801FE0000007800FF000 000F8007F000001F8003FC00003F8001FE00007F8000FF8001FF80003FF007DF80000FFFFF8780 0003FFFE038000003FF00180> 41 41 -4 0 50] 67 @pc restore 50 r m (on) -1 (v) -1 (ergence) ks cmr10.329 @sf 74 1809 p m (In) 16 (section) 16 (2,) 14 (w) 0 (e) 14 (men) 0 (tioned) 15 (that) 15 (computing) 15 (an) 15 (eigenpair) 17 (of) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 18 r m (reduces) 16 (to) 15 (computing) 16 (a) 15 (zero) 15 (of) ks cmmi10.329 @sf 760 1955 p save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 789 1962 p m (s) s cmr10.329 @sf 807 1955 p m (\() s cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 11 (=) ks cmex10.300 @sf 976 1883 p save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pc restore cmmi10.329 @sf 1029 1928 p m (H) 4 (x) ks cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (\025x) s 1041 1983 p m (e) s cmmi8.300 @sf 1062 1968 p m (T) s 1062 1994 p m (s) s cmmi10.329 @sf 1089 1983 p m (x) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 11 r m (1) s cmex10.300 @sf 1226 1883 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1266 1955 p m (:) s cmr10.329 @sf 74 2100 p m (The) 16 (Jacobian) 16 (of) ks cmmi10.329 @sf 14 r save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 438 2107 p m (s) s cmr10.329 @sf 472 2100 p m (at) 15 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 13 (is) ks cmmi10.329 @sf 288 2245 p m (D) s cmr8.300 @sf 326 2254 p save [<0102040C1818303070606060E0E0E0E0E0E0E0E0E0E060606070303018180C040201> 8 34 -3 9 14] 40 @pc restore cmmi8.300 @sf 14 r m (x;) s save [ 16 23 -2 0 21] 21 @pc restore cmr8.300 @sf 21 r save [<8040203018180C0C0E060606070707070707070707070606060E0C0C181830204080> 8 34 -2 9 14] 41 @pc restore cmmi10.329 @sf 406 2245 p save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 435 2252 p m (s) s cmr10.329 @sf 453 2245 p m (\() s cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 11 (=) ks cmex10.300 @sf 622 2173 p save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pc restore cmmi10.329 @sf 675 2218 p m (D) s cmmi8.300 @sf 713 2225 p m (x) s cmr10.329 @sf 735 2218 p m (\() s cmmi10.329 @sf m (H) 4 (x) ks cmsy10.329 @sf 9 r m (\000) s cmmi10.329 @sf 11 r m (\025x) s cmr10.329 @sf m (\)) s cmmi10.329 @sf 987 2218 p m (D) s cmmi8.300 @sf 1025 2225 p save [ 16 23 -2 0 21] 21 @pc restore cmr10.329 @sf 1048 2218 p m (\() s cmmi10.329 @sf m (H) 4 (x) ks cmsy10.329 @sf 9 r m (\000) s cmmi10.329 @sf 10 r m (\025x) s cmr10.329 @sf m (\)) s cmmi10.329 @sf 700 2273 p m (D) s cmmi8.300 @sf 738 2280 p m (x) s cmr10.329 @sf 759 2273 p m (\() s cmmi10.329 @sf m (e) s cmmi8.300 @sf 798 2258 p m (T) s 798 2285 p m (s) s cmsy10.329 @sf 836 2273 p m (\000) s cmr10.329 @sf 10 r m (1\)) s cmmi10.329 @sf 1012 2273 p m (D) s cmmi8.300 @sf 1050 2280 p save [ 16 23 -2 0 21] 21 @pc restore cmr10.329 @sf 1072 2273 p m (\() s cmmi10.329 @sf m (e) s cmmi8.300 @sf 1111 2258 p m (T) s 1111 2285 p m (s) s cmsy10.329 @sf 1148 2273 p m (\000) s cmr10.329 @sf 11 r m (1\)) s cmex10.300 @sf 1279 2173 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1325 2245 p m (=) s cmex10.300 @sf 1373 2173 p save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pc restore cmmi10.329 @sf 1426 2218 p m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmsy10.329 @sf 1615 2218 p m (\000) s cmmi10.329 @sf m (x) s 1476 2273 p m (e) s cmmi8.300 @sf 1497 2258 p m (T) s 1497 2285 p m (s) s cmr10.329 @sf 1634 2273 p m (0) s cmex10.300 @sf 1697 2173 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1737 2245 p m (;) s cmr10.329 @sf 74 2390 p m (where) s cmmi10.329 @sf 19 r m (D) s cmmi8.300 @sf 247 2397 p m (x) s cmr10.329 @sf 269 2390 p m (\() s cmmi10.329 @sf save [ 32 31 -2 0 29] 70 @pc restore cmr10.329 @sf 35 r m (\)) 19 (denotes) 19 (the) 19 (deriv) -2 (ativ) 0 (e) 18 (with) 19 (resp) 1 (ect) 20 (to) ks cmmi10.329 @sf 18 r m (x) s cmr10.329 @sf 19 r m (of) 18 (the) 19 (function) ks cmmi10.329 @sf 20 r save [ 32 31 -2 0 29] 70 @pc restore cmr10.329 @sf 35 r m (.) 31 (In) 20 (this) 19 (section,) 20 (w) 0 (e) ks 74 2490 p m (giv) 0 (e) 18 (su\016cien) 0 (t) 18 (conditions) 20 (for) 17 (the) 19 (con) 0 (v) -1 (ergence) 17 (of) 18 (our) 19 (pro) 1 (cedure.) 30 (The) 19 (result) 18 (is) 19 (a) 18 (v) 0 (ersion) 18 (of) 18 (the) ks 74 2590 p m (Kan) 0 (toro) -1 (vic) -1 (h) 14 (theorem) 15 (as) 15 (it) 15 (applies) 17 (to) 14 (our) 15 (case.) ks @eop 19 @bop0 cmmi8.300 @sf [<1F0060C04020C010C000C000C000C000FFC06020601030101C2007C0> 12 14 -2 0 16] 101 @dc 19 @bop1 cmr10.329 @sf 1919 -77 p m (19) s 74 67 p m (the) 16 (de\014nition) 17 (of) ks cmmi10.329 @sf 16 r m (H) s cmsy8.300 @sf 450 52 p m (0) s cmr10.329 @sf 461 67 p m (\).) 21 (Ho) 0 (w) -1 (ev) -1 (er,) 13 (this) 17 (will) 17 (in) 16 (general) 17 (result) 16 (in) 16 (in) 0 (tro) 1 (ducing) 16 (non-zero) 16 (en) 0 (tries) 15 (b) 1 (elo) 0 (w) ks 74 167 p m (the) 14 (sub) 1 (diagonal) 14 (of) ks cmmi10.329 @sf 13 r m (H) s cmr10.329 @sf 17 r m (and) 13 (therefore) ks cmmi10.329 @sf 13 r m (H) s cmr10.329 @sf 17 r m (needs) 14 (to) 13 (b) 1 (e) 14 (reduced) 14 (to) 13 (upp) 1 (er-Hessen) 0 (b) 1 (erg) 14 (form) 13 (again.) 19 (W) -3 (e) ks 74 266 p m (refer) 15 (the) 14 (reader) 15 (to) 14 ([) 0 (2) ks 485 266 p m (]) 14 (for) 14 (an) 14 (example) 16 (of) 14 (suc) 0 (h) 14 (an) 14 (algorithm;) 15 (the) 14 (generalization) 16 (of) 14 (that) 14 (algorithm) ks 74 366 p m (to) 15 (the) 15 (case) 15 (where) 16 (the) 15 (eigen) 0 (v) -2 (alue) 15 (to) 15 (b) 1 (e) 16 (de\015ated) 15 (is) 16 (complex) 16 (is) 16 (straigh) 0 (tfo) -1 (rw) -1 (ar) -1 (d.) ks 124 507 p m (In) 18 (addition) 18 (to) 17 (the) 18 (di\016cult) 0 (y) 17 (just) 17 (men) 0 (tioned,) 18 (the) 17 (de\015ation) 18 (with) 18 (plane) 18 (rotations,) 17 (su\013ers) 17 (from) ks 74 607 p m (the) 19 (fact) 18 (that) 17 (the) 19 (de\015ated) 19 (matrix) 18 (will) 20 (b) 1 (e) 19 (complex) 20 (if) 19 (the) 18 (eigen) 0 (v) -2 (alue) 19 (to) 17 (b) 1 (e) 20 (de\015ated) 19 (is) 19 (complex.) ks 74 706 p m (Indeed,) 14 (it) 12 (is) 12 (unfortunately) 12 (not) 11 (true) 12 (in) 12 (general) 13 (that) 11 (when) 12 (an) 11 (eigen) 0 (v) -2 (alue) 12 (and) 12 (its) 12 (complex) 12 (conjugate) ks 74 806 p m (are) 15 (de\015ated) 16 (b) 0 (y) 14 (this) 16 (metho) 1 (d,) 15 (the) 15 (resulting) 16 (matrix) 15 (is) 16 (real.) ks cmbx10.329 @sf 74 992 p save [ 30 31 -2 0 34] 69 @pc restore 34 r save [ 25 20 -1 0 28] 120 @pc restore 28 r save [<0FE07E3FF8FE7E0DE0FC05E0F803E0F803E0F803E07C03E03C03E01F03E007FBE0007FE00003E0 0C03E03F03E03F03E03F07C03F0F801FFF0007FC00> 23 20 -1 0 25] 97 @pc restore 25 r save [ 39 20 -3 0 46] 109 @pc restore 46 r save [ 24 29 -2 9 29] 112 @pc restore 29 r save [ 11 32 -2 0 14] 108 @pc restore 14 r save [<00FF8007FFE00F80701E00183E00187C00007C0000FC0000FC0000FC0000FFFFF8FFFFF8FC00F8 7C00F87C00F03E00F01E01E00F83C007FF8001FE00> 21 20 -1 0 24] 101 @pc restore 40 r save [<03FC001FFF803C0FC07807E0FC03F0FE03F0FE03F8FE03F87C03F83803F80003F80003F00003E0 0007C0000F8001FC0001FC00001F00000F80000FC01E0FC03F07E03F07E03F07E03F07E01E0FC0 0E0F8007FF0001FC00> 21 29 -2 0 26] 51 @pc restore 26 r m (.) s save [ 17 29 -4 0 26] 49 @pc restore cmti10.329 @sf 380 992 p save [<04000800000006000800000006000C00000007001E00000007001E00000007801F00000007801F 0000000FC01E8000000F601E8000000F201E4000000F101E4000000F101E2000000F081E200000 0F081E1000000F041E0800000F041E0800000F021E0400000F021E0400000F011E0200000F009E 0200000F009E0100000F005E0100000F005E0080000F003E00C0000F003E0040000F003C002000 0F003C0020000F003C0010000F003C0010001F003C0018001F003E001C00FFF1FFC0FF80> 41 32 -9 1 45] 87 @pc restore 45 r m (hen) 16 (the) 16 (two) 17 (c) -1 (omplex) 15 (eigenvalues) 15 (of) 17 (the) ks cmr10.329 @sf 16 r m (4) s cmsy10.329 @sf 10 r m (\002) s cmr10.329 @sf 11 r m (4) s cmti10.329 @sf 16 r m (upp) -1 (er-Hessenb) -3 (er) -2 (g) 14 (matrix,) ks cmex10.300 @sf 577 1049 p m (0) s 577 1123 p m (B) s 577 1148 p m (B) s 577 1173 p m (B) s 577 1200 p m (@) s cmr10.329 @sf 651 1087 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (2190) s cmsy10.329 @sf 837 1087 p m (\000) s cmr10.329 @sf m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (0756) s 1058 1087 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (6787) s cmsy10.329 @sf 1243 1087 p m (\000) s cmr10.329 @sf m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (6391) s cmsy10.329 @sf 634 1143 p m (\000) s cmr10.329 @sf m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (9615) s 854 1143 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (9032) s cmsy10.329 @sf 1040 1143 p m (\000) s cmr10.329 @sf m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (4571) s 1261 1143 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (8804) s 703 1199 p m (0) s cmsy10.329 @sf 837 1199 p m (\000) s cmr10.329 @sf m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (3822) s 1058 1199 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (4526) s cmsy10.329 @sf 1243 1199 p m (\000) s cmr10.329 @sf m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (0641) s 703 1256 p m (0) s 906 1256 p m (0) s cmsy10.329 @sf 1040 1256 p m (\000) s cmr10.329 @sf m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (1069) s cmsy10.329 @sf 1243 1256 p m (\000) s cmr10.329 @sf m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (0252) s cmex10.300 @sf 1425 1049 p m (1) s 1425 1123 p m (C) s 1425 1148 p m (C) s 1425 1173 p m (C) s 1425 1200 p m (A) s cmti10.329 @sf 74 1350 p m (ar) -1 (e) 15 (de) ks save [<3C00000062000000F3000000798000003180000001C0000001C0000000C0000000E0000000E001 C000E0032000E00710007007100070071000700710007003880070038000380380003803800038 01C0003801C0003801C0001C01C0001C00E0001C00E0001C00E0001C00E0001E007000FFFFF000 0E0070000E0070000E0038000E003800070038000700380007001C000300DC000381FC000181FC 0000E0EE00003FCE> 31 41 2 9 27] 13 @pc restore 27 r m (ate) -1 (d) 16 (using) 15 (plane) 16 (r) -1 (otations) 15 (as) ks 16 r save [<3C0000630000F1800079C00030E00000E00000E000007000007000007000007000003800003800 003800003800001C00001C00001C00001C00000E00000E00000E00020E00010700010700008700 008700004600003C000000000000000000000000000000000000000000000003800003C00003C0 000180> 18 40 2 9 14] 106 @pc restore 14 r m (ust) 17 (describ) -1 (e) -3 (d) 15 (we) 16 (obtain) ks cmex10.300 @sf 225 1407 p m (0) s 225 1480 p m (B) s 225 1505 p m (B) s 225 1530 p m (B) s 225 1557 p m (@) s cmr10.329 @sf 299 1444 p m (1) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (1593) s cmsy10.329 @sf 9 r m (\000) s cmr10.329 @sf 10 r m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (0000) s cmmi10.329 @sf m (i) s cmr10.329 @sf 682 1444 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (0000) 9 (+) 10 (1) ks cmmi10.329 @sf m (:) s cmr10.329 @sf m (0129) s cmmi10.329 @sf m (i) s cmr10.329 @sf 1047 1444 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (0000) 9 (+) 10 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf m (0000) s cmmi10.329 @sf m (i) s cmr10.329 @sf 1413 1444 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (0000) 8 (+) 11 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf m (0000) s cmmi10.329 @sf m (i) s cmr10.329 @sf 299 1501 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (0000) s cmsy10.329 @sf 9 r m (\000) s cmr10.329 @sf 10 r m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (3053) s cmmi10.329 @sf m (i) s cmr10.329 @sf 682 1501 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (1740) s cmsy10.329 @sf 9 r m (\000) s cmr10.329 @sf 10 r m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (0000) s cmmi10.329 @sf m (i) s cmr10.329 @sf 1047 1501 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (0000) 9 (+) 10 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf m (0000) s cmmi10.329 @sf m (i) s cmr10.329 @sf 1413 1501 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (0000) 8 (+) 11 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf m (0000) s cmmi10.329 @sf m (i) s cmsy10.329 @sf 282 1557 p m (\000) s cmr10.329 @sf m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (1534) s cmsy10.329 @sf 8 r m (\000) s cmr10.329 @sf 11 r m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (3540) s cmmi10.329 @sf m (i) s cmr10.329 @sf 682 1557 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (5717) 9 (+) 10 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf m (0112) s cmmi10.329 @sf m (i) s cmr10.329 @sf 1047 1557 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (1082) s cmsy10.329 @sf 9 r m (\000) s cmr10.329 @sf 10 r m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (4681) s cmmi10.329 @sf m (i) s cmr10.329 @sf 1413 1557 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (0000) 8 (+) 11 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf m (0000) s cmmi10.329 @sf m (i) s cmsy10.329 @sf 282 1614 p m (\000) s cmr10.329 @sf m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (4640) 8 (+) 11 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf m (1988) s cmmi10.329 @sf m (i) s cmr10.329 @sf 682 1614 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (2187) s cmsy10.329 @sf 9 r m (\000) s cmr10.329 @sf 10 r m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (3465) s cmmi10.329 @sf m (i) s cmr10.329 @sf 1047 1614 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (3964) 9 (+) 10 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf m (0611) s cmmi10.329 @sf m (i) s cmr10.329 @sf 1413 1614 p m (0) s cmmi10.329 @sf m (:) s cmr10.329 @sf m (1082) 8 (+) 11 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf m (4681) s cmmi10.329 @sf m (i) s cmex10.300 @sf 1757 1407 p m (1) s 1757 1480 p m (C) s 1757 1505 p m (C) s 1757 1530 p m (C) s 1757 1557 p m (A) s cmmi10.329 @sf 1801 1529 p m (:) s cmti10.329 @sf 74 1711 p m (After) 15 (the) 15 (de) ks save [<3C00000062000000F3000000798000003180000001C0000001C0000000C0000000E0000000E001 C000E0032000E00710007007100070071000700710007003880070038000380380003803800038 01C0003801C0003801C0001C01C0001C00E0001C00E0001C00E0001C00E0001E007000FFFFF000 0E0070000E0070000E0038000E003800070038000700380007001C000300DC000381FC000181FC 0000E0EE00003FCE> 31 41 2 9 27] 13 @pc restore 27 r m (ation,) 15 (we) 16 (wil) 2 (l) 14 (b) -1 (e) 14 (working) 15 (with) 15 (the) 15 (upp) -1 (er) ks cmr10.329 @sf 15 r m (2) s cmsy10.329 @sf 7 r m (\002) s cmr10.329 @sf 7 r m (2) s cmti10.329 @sf 16 r m (blo) -1 (ck) 13 (of) ks cmmi10.329 @sf 15 r m (H) s cmsy8.300 @sf 1452 1696 p m (0) s cmti10.329 @sf 1478 1711 p m (which) 16 (cle) -1 (arly) 13 (is) 14 (c) -1 (omplex.) ks cmbx12.300 @sf 74 1874 p save [<01FE000FFFC01E07F07801F87E01FCFF00FCFF00FEFF00FEFF00FE7E00FE3C00FE0000FC0000FC 0001F80001F00007C001FF0001FE00001F800007C00003E00003F01F03F01F03F83F81F83F81F8 3F81F83F03F01E03F00F07E007FFC000FE00> 23 32 -2 0 28] 51 @pc restore 28 r m (.) s save [<00FFFE00FFFE0007E00007E00007E00007E00007E00007E00007E0FFFFFEFFFFFEE007E07007E0 3807E01807E00C07E00E07E00707E00307E00187E001C7E000E7E00077E00037E0001FE0001FE0 000FE00007E00003E00003E00001E00000E0> 23 32 -2 0 28] 52 @pc restore 202 1874 p save [ 39 34 -2 0 42] 82 @pc restore 42 r m (emar) s save [ 26 35 -2 0 30] 107 @pc restore 30 r m (s) 16 (on) 19 (iden) -1 (ti) ks save [<7FF8007FF8000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F8000 0F80000F80000F80000F80000F80000F80000F8000FFFC00FFFC000F80000F80000F80000F8000 0F80000F80000F83C00F87E007C7E003C7E001E3E000FFC0003F80> 19 35 -1 0 17] 102 @pc restore 17 r m (ying) 16 (duplicate) 18 (eigen) ks -1 r save [<000E0000000E0000001F0000001F0000003F8000003F8000007FC000007CC000007CC00000F860 0000F8600001F0300001F0300003E0180003E0180007E01C0007C00C000FC00E000F8006000F80 0600FFE01FE0FFE01FE0> 27 22 -1 0 30] 118 @pc restore 27 r m (alue) -1 (s) ks cmr10.329 @sf 74 2045 p m (W) -3 (e) 22 (ha) 0 (v) -1 (e) 21 (already) 22 (remark) 0 (ed) 21 (that) 22 (the) 22 (computed) 23 (eigenpairs) 24 (from) 21 (our) 22 (algorithm) 23 (are) 22 (the) 22 (exact) ks 74 2144 p m (eigenpairs) 17 (of) 14 (a) 15 (nearb) 0 (y) 14 (matrix.) 20 (Under) 16 (those) 15 (conditions) 16 (\([) 0 (8) ks 1218 2144 p m (]\),) s cmsy10.329 @sf 791 2285 p m (j) s cmmi10.329 @sf m (\025) s cmsy10.329 @sf 9 r m (\000) s cmmi10.329 @sf 10 r m (\025) s cmmi8.300 @sf 912 2292 p m (e) s cmsy10.329 @sf 930 2285 p m (j) 13 (\024) 13 (k) ks cmmi10.329 @sf save [ 32 31 -2 0 34] 69 @pc restore cmsy10.329 @sf 37 r m (k) s cmmi10.329 @sf m (=) s cmsy10.329 @sf m (j) s cmmi10.329 @sf m (s) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (\025) s cmmi8.300 @sf 1188 2292 p m (e) s cmr10.329 @sf 1205 2285 p m (\)) s cmsy10.329 @sf m (j) s cmmi10.329 @sf m (;) s cmr10.329 @sf 74 2427 p m (where) s cmmi10.329 @sf 16 r save [ 32 31 -2 0 34] 69 @pc restore cmr10.329 @sf 52 r m (is) 16 (the) 16 (error) 15 (in) 16 (the) 16 (matrix,) 15 (and) ks cmsy10.329 @sf 16 r m (j) s cmmi10.329 @sf m (s) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (\025) s cmmi8.300 @sf 956 2434 p m (e) s cmr10.329 @sf 974 2427 p m (\)) s cmsy10.329 @sf m (j) s cmr10.329 @sf 15 r m (is) 16 (the) 16 (condition) 17 (n) 0 (um) -1 (b) 1 (er) 15 (of) 15 (the) 16 (exact) 15 (eigen) 0 (v) -2 (alue) ks cmmi10.329 @sf 74 2526 p m (\025) s cmmi8.300 @sf 101 2533 p m (e) s cmr10.329 @sf 132 2526 p m (of) 13 (the) 13 (original) 14 (matrix) ks cmmi10.329 @sf 12 r m (H) s cmr10.329 @sf 4 r m (.) 19 (When) ks cmmi10.329 @sf 13 r m (\025) s cmmi8.300 @sf 796 2533 p m (e) s cmr10.329 @sf 827 2526 p m (is) 14 (ill-condi) 1 (tioned) 15 (w) 0 (e) 12 (can) 13 (exp) 1 (ect) 14 (unpredictably) 15 (large) 13 (errors) ks 74 2626 p m (\(compared) 21 (to) 21 (the) 21 (tolerated) 21 (size) 22 (of) 21 (the) 22 (residual\)) 22 (in) 22 (the) 21 (computed) 22 (appro) 0 (ximations) 20 (to) ks cmmi10.329 @sf 21 r m (\025) s cmmi8.300 @sf 1852 2633 p m (e) s cmr10.329 @sf 1891 2626 p m (and) s 74 2726 p m (therefore) 19 (in) 20 (the) 19 (duplicates) 20 (if) 20 (an) 0 (y) 17 (and) 19 (iden) 0 (tifying) 20 (these) 19 (duplic) 1 (ates) 20 (b) 1 (ecomes) 20 (a) 18 (rather) 19 (daun) 0 (ting) ks @eop 18 @bop0 cmmi8.300 @sf [<3000300018001800180018000C000C000C008C0046304638451838F0> 13 14 -1 0 16] 114 @dc cmex10.300 @sf [<800F80601FE03078301FE01807C004> 22 5 0 -25 23] 101 @dc 18 @bop1 cmr10.329 @sf 1919 -77 p m (18) s 74 67 p m (end) 20 (of) 18 (the) ks cmmi10.329 @sf 19 r m (n) s cmsy10.329 @sf 12 r m (\000) s cmr10.329 @sf 13 r m (1) 19 (steps) 18 (just) 19 (describ) 1 (ed) 21 (the) 18 (last) 19 (column) 20 (is) 19 (zero.) 30 (Let) 19 (us) 19 (set) ks cmsy10.329 @sf 19 r save [<1FC000007FF000007E0C00003806000000030000000380000001C0000001C0000FE0E0001FF8E0 003F06F0007E0370007C01F000F800F800F8007800F0007800F0003C00F0003C00F0001C00F000 1C00F0000E0070000200700000007800000038000000380000001C0000001C0030000E0018000E 000C0007000E0003000700008007000060078000181F80000FFF800001FE00> 25 37 -2 5 27] 71 @pc restore cmr10.329 @sf 48 r m (=) s cmmi10.329 @sf 19 r save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmr8.300 @sf 1713 74 p m (1) s cmr10.329 @sf 1740 67 p m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 1801 67 p save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 1837 74 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 1924 67 p m (to) s 74 167 p m (simplify) 17 (the) 15 (notation.) 20 (Then,) ks cmsy10.329 @sf 761 266 p save [<1FC000007FF000007E0C00003806000000030000000380000001C0000001C0000FE0E0001FF8E0 003F06F0007E0370007C01F000F800F800F8007800F0007800F0003C00F0003C00F0001C00F000 1C00F0000E0070000200700000007800000038000000380000001C0000001C0030000E0018000E 000C0007000E0003000700008007000060078000181F80000FFF800001FE00> 25 37 -2 5 27] 71 @pc restore cmsy8.300 @sf 791 248 p m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 851 266 p m (=) s cmsy10.329 @sf 13 r save [<1FC000007FF000007E0C00003806000000030000000380000001C0000001C0000FE0E0001FF8E0 003F06F0007E0370007C01F000F800F800F8007800F0007800F0003C00F0003C00F0001C00F000 1C00F0000E0070000200700000007800000038000000380000001C0000001C0030000E0018000E 000C0007000E0003000700008007000060078000181F80000FFF800001FE00> 25 37 -2 5 27] 71 @pc restore cmmi8.300 @sf 929 248 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 975 266 p m (=) s cmmi10.329 @sf 13 r save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 1059 248 p save [ 29 23 -1 0 29] 72 @pc restore 1059 278 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 1135 266 p m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 1195 266 p save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 1231 248 p save [ 29 23 -1 0 29] 72 @pc restore cmr8.300 @sf 1231 278 p m (1) s cmmi10.329 @sf 1264 266 p m (;) s cmr10.329 @sf 74 393 p m (and) 23 (it) 23 (is) 23 (straigh) 0 (tforw) -2 (ard) 21 (to) 22 (v) 0 (erify) 22 (that) 22 (the) 23 (zeros) 22 (of) 23 (the) 22 (last) 23 (column) 24 (of) 22 (\() ks cmmi10.329 @sf m (H) s cmsy10.329 @sf 18 r m (\000) s cmmi10.329 @sf 16 r m (\025I) s cmr10.329 @sf 4 r m (\)) s cmsy10.329 @sf save [<1FC000007FF000007E0C00003806000000030000000380000001C0000001C0000FE0E0001FF8E0 003F06F0007E0370007C01F000F800F800F8007800F0007800F0003C00F0003C00F0001C00F000 1C00F0000E0070000200700000007800000038000000380000001C0000001C0030000E0018000E 000C0007000E0003000700008007000060078000181F80000FFF800001FE00> 25 37 -2 5 27] 71 @pc restore cmr10.329 @sf 51 r m (will) 24 (b) 1 (e) ks 74 493 p m (preserv) 0 (ed) 11 (when) 12 (it) 11 (is) 12 (pre-m) 0 (ultiplied) 13 (b) 0 (y) ks cmsy10.329 @sf 11 r save [<1FC000007FF000007E0C00003806000000030000000380000001C0000001C0000FE0E0001FF8E0 003F06F0007E0370007C01F000F800F800F8007800F0007800F0003C00F0003C00F0001C00F000 1C00F0000E0070000200700000007800000038000000380000001C0000001C0030000E0018000E 000C0007000E0003000700008007000060078000181F80000FFF800001FE00> 25 37 -2 5 27] 71 @pc restore cmsy8.300 @sf 851 478 p m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 898 493 p m (,) 11 (b) 1 (ecause) 13 (the) 11 (successiv) 0 (e) 12 (pre-m) 0 (ultiplications) 13 (b) 0 (y) ks cmmi10.329 @sf 10 r save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 1847 478 p m (T) s 1847 504 p m (r) s cmmi10.329 @sf 1874 493 p m (;) 8 (r) ks cmr10.329 @sf 13 r m (=) s 74 592 p m (1) s cmmi10.329 @sf m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 7 (.) ks cmmi10.329 @sf 178 592 p m (;) 8 (n) ks cmsy10.329 @sf 9 r m (\000) s cmr10.329 @sf 11 r m (1,) 14 (will) 17 (preserv) 0 (e) 14 (those) 15 (zeros.) 20 (Therefore) 15 (the) 15 (last) 15 (column) 17 (of) ks cmex10.300 @sf 789 726 p m (e) s cmmi10.329 @sf 778 739 p m (H) s cmr10.329 @sf 832 738 p m (=) s cmsy10.329 @sf 13 r save [<1FC000007FF000007E0C00003806000000030000000380000001C0000001C0000FE0E0001FF8E0 003F06F0007E0370007C01F000F800F800F8007800F0007800F0003C00F0003C00F0001C00F000 1C00F0000E0070000200700000007800000038000000380000001C0000001C0030000E0018000E 000C0007000E0003000700008007000060078000181F80000FFF800001FE00> 25 37 -2 5 27] 71 @pc restore cmmi8.300 @sf 910 720 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 943 738 p m (\() s cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (\025I) s cmr10.329 @sf 4 r m (\)) s cmsy10.329 @sf save [<1FC000007FF000007E0C00003806000000030000000380000001C0000001C0000FE0E0001FF8E0 003F06F0007E0370007C01F000F800F800F8007800F0007800F0003C00F0003C00F0001C00F000 1C00F0000E0070000200700000007800000038000000380000001C0000001C0030000E0018000E 000C0007000E0003000700008007000060078000181F80000FFF800001FE00> 25 37 -2 5 27] 71 @pc restore cmr10.329 @sf 38 r m (+) s cmmi10.329 @sf 11 r m (\025I) s cmr10.329 @sf 74 883 p m (is) 20 (equal) 20 (to) ks cmmi10.329 @sf 19 r m (\025e) s cmmi8.300 @sf 356 890 p m (n) s cmr10.329 @sf 379 883 p m (.) 33 (The) 19 (eigen) 0 (v) 0 (ector) 18 (of) ks cmex10.300 @sf 830 871 p m (e) s cmmi10.329 @sf 819 884 p m (H) s cmr10.329 @sf 879 883 p m (corresp) 1 (onding) 21 (to) ks cmmi10.329 @sf 19 r m (\025) s cmr10.329 @sf 18 r m (is) s cmmi10.329 @sf 20 r m (e) s cmmi8.300 @sf 1352 890 p m (n) s cmr10.329 @sf 1376 883 p m (.) 32 (Note) 20 (that) ks cmex10.300 @sf 1650 871 p m (e) s cmmi10.329 @sf 1638 884 p m (H) s cmr10.329 @sf 1699 883 p m (is) 20 (not) 19 (upp) 1 (er-) ks 74 982 p m (Hessen) 0 (b) 1 (erg) 15 (in) 15 (this) 16 (case) 15 (though.) 19 (Indeed,) 17 (non) 15 (zero) 15 (elemen) 0 (ts) 14 (will) 17 (b) 1 (e) 16 (in) 0 (tro) 1 (duced) 15 (in) 16 (the) 15 (last) 14 (ro) 0 (w) 14 (of) ks cmex10.300 @sf 86 1070 p m (e) s cmmi10.329 @sf 74 1083 p m (H) s cmr10.329 @sf 116 1082 p m (;) 14 (in) 16 (fact) 15 (,) ks cmex10.300 @sf 766 1222 p m (e) s cmmi10.329 @sf 754 1235 p m (H) s cmr10.329 @sf 808 1234 p m (=) s cmex10.300 @sf 856 1100 p m (0) s 856 1173 p m (B) s 856 1198 p m (B) s 856 1223 p m (B) s 856 1248 p m (B) s 856 1275 p m (@) s cmsy10.329 @sf 913 1135 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore 977 1135 p m (\001) 8 (\001) 8 (\001) ks 1110 1135 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore 913 1171 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore cmr10.329 @sf 980 1214 p m (.) s 998 1226 p m (.) s 1015 1239 p m (.) s 1120 1210 p m (.) s 1120 1227 p m (.) s 1120 1244 p m (.) s cmsy10.329 @sf 1072 1298 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore 38 r save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore 913 1334 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore 977 1334 p m (\001) 8 (\001) 8 (\001) ks 1110 1334 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore 1174 1197 p save [<003F800000E0E0000380380007001C000F001E000E000E001E000F001C0007003C0007803C0007 803C0007807C0007C0780003C0780003C0780003C0F80003E0F80003E0F80003E0F80003E0F800 03E0F80003E0F80003E0F80003E0F80003E0F80003E0F80003E0F80003E0F80003E0F80003E0F8 0003E0F80003E0F80003E0F80003E0780003C0780003C0780003C0780003C03C0007803C000780 3C0007801C0007001E000F000E000E000F001E0007001C000380380000E0E000003F8000> 27 48 -3 1 33] 48 @pc restore cmmi10.329 @sf 1177 1322 p m (\025) s cmex10.300 @sf 1228 1100 p m (1) s 1228 1173 p m (C) s 1228 1198 p m (C) s 1228 1223 p m (C) s 1228 1248 p m (C) s 1228 1275 p m (A) s cmmi10.329 @sf 1272 1234 p m (:) s cmr10.329 @sf 74 1425 p m (This) 18 (is) 17 (not) 17 (disturbing) 18 (since) 18 (if) ks cmmi10.329 @sf 18 r m (H) s cmsy8.300 @sf 728 1410 p m (0) s cmr10.329 @sf 756 1425 p m (is) 17 (the) 18 (leading) 18 (principal) 19 (submatrix) 17 (of) ks cmex10.300 @sf 1517 1413 p m (e) s cmmi10.329 @sf 1505 1426 p m (H) s cmr10.329 @sf 1563 1425 p m (of) 17 (order) ks cmmi10.329 @sf 17 r m (n) s cmsy10.329 @sf 11 r m (\000) s cmr10.329 @sf 12 r m (1,) 17 (then) ks cmmi10.329 @sf 74 1525 p m (H) s cmsy8.300 @sf 116 1510 p m (0) s cmr10.329 @sf 142 1525 p m (is) 16 (upp) 1 (er-Hessen) 0 (b) 1 (erg) 16 (and) ks cmmi10.329 @sf 15 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmsy8.300 @sf 731 1510 p m (0) s cmr10.329 @sf 742 1525 p m (\)) 12 (=) ks cmmi10.329 @sf 13 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmr10.329 @sf 4 r m (\)) s cmsy10.329 @sf 9 r m (\000) 10 (f) ks cmmi10.329 @sf m (\025) s cmsy10.329 @sf m (g) s cmr10.329 @sf m (.) s 124 1666 p m (If) s cmmi10.329 @sf 16 r m (\025) s cmr10.329 @sf 15 r m (is) 17 (a) 15 (m) 0 (ultiple) 17 (eigen) 0 (v) -2 (alue) 16 (of) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 20 r m (of) 15 (\(algebraic\)) 16 (m) 0 (ultiplicit) 0 (y) ks cmmi10.329 @sf 16 r m (m) s cmr10.329 @sf 16 r m (then) s cmmi10.329 @sf 16 r m (\025) s cmr10.329 @sf 16 r m (is) 16 (an) 16 (eigen) 0 (v) -2 (alue) 16 (of) ks cmmi10.329 @sf 15 r m (H) s cmsy8.300 @sf 1953 1651 p m (0) s cmr10.329 @sf 74 1766 p m (of) 15 (m) 0 (ultiplicit) 0 (y) ks cmmi10.329 @sf 16 r m (m) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 10 r m (1.) s 124 1907 p m (So) 19 (far) 19 (w) 0 (e) 19 (ha) 0 (v) -1 (e) 18 (assumed) 19 (that) 19 (the) 20 (eigenpair) 21 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 17 (is) 20 (exact.) 33 (In) 20 (practice,) 21 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 17 (will) 21 (only) 20 (b) 1 (e) ks 74 2006 p m (appro) 0 (ximate,) 12 (in) 14 (the) 13 (sense) 13 (that) ks cmmi10.329 @sf 12 r m (H) 4 (x) ks cmsy10.329 @sf 6 r m (\000) s cmmi10.329 @sf 6 r m (\025x) s cmr10.329 @sf 11 r m (=) s cmmi10.329 @sf 13 r m (r) s cmr10.329 @sf 1 r m (,) 13 (is) 14 (of) 12 (the) 13 (order) 13 (of) 12 (the) 13 (mac) 0 (hine) ks cmmi10.329 @sf 13 r m (\017) s cmr10.329 @sf m (.) 20 (In) 13 (this) 14 (case) 13 (round-) ks 74 2106 p m (o\013) 12 (errors) 12 (will) 15 (in) 13 (general) 14 (prev) 0 (en) 0 (t) ks cmmi10.329 @sf 10 r save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 748 2113 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 829 2106 p m (from) 13 (annihilating) 15 (the) 13 (\(1) ks cmmi10.329 @sf m (;) 8 (n) ks cmr10.329 @sf m (\)) 11 (en) 0 (try) -3 (.) 17 (In) 13 (fact,) 13 (the) 13 (accuracy) 13 (of) ks 74 2206 p m (the) 14 (computed) 14 (eigen) 0 (v) -2 (alue) ks cmmi10.329 @sf 14 r m (\025) s cmr10.329 @sf 13 r m (will) 16 (come) 14 (in) 0 (to) 12 (pla) 0 (y) -3 (.) 18 (If) ks cmmi10.329 @sf 14 r m (\025) s cmr10.329 @sf 14 r m (corresp) 1 (onds) 14 (to) 13 (an) 14 (ill-condi) 1 (tioned) 16 (eigen) 0 (v) -2 (alue) ks 74 2305 p m (of) s cmmi10.329 @sf 17 r m (H) s cmr10.329 @sf 4 r m (,) 17 (then) 18 (it) 17 (is) 18 (p) 1 (ossible) 19 (that) ks cmmi10.329 @sf 17 r m (\025) s cmr10.329 @sf 16 r m (b) 1 (e) 18 (a) 17 (rather) 17 (p) 1 (o) 1 (or) 17 (appro) 0 (ximation) 17 (of) 16 (the) 18 (exact) 17 (eigen) 0 (v) -2 (alue.) 26 (As) 17 (a) ks 74 2405 p m (consequence) 18 (the) 16 (\(1) ks cmmi10.329 @sf m (;) 8 (n) ks cmr10.329 @sf m (\)) 15 (en) 0 (try) 15 (migh) 0 (t) 15 (not) 16 (b) 1 (e) 16 (negligib) 1 (le) 19 (at) 15 (all) 17 (and) 17 (examples) 17 (do) 16 (exist) 16 (where) 17 (this) 17 (is) ks 74 2504 p m (indeed) 13 (the) 11 (case) 11 ([) 0 (17) ks 438 2504 p m (].) 18 (A) 11 (w) 0 (a) -1 (y) 9 (around) 11 (this) 12 (di\016cult) 0 (y) 11 (is) 12 (to) 10 (construct) 11 (the) 11 (plane) 12 (rotations) ks cmmi10.329 @sf 10 r save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmr8.300 @sf 1739 2511 p m (1) s cmmi10.329 @sf 1759 2504 p m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 7 (.) ks cmmi10.329 @sf 1840 2504 p m (;) s 8 r save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 1897 2511 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 74 2604 p m (in) 13 (a) 12 (w) 0 (a) -1 (y) 10 (to) 12 (reduce) 13 (the) 12 (v) 0 (ector) ks cmmi10.329 @sf 10 r m (x) s cmr10.329 @sf 13 r m (to) s cmmi10.329 @sf 11 r m (e) s cmmi8.300 @sf 762 2611 p m (n) s cmr10.329 @sf 798 2604 p m (and) 12 (then) 13 (apply) 13 (the) 12 (corresp) 1 (onding) 13 (similarit) 0 (y) 12 (transformation) ks 74 2704 p m (to) s cmmi10.329 @sf 18 r m (H) s cmr10.329 @sf 4 r m (.) 28 (Inequalit) 0 (y) 19 (\(10\)) 17 (from) 17 (section) 19 (3.1) 17 (holds) 19 (when) 19 (this) 19 (is) 19 (done) 18 (\(with) 18 (ob) 0 (vious) 18 (mo) 1 (di\014cation) 19 (in) ks @eop 17 @bop0 17 @bop1 cmr10.329 @sf 1919 -77 p m (17) s 124 67 p m (The) 16 (strategy) 15 (consists) 16 (of) ks cmmi10.329 @sf 16 r m (n) s cmsy10.329 @sf 11 r m (\000) s cmr10.329 @sf 11 r m (1) 15 (ma) 3 (jor) 15 (steps,) 16 (at) 15 (eac) 0 (h) 15 (of) 16 (whic) 0 (h) 16 (a) 15 (new) 17 (zero) 15 (is) 17 (in) 0 (tro) 1 (duced) 16 (in) 17 (the) ks 74 167 p m (last) 15 (column) 16 (of) ks cmmi10.329 @sf 15 r m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmr10.329 @sf 18 r m (starting) 14 (from) 14 (the) 15 (b) 1 (ottom.) 19 (The) 16 (con\014guration) 15 (at) 14 (the) 15 (b) 1 (eginnin) 1 (g) 16 (of) 15 (the) ks cmmi10.329 @sf 15 r m (r) s 1926 152 p save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 18 26 -1 0 21] 104 @pc restore cmr10.329 @sf 74 266 p m (step) 15 (lo) 1 (oks) 16 (lik) 0 (e) ks cmex10.300 @sf 795 394 p m (e) s cmmi10.329 @sf 783 407 p m (H) s cmr10.329 @sf 837 406 p m (=) s cmex10.300 @sf 885 285 p m (0) s 885 358 p m (B) s 885 383 p m (B) s 885 408 p m (B) s 885 435 p m (@) s cmsy10.329 @sf 942 324 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore 1006 324 p m (\001) 8 (\001) 8 (\001) ks 1101 324 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore 942 360 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore cmr10.329 @sf 1009 404 p m (.) s 1027 416 p m (.) s 1044 429 p m (.) s 1111 400 p m (.) s 1111 417 p m (.) s 1111 434 p m (.) s cmsy10.329 @sf 1101 488 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore 1170 319 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore cmr10.329 @sf 1175 358 p m (.) s 1175 375 p m (.) s 1175 392 p m (.) s cmsy10.329 @sf 1170 430 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore 1165 494 p save [<003F800000E0E0000380380007001C000F001E000E000E001E000F001C0007003C0007803C0007 803C0007807C0007C0780003C0780003C0780003C0F80003E0F80003E0F80003E0F80003E0F800 03E0F80003E0F80003E0F80003E0F80003E0F80003E0F80003E0F80003E0F80003E0F80003E0F8 0003E0F80003E0F80003E0F80003E0780003C0780003C0780003C0780003C03C0007803C000780 3C0007801C0007001E000F000E000E000F001E0007001C000380380000E0E000003F8000> 27 48 -3 1 33] 48 @pc restore cmex10.300 @sf 1219 285 p m (1) s 1219 358 p m (C) s 1219 383 p m (C) s 1219 408 p m (C) s 1219 435 p m (A) s cmr10.329 @sf 74 584 p m (with) 20 (zeros) 19 (in) 20 (the) 20 (last) ks cmmi10.329 @sf 19 r m (r) s cmsy10.329 @sf 14 r m (\000) s cmr10.329 @sf 13 r m (1) 19 (comp) 1 (onen) 0 (ts) 18 (of) 19 (the) 20 (last) 19 (column.) 33 (The) ks cmmi10.329 @sf 20 r m (r) s 1447 569 p save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 18 26 -1 0 21] 104 @pc restore cmr10.329 @sf 1504 584 p m (step) 20 (then) 20 (consists) 19 (in) 20 (a) ks 74 684 p m (p) 1 (ost-m) 0 (ultiplication) 19 (b) 0 (y) ks cmmi10.329 @sf 16 r save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 569 691 p m (r) s cmr10.329 @sf 587 684 p m (,) 18 (where) ks cmmi10.329 @sf 17 r save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 787 691 p m (r) s cmr10.329 @sf 823 684 p m (is) 17 (the) 17 (\(p) 1 (ossibly) 19 (complex\)) 17 (rotation) 17 (in) 17 (the) 18 (plane) 18 (\() ks cmmi10.329 @sf m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 12 r m (r) 0 (;) 7 (n) ks cmr10.329 @sf m (\)) s 74 783 p m (designed) 17 (to) 14 (annihil) 1 (ate) 16 (the) 16 (\() ks cmmi10.329 @sf m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (r) 0 (;) 8 (n) ks cmr10.329 @sf m (\)) 13 (elemen) 0 (t:) ks cmmi10.329 @sf 651 1012 p save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 687 1019 p m (r) s cmr10.329 @sf 719 1012 p m (=) s cmex10.300 @sf 767 853 p m (0) s 767 926 p m (B) s 767 951 p m (B) s 767 976 p m (B) s 767 1001 p m (B) s 767 1026 p m (B) s 767 1051 p m (B) s 767 1078 p m (@) s cmr10.329 @sf 824 884 p m (1) s 891 923 p m (.) s 908 935 p m (.) s 926 948 p m (.) s 983 986 p m (1) s cmmi10.329 @sf 1020 1006 p m (c) s cmmi8.300 @sf 1040 1013 p m (r) s cmr10.329 @sf 1074 1031 p m (1) s cmsy10.329 @sf 1233 1006 p m (\000) s cmmi10.329 @sf m (s) s cmmi8.300 @sf 1289 1013 p m (r) s cmr10.329 @sf 1141 1052 p m (.) s 1159 1065 p m (.) s 1176 1078 p m (.) s cmmi10.329 @sf 1020 1125 p m (s) s cmmi8.300 @sf 1041 1132 p m (r) s cmr10.329 @sf 1233 1125 p m (1) s cmmi10.329 @sf 1271 1150 p m (c) s cmmi8.300 @sf 1291 1157 p m (r) s cmex10.300 @sf 1330 853 p m (1) s 1330 926 p m (C) s 1330 951 p m (C) s 1330 976 p m (C) s 1330 1001 p m (C) s 1330 1026 p m (C) s 1330 1051 p m (C) s 1330 1078 p m (A) s cmmi10.329 @sf 1374 1012 p m (;) s cmr10.329 @sf 74 1245 p m (where) s cmsy10.329 @sf 19 r m (k) s cmmi10.329 @sf m (c) s cmmi8.300 @sf 252 1252 p m (r) s cmsy10.329 @sf 271 1245 p m (k) s cmr8.300 @sf 294 1230 p m (2) s cmr10.329 @sf 326 1245 p m (+) s cmsy10.329 @sf 13 r m (k) s cmmi10.329 @sf m (s) s cmmi8.300 @sf 418 1252 p m (r) s cmsy10.329 @sf 437 1245 p m (k) s cmr8.300 @sf 460 1230 p m (2) s cmr10.329 @sf 498 1245 p m (=) 20 (1.) 31 (This) 20 (p) 1 (ost-m) 0 (ultiplication) 20 (will) 21 (a\013ect) 18 (columns) ks cmmi10.329 @sf 20 r m (n) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 13 r m (r) s cmr10.329 @sf 20 r m (and) s cmmi10.329 @sf 19 r m (n) s cmr10.329 @sf 19 r m (only) 20 (and) ks 74 1344 p m (therefore) 17 (will) 18 (not) 17 (disturb) 17 (zeros) 17 (previously) 18 (in) 0 (tro) 1 (duced) 17 (in) 18 (the) 17 (last) 17 (column.) 25 (A) 0 (t) 16 (the) 17 (\() ks cmmi10.329 @sf m (n) s cmsy10.329 @sf 11 r m (\000) s cmr10.329 @sf 11 r m (1\)) 16 (step,) ks cmmi10.329 @sf 74 1444 p save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 110 1451 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 195 1444 p m (whic) 0 (h) 15 (is) 17 (constructed) 16 (to) 16 (zero) 16 (the) 16 (\(2) ks cmmi10.329 @sf m (;) 8 (n) ks cmr10.329 @sf m (\)) 14 (elemen) 0 (t,) 16 (will) 18 (also) 16 (zero) 16 (the) 16 (\(1) ks cmmi10.329 @sf m (;) 8 (n) ks cmr10.329 @sf m (\)) 15 (elemen) 0 (t.) 22 (Indeed,) ks 74 1544 p m (assume) 13 (that) 12 (after) 12 (the) 13 (\(2) ks cmmi10.329 @sf m (;) 8 (n) ks cmr10.329 @sf m (\)) 11 (elemen) 0 (t) 13 (has) 12 (b) 1 (een) 14 (zero) 1 (ed) 13 (w) 0 (e) 12 (ha) 0 (v) -1 (e) 11 (some) 13 (v) -2 (alue) ks cmmi10.329 @sf 13 r m (\013) s cmr10.329 @sf 13 r m (in) 13 (the) 13 (\(1) ks cmmi10.329 @sf m (;) 8 (n) ks cmr10.329 @sf m (\)) 11 (p) 1 (osition;) ks 74 1643 p m (then) 16 (w) 0 (e) 14 (ha) 0 (v) -1 (e) ks 589 1771 p m (\() s cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmr10.329 @sf 4 r m (\)) s cmmi10.329 @sf save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmr8.300 @sf 808 1778 p m (1) s cmr10.329 @sf 834 1771 p m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 895 1771 p save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 931 1778 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 1012 1771 p m (=) s cmex10.300 @sf 1059 1649 p m (0) s 1059 1722 p m (B) s 1059 1747 p m (B) s 1059 1772 p m (B) s 1059 1799 p m (@) s cmsy10.329 @sf 1117 1689 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore 1181 1689 p m (\001) 8 (\001) 8 (\001) ks 1275 1689 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore 1117 1725 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore cmr10.329 @sf 1183 1768 p m (.) s 1201 1780 p m (.) s 1219 1793 p m (.) s 1285 1764 p m (.) s 1285 1781 p m (.) s 1285 1798 p m (.) s cmsy10.329 @sf 1275 1853 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @pc restore cmmi10.329 @sf 1341 1707 p m (\013) s 1340 1835 p save [<003F800000E0E0000380380007001C000F001E000E000E001E000F001C0007003C0007803C0007 803C0007807C0007C0780003C0780003C0780003C0F80003E0F80003E0F80003E0F80003E0F800 03E0F80003E0F80003E0F80003E0F80003E0F80003E0F80003E0F80003E0F80003E0F80003E0F8 0003E0F80003E0F80003E0F80003E0780003C0780003C0780003C0780003C03C0007803C000780 3C0007801C0007001E000F000E000E000F001E0007001C000380380000E0E000003F8000> 27 48 -3 1 33] 48 @pc restore cmex10.300 @sf 1393 1649 p m (1) s 1393 1722 p m (C) s 1393 1747 p m (C) s 1393 1772 p m (C) s 1393 1799 p m (A) s cmmi10.329 @sf 1437 1771 p m (:) s cmr10.329 @sf 74 1934 p m (No) 0 (w) 14 (if) 15 (w) 0 (e) 14 (dev) 0 (elop) 15 (the) 16 (determinan) 0 (t) 14 (of) 15 (this) 16 (matrix) 14 (b) 0 (y) 15 (the) 15 (last) 15 (column) 16 (w) 0 (e) 14 (get) ks 621 2079 p m (det) s 684 2079 p m ([\() s cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmr10.329 @sf 4 r m (\)) s cmmi10.329 @sf save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmr8.300 @sf 916 2086 p m (1) s cmr10.329 @sf 942 2079 p m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 1003 2079 p save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 1039 2086 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 1107 2079 p m (]) 12 (=) ks cmmi10.329 @sf 13 r m (\013) s save [<1F0031C060E06070E038E03CE01CE01EE01EE01E700F700F700F700F380F380F3C0E3A0E1D0C1C F01C001C000E000E000E000E0007000700070007003F800780> 16 32 -2 0 20] 98 @pc restore cmr8.300 @sf 1229 2086 p m (1) s cmr10.329 @sf 1256 2079 p m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 1317 2079 p save [<1F0031C060E06070E038E03CE01CE01EE01EE01E700F700F700F700F380F380F3C0E3A0E1D0C1C F01C001C000E000E000E000E0007000700070007003F800780> 16 32 -2 0 20] 98 @pc restore cmmi8.300 @sf 1337 2086 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1405 2079 p m (;) s cmr10.329 @sf 74 2225 p m (where) s cmmi10.329 @sf 16 r save [<1F0031C060E06070E038E03CE01CE01EE01EE01E700F700F700F700F380F380F3C0E3A0E1D0C1C F01C001C000E000E000E000E0007000700070007003F800780> 16 32 -2 0 20] 98 @pc restore cmmi8.300 @sf 226 2232 p m (r) s cmr10.329 @sf 259 2225 p m (is) 16 (the) ks cmmi10.329 @sf 15 r m (r) s 405 2210 p save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 18 26 -1 0 21] 104 @pc restore cmr10.329 @sf 458 2225 p m (sub) 1 (diagonal) 17 (elemen) 0 (t) 15 (of) 15 (\() ks cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmr10.329 @sf 4 r m (\)) s cmmi10.329 @sf save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmr8.300 @sf 1149 2232 p m (1) s cmr10.329 @sf 1175 2225 p m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 1236 2225 p save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 1272 2232 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 1340 2225 p m (.) s 569 2370 p m (det) s 632 2370 p m ([\() s cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmr10.329 @sf 4 r m (\)) s cmmi10.329 @sf save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmr8.300 @sf 864 2377 p m (1) s cmr10.329 @sf 890 2370 p m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 951 2370 p save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 987 2377 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 1055 2370 p m (]) 12 (=) 13 (det) ks 1191 2370 p m (\() s cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (\025I) s cmr10.329 @sf 4 r m (\)) 11 (=) 13 (0) ks cmmi10.329 @sf m (;) s cmr10.329 @sf 74 2515 p m (since) 19 (\() 0 (det) ks 269 2515 p m (\() s cmmi10.329 @sf save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 323 2522 p m (r) s cmr10.329 @sf 341 2515 p m (\)) 16 (=) 17 (1\)) 17 (for) ks cmmi10.329 @sf 17 r m (r) s cmr10.329 @sf 17 r m (=) 16 (1) ks cmmi10.329 @sf m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 750 2515 p m (;) 8 (n) ks cmsy10.329 @sf 11 r m (\000) s cmr10.329 @sf 12 r m (1.) 26 (But) ks cmmi10.329 @sf 18 r save [<1F0031C060E06070E038E03CE01CE01EE01EE01E700F700F700F700F380F380F3C0E3A0E1D0C1C F01C001C000E000E000E000E0007000700070007003F800780> 16 32 -2 0 20] 98 @pc restore cmmi8.300 @sf 1031 2522 p m (r) s cmsy10.329 @sf 1066 2515 p m (6) s cmr10.329 @sf m (=) 17 (0) 17 (for) 17 (all) ks cmmi10.329 @sf 18 r m (r) s cmr10.329 @sf 1 r m (,) 17 (since) 19 (w) 0 (e) 16 (ha) 0 (v) 0 (e) 15 (assumed) 18 (that) ks cmmi10.329 @sf 17 r m (H) s cmr10.329 @sf 74 2615 p m (had) 19 (no) 18 (zeros) 19 (on) 18 (the) 19 (sub) 1 (diagonal) 20 (and) 19 (since) 20 (p) 1 (ost-m) 0 (ultiplication) 20 (b) 0 (y) 17 (a) ks cmmi10.329 @sf 18 r save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmmi8.300 @sf 1498 2622 p m (r) s cmr10.329 @sf 1536 2615 p m (can) 18 (only) 19 (increase) 20 (the) ks 74 2715 p m (mo) 1 (dulus) 18 (of) 17 (a) 17 (sub) 1 (diagonal) 18 (elemen) 0 (t) 17 (in) ks cmmi10.329 @sf 18 r m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 12 r m (\025I) s cmr10.329 @sf 4 r m (.) 24 (Th) 0 (us) 16 (w) 0 (e) 16 (m) 0 (ust) 15 (ha) 0 (v) 0 (e) ks cmmi10.329 @sf 15 r m (\013) s cmr10.329 @sf 16 r m (=) 16 (0) 17 (and) 17 (therefore) 17 (at) 16 (the) ks @eop 16 @bop0 16 @bop1 cmr10.329 @sf 1919 -77 p m (16) s cmmi10.329 @sf 74 67 p m (n) s cmsy10.329 @sf 11 r m (\000) s cmr10.329 @sf 10 r m (1,) 14 (then,) ks 490 167 p m (\() s cmmi10.329 @sf m (I) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (y) 2 (y) ks cmmi8.300 @sf 635 149 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 668 167 p m (\)) s cmmi10.329 @sf save [<80700040F80061FC003F060010030008010004008002000001000000C000006000001000000800 0004000002000801000C1F8007F8C003F04001E020> 19 20 -2 0 21] 122 @pc restore cmr10.329 @sf 36 r m (=) s cmmi10.329 @sf 13 r save [<80700040F80061FC003F060010030008010004008002000001000000C000006000001000000800 0004000002000801000C1F8007F8C003F04001E020> 19 20 -2 0 21] 122 @pc restore cmsy10.329 @sf 33 r m (\000) s cmr10.329 @sf 10 r m (\() s cmmi10.329 @sf m (y) s cmmi8.300 @sf 890 149 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 923 167 p save [<80700040F80061FC003F060010030008010004008002000001000000C000006000001000000800 0004000002000801000C1F8007F8C003F04001E020> 19 20 -2 0 21] 122 @pc restore cmr10.329 @sf 23 r m (\)) s cmmi10.329 @sf m (y) s cmr10.329 @sf 15 r m (=) s cmmi10.329 @sf 13 r m (\013) 0 (x) ks cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 11 r save [ 37 31 -1 0 38] 88 @pc restore 42 r m (v) s cmsy10.329 @sf 11 r m (\000) s cmr10.329 @sf 10 r m (\() s cmmi10.329 @sf m (\013) 0 (y) ks cmmi8.300 @sf 1351 149 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 1384 167 p m (x) s cmr10.329 @sf m (\)) s cmmi10.329 @sf m (y) s cmsy10.329 @sf 15 r m (\031) s cmmi10.329 @sf 13 r save [<80700040F80061FC003F060010030008010004008002000001000000C000006000001000000800 0004000002000801000C1F8007F8C003F04001E020> 19 20 -2 0 21] 122 @pc restore 23 r m (;) s cmr10.329 @sf 74 285 p m (sho) 0 (wing) 13 (that) ks cmmi10.329 @sf 13 r save [<80700040F80061FC003F060010030008010004008002000001000000C000006000001000000800 0004000002000801000C1F8007F8C003F04001E020> 19 20 -2 0 21] 122 @pc restore cmr10.329 @sf 37 r m (is) 14 (hardly) 15 (mo) 1 (di\014ed) 15 (b) 0 (y) 12 (the) 14 (pro) 3 (jection) 14 (and) 14 (therefore) 13 (suggesting) 14 (that) 13 (the) 14 (algorithm) ks 74 385 p m (will) 17 (not) 15 (necessarily) 16 (prev) 0 (en) 0 (t) 13 (a) 15 (second) 16 (con) 0 (v) 0 (erg) -1 (ence) 14 (to) 15 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\).) s 124 526 p m (The) 19 (algorithm) 19 (generalizes) 20 (to) 18 (the) 18 (case) 19 (when) ks cmmi10.329 @sf 19 r m (\025) s cmr10.329 @sf 18 r m (is) 20 (m) 0 (ultiple) 19 (in) 20 (the) 18 (follo) 0 (wing) 19 (w) 0 (a) -1 (y:) 25 (let) ks cmmi10.329 @sf 19 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 55 r m (b) 1 (e) 19 (a) ks 74 625 p m (righ) 0 (t) 14 (in) 0 (v) -2 (arian) 0 (t) 13 (subspace) 16 (corresp) 1 (onding) 16 (to) ks cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf m (.) 19 (Let) 15 (\() ks cmmi10.329 @sf save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore 30 r m (;) s 8 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmmi8.300 @sf 1149 632 p save [<3F0060C0C020C01080008000C000C000C0006000207010700C2007C0> 12 14 -2 0 15] 99 @pc restore cmr10.329 @sf 1164 625 p m (\)) 15 (b) 1 (e) 16 (suc) 0 (h) 14 (that) ks 693 754 p m (\() s cmmi10.329 @sf save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore 30 r m (;) s 8 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmmi8.300 @sf 788 761 p save [<3F0060C0C020C01080008000C000C000C0006000207010700C2007C0> 12 14 -2 0 15] 99 @pc restore cmr10.329 @sf 804 754 p m (\)) s cmsy8.300 @sf 822 736 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 868 754 p m (H) s cmr10.329 @sf 4 r m (\() s cmmi10.329 @sf save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore 30 r m (;) s 8 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmmi8.300 @sf 1005 761 p save [<3F0060C0C020C01080008000C000C000C0006000207010700C2007C0> 12 14 -2 0 15] 99 @pc restore cmr10.329 @sf 1021 754 p m (\)) 12 (=) ks cmex10.300 @sf 1099 682 p save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pc restore cmmi10.329 @sf 1153 727 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmmi8.300 @sf 1178 734 p save [ 16 23 -2 0 21] 21 @pc restore cmr10.329 @sf 1245 727 p m (0) s 1165 782 p m (0) s cmmi10.329 @sf 1242 782 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmex10.300 @sf 1292 682 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1333 754 p m (;) s cmr10.329 @sf 74 882 p m (where) 20 (the) 20 (righ) 0 (t) 19 (hand) 21 (side) 21 (is) 20 (again) 20 (the) 20 (Jordan) 20 (canonical) 21 (form) 20 (of) ks cmmi10.329 @sf 19 r m (H) s cmr10.329 @sf 4 r m (.) s cmmi10.329 @sf 34 r save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmmi8.300 @sf 1526 889 p save [ 16 23 -2 0 21] 21 @pc restore cmr10.329 @sf 1569 882 p m (is) 20 (the) 20 (Jordan) 20 (blo) 1 (c) 0 (k) ks 74 982 p m (corresp) 1 (onding) 18 (to) ks cmmi10.329 @sf 16 r m (\025) s cmr10.329 @sf m (;) 16 (since) ks cmmi10.329 @sf 18 r m (H) s cmr10.329 @sf 20 r m (is) 17 (assumed) 16 (to) 16 (b) 1 (e) 18 (unreduced,) 18 (there) 16 (can) 17 (b) 1 (e) 17 (only) 17 (one) 17 (suc) 0 (h) 16 (blo) 1 (c) 0 (k.) 24 (If) ks 74 1081 p m (w) 0 (e) 14 (set) ks 802 1181 p m (\() s cmmi10.329 @sf save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore 30 r m (;) s 8 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmmi8.300 @sf 898 1188 p save [<3F0060C0C020C01080008000C000C000C0006000207010700C2007C0> 12 14 -2 0 15] 99 @pc restore cmr10.329 @sf 913 1181 p m (\)) s cmsy8.300 @sf 931 1163 p m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 991 1181 p m (=) s cmex10.300 @sf 1039 1109 p save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pc restore cmmi10.329 @sf 1092 1154 p m (U) s cmmi8.300 @sf 1128 1138 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 1103 1209 p save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmex10.300 @sf 1183 1109 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1223 1181 p m (;) s cmr10.329 @sf 74 1299 p m (then) 16 (clearly) ks cmmi10.329 @sf 16 r m (U) s cmmi8.300 @sf 359 1284 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 408 1299 p m (is) 15 (a) 15 (left) 16 (in) 0 (v) -2 (arian) 0 (t) 13 (subspace) 16 (corresp) 1 (onding) 16 (to) ks cmmi10.329 @sf 14 r m (\025) s cmr10.329 @sf 15 r m (and) 15 (furthermore) ks cmmi10.329 @sf 914 1428 p m (U) s cmmi8.300 @sf 950 1410 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 984 1428 p save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmmi8.300 @sf 1011 1435 p save [<3F0060C0C020C01080008000C000C000C0006000207010700C2007C0> 12 14 -2 0 15] 99 @pc restore cmr10.329 @sf 1041 1428 p m (=) 13 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf 74 1556 p m (This) 21 (last) 19 (prop) 1 (ert) 0 (y) 19 (will) 22 (allo) 0 (w) ks cmmi10.329 @sf 19 r m (U) s cmmi8.300 @sf 713 1541 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 766 1556 p m (to) 19 (b) 1 (e) 21 (used) 21 (in) 20 (m) 0 (uc) 0 (h) 18 (the) 20 (same) 20 (w) 0 (a) -1 (y) 18 (the) 20 (left) 20 (eigen) 0 (v) 0 (ector) 18 (w) 0 (as) ks 74 1656 p m (used) 15 (earlier.) 21 (Ho) 0 (w) -1 (ev) -1 (er,) 12 (the) 15 (practical) 15 (usefulness) 16 (of) 14 (this) 15 (metho) 1 (d) 15 (is) 15 (restricted) 15 (to) 14 (the) 14 (case) 15 (when) 15 (the) ks 74 1755 p m (eigen) 0 (v) -2 (alue) ks cmmi10.329 @sf 19 r m (\025) s cmr10.329 @sf 18 r m (is) 20 (simple:) 29 (indeed,) 21 (the) 19 (problem) 20 (of) 18 (determining) 21 (the) 19 (in) 0 (v) -2 (arian) 0 (t) 16 (subspace) 20 (asso) 1 (ciated) ks 74 1855 p m (with) 16 (a) 15 (m) 0 (ultiple) 16 (eigen) 0 (v) -2 (alue) ks cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf 14 r m (is) 16 (an) 15 (extremely) 16 (di\016cult) 17 (one) 15 (and) 15 (can) 16 (b) 1 (e) 16 (prohibitiv) 0 (ely) 16 (exp) 1 (ensiv) 0 (e.) ks 124 1996 p m (This) 20 (metho) 1 (d) 19 (in) 20 (its) 19 (simplest) 20 (form) 19 (\(using) 19 (the) 19 (left) 20 (eigen) 0 (v) 0 (ector\)) 16 (adds) ks cmmi10.329 @sf 20 r m (O) s cmr10.329 @sf 1 r m (\() s cmmi10.329 @sf m (n) s cmr8.300 @sf 1573 1981 p m (2) s cmr10.329 @sf 1592 1996 p m (\)) 19 (w) 0 (ork) 17 (to) 18 (the) 20 (cost) ks 74 2096 p m (of) 17 (\014nding) 19 (one) 17 (eigenpair) 19 (distinct) 18 (from) 17 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\):) 22 (this) 18 (is) 18 (the) 17 (cost) 17 (of) 17 (computing) 18 (the) 17 (left) 18 (eigen) 0 (v) 0 (ector) ks 74 2195 p m (corresp) 1 (onding) 16 (to) ks cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf m (;) 14 (the) 15 (cost) 15 (of) 15 (a) 15 (single) 16 (pro) 3 (jection) 15 (is) ks cmmi10.329 @sf 16 r m (O) s cmr10.329 @sf 1 r m (\() s cmmi10.329 @sf m (n) s cmr10.329 @sf m (\).) s cmbx12.300 @sf 74 2356 p save [<01FE000FFFC01E07F07801F87E01FCFF00FCFF00FEFF00FEFF00FE7E00FE3C00FE0000FC0000FC 0001F80001F00007C001FF0001FE00001F800007C00003E00003F01F03F01F03F83F81F83F81F8 3F81F83F03F01E03F00F07E007FFC000FE00> 23 32 -2 0 28] 51 @pc restore 28 r m (.) s save [<01FE000FFFC01E07F07801F87E01FCFF00FCFF00FEFF00FEFF00FE7E00FE3C00FE0000FC0000FC 0001F80001F00007C001FF0001FE00001F800007C00003E00003F01F03F01F03F83F81F83F81F8 3F81F83F03F01E03F00F07E007FFC000FE00> 23 32 -2 0 28] 51 @pc restore 202 2356 p save [ 37 34 -2 0 43] 68 @pc restore 43 r m (e) s save [<7FF0FFE07FF0FFE00F801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F 000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F80 1F00FFFFFF00FFFFFF000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F 803F0007C03F0003E03F0001F83F00007FFF00000FFF00> 27 35 -1 0 31] 13 @pc restore 31 r m (ation) s 18 r save [<001800C000003800E000003C01E000007C01F000007E03F000007E03F00000FE03D80000FB07D8 0001FB079C0001F38F8C0001F18F0C0003E18F060003E0DF060007E0DE070007C0DE030007C07E 03000F807C01800F807C01800F807801801F007800C0FFE7FF07F8FFE7FF07F8> 37 22 -1 0 40] 119 @pc restore 40 r m (ith) 19 (orthogonal) 18 (trans) ks save [<7FF8007FF8000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F8000 0F80000F80000F80000F80000F80000F80000F8000FFFC00FFFC000F80000F80000F80000F8000 0F80000F80000F83C00F87E007C7E003C7E001E3E000FFC0003F80> 19 35 -1 0 17] 102 @pc restore 17 r m (ormations) s cmr10.329 @sf 74 2526 p m (W) -3 (e) 17 (presen) 0 (t) 17 (no) 0 (w) 17 (a) 18 (v) 0 (ery) 16 (stable) 19 (metho) 1 (d) 18 (for) 17 (obtaining) 19 (an) 18 (upp) 1 (er-Hessen) 0 (b) 1 (erg) 19 (matrix) ks cmmi10.329 @sf 18 r m (H) s cmsy8.300 @sf 1766 2511 p m (0) s cmr10.329 @sf 1795 2526 p m (with) 18 (the) ks 74 2626 p m (prop) 1 (ert) 0 (y) 18 (that) 18 (it) 19 (has) 19 (all) 20 (the) 19 (eigen) 0 (v) -2 (alues) 19 (of) ks cmmi10.329 @sf 18 r m (H) s cmr10.329 @sf 23 r m (except) 19 (for) ks cmmi10.329 @sf 19 r m (\025) s cmr10.329 @sf 18 r m ([) 0 (17) ks 1327 2626 p m (].) 31 (W) -3 (e) 18 (assume) 19 (for) 18 (no) 0 (w) 18 (that) 18 (the) ks 74 2726 p m (eigenpair) 17 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 13 (is) ks cmti10.329 @sf 16 r m (exact) s cmr10.329 @sf m (.) s @eop 15 @bop0 15 @bop1 cmr10.329 @sf 1919 -77 p m (15) s 74 67 p m (where) 16 (the) 15 (righ) 0 (t) 14 (hand) 15 (side) 17 (is) 15 (the) 16 (Jordan) 15 (canonical) 16 (form) 15 (of) 15 (H.) 14 (No) 0 (w) 14 (set) ks 811 212 p m (\() s cmmi10.329 @sf m (x;) s 8 r save [ 37 31 -1 0 38] 88 @pc restore cmr10.329 @sf 42 r m (\)) s cmsy8.300 @sf 936 194 p m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 994 212 p m (=) s cmex10.300 @sf 1042 140 p save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pc restore cmmi10.329 @sf 1096 185 p m (y) s cmmi8.300 @sf 1120 170 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 1106 241 p save [<3FFF000001E0000000F0000000F0000000F0000000F00000007000000078000000780000007800 0000380000003C0000003C0000003E0000007D0000007D00000078800000F8400000F0200000F0 100001F0180001E0080003E0040003E0020003C0010007C0018007C00080078000400F8000600F 800078FFF801FF> 32 31 -1 0 26] 89 @pc restore cmex10.300 @sf 1174 140 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1214 212 p m (:) s cmr10.329 @sf 74 358 p m (Then) 16 (it) 15 (is) 16 (clear) 16 (that) ks cmmi10.329 @sf 14 r m (y) s cmmi8.300 @sf 515 343 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 564 358 p m (is) 16 (a) 14 (left) 16 (eigen) 0 (v) 0 (ector) 13 (of) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 19 r m (corresp) 1 (onding) 16 (to) ks cmmi10.329 @sf 14 r m (\025) s cmr10.329 @sf 15 r m (and) 15 (furthermore) 15 (that) ks cmmi10.329 @sf 922 503 p m (y) s cmmi8.300 @sf 946 485 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 979 503 p save [ 37 31 -1 0 38] 88 @pc restore cmr10.329 @sf 54 r m (=) 13 (0) ks cmmi10.329 @sf m (:) s cmr10.329 @sf 74 648 p m (This) 21 (prop) 1 (ert) 0 (y) 18 (can) 20 (b) 1 (e) 20 (used) 21 (to) 19 (mo) 1 (dify) 20 (Newton's) 19 (metho) 1 (d) 20 (to) 19 (a) 0 (v) 0 (o) -1 (id) 19 (con) 0 (v) 0 (erg) -1 (ing) 19 (to) 19 (the) 20 (eigenpair) ks 74 748 p m (\() s cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 17 (a) 19 (second) 19 (time.) 32 (Indeed,) 21 (giv) 0 (en) ks cmmi10.329 @sf 19 r m (\025) s cmr10.329 @sf 18 r m (w) 0 (e) 18 (can) 19 (compute) 19 (the) 19 (left) 20 (eigen) 0 (v) 0 (ector) ks cmmi10.329 @sf 17 r m (y) s cmmi8.300 @sf 1635 733 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 1687 748 p m (corresp) 1 (onding) ks 74 848 p m (to) 19 (it) 20 (and) 19 (use) 20 (it) 20 (to) 18 (con\014ne) 21 (the) 19 (curren) 0 (t) 18 (eigen) 0 (v) 0 (ector) 18 (to) 19 (the) 19 (space) ks cmmi10.329 @sf 20 r save [ 37 31 -1 0 38] 88 @pc restore cmr10.329 @sf 42 r m (.) 31 (Therefore) 20 (w) 0 (e) 18 (can) 19 (exp) 1 (ect) ks 74 947 p m (to) 16 (con) 0 (v) -1 (erge) 15 (to) 15 (an) 17 (eigen) 0 (v) 0 (ector) 14 (linearly) 18 (indep) 1 (end) 1 (en) 0 (t) 17 (of) ks cmmi10.329 @sf 16 r m (x) s cmr10.329 @sf 16 r m (and) 16 (hence) 18 (corresp) 1 (onding) 17 (to) 16 (a) 16 (di\013eren) 0 (t) ks 74 1047 p m (eigenpair) 21 (\(since) 20 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 17 (w) 0 (as) 18 (assumed) 19 (to) 19 (b) 1 (e) 20 (simple\).) 33 (When) 19 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 18 (has) 19 (b) 1 (een) 20 (obtained) 20 (once,) 20 (our) ks 74 1146 p m (algorithm) 15 (for) 15 (a) 0 (v) -1 (oiding) 14 (it) 16 (then) 15 (consists) 16 (of) 15 (the) 15 (follo) 0 (wing) 15 (ma) 3 (jor) 14 (steps:) ks 176 1325 p m (Compute) 15 (the) 16 (left) 15 (eigen) 0 (v) 0 (ector) ks cmmi10.329 @sf 13 r m (y) s cmmi8.300 @sf 791 1310 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 840 1325 p m (corresp) 1 (onding) 16 (to) ks cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf m (,) 14 (with) ks cmsy10.329 @sf 16 r m (k) s cmmi10.329 @sf m (y) s cmsy10.329 @sf 2 r m (k) s cmr8.300 @sf 1416 1332 p m (2) s cmr10.329 @sf 1447 1325 p m (=) 13 (1;) ks 176 1425 p m (Giv) 0 (en) 15 (the) 15 (curren) 0 (t) 14 (eigenpair) 17 (\() ks cmmi10.329 @sf save [<80700040F80061FC003F060010030008010004008002000001000000C000006000001000000800 0004000002000801000C1F8007F8C003F04001E020> 19 20 -2 0 21] 122 @pc restore 23 r m (;) 8 (\026) ks cmr10.329 @sf m (\)) 14 (compute) 16 (the) 15 (Newton) 15 (correction) 15 (from) 15 (algorithm) 15 (2.1;) ks 176 1524 p m (Let) s cmmi10.329 @sf 16 r save [<80700040F80061FC003F060010030008010004008002000001000000C000006000001000000800 0004000002000801000C1F8007F8C003F04001E020> 19 20 -2 0 21] 122 @pc restore cmsy8.300 @sf 281 1509 p m (0) s cmr10.329 @sf 308 1524 p m (b) 1 (e) 16 (the) 15 (appro) 0 (ximate) 14 (eigen) 0 (v) 0 (ector) 13 (obtained) 16 (after) 14 (adding) 16 (the) 16 (Newton) 14 (correction) ks 176 1624 p m (to) s cmmi10.329 @sf 15 r save [<80700040F80061FC003F060010030008010004008002000001000000C000006000001000000800 0004000002000801000C1F8007F8C003F04001E020> 19 20 -2 0 21] 122 @pc restore cmr10.329 @sf 23 r m (,) 15 (c) 0 (ho) 1 (ose) 14 (the) 15 (next) 16 (eigen) 0 (v) 0 (ector) ks cmmi10.329 @sf 13 r save [<80700040F80061FC003F060010030008010004008002000001000000C000006000001000000800 0004000002000801000C1F8007F8C003F04001E020> 19 20 -2 0 21] 122 @pc restore cmsy8.300 @sf 867 1609 p m (00) s cmr10.329 @sf 903 1624 p m (as:) s cmmi10.329 @sf 845 1802 p save [<80700040F80061FC003F060010030008010004008002000001000000C000006000001000000800 0004000002000801000C1F8007F8C003F04001E020> 19 20 -2 0 21] 122 @pc restore cmsy8.300 @sf 868 1784 p m (00) s cmr10.329 @sf 902 1802 p m (=) 13 (\() ks cmmi10.329 @sf m (I) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (y) 2 (y) ks cmmi8.300 @sf 1095 1784 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 1128 1802 p m (\)) s cmmi10.329 @sf save [<80700040F80061FC003F060010030008010004008002000001000000C000006000001000000800 0004000002000801000C1F8007F8C003F04001E020> 19 20 -2 0 21] 122 @pc restore cmsy8.300 @sf 1169 1784 p m (0) s cmr10.329 @sf 1181 1802 p m (;) s 74 1929 p m (In) 17 (the) 16 (last) 16 (step) 17 (w) 0 (e) 15 (are) 16 (just) 16 (pro) 3 (jecting) ks cmmi10.329 @sf 16 r save [<80700040F80061FC003F060010030008010004008002000001000000C000006000001000000800 0004000002000801000C1F8007F8C003F04001E020> 19 20 -2 0 21] 122 @pc restore cmsy8.300 @sf 872 1914 p m (0) s cmr10.329 @sf 900 1929 p m (on) 0 (to) 14 (the) 16 (space) ks cmmi10.329 @sf 17 r save [ 37 31 -1 0 38] 88 @pc restore cmr10.329 @sf 42 r m (.) 22 (W) -3 (e) 15 (note) 16 (that) 16 (when) 16 (this) 17 (algorithm) ks 74 2029 p m (is) 15 (applied,) 16 (it) 15 (could) 16 (happ) 1 (en) 15 (\(as) 14 (with) 15 (all) 16 (the) 14 (de\015ation) 16 (metho) 1 (ds) 14 (w) 0 (e) 13 (are) 15 (describing\)) 16 (that) 14 (w) 0 (e) 13 (obtain) ks 74 2128 p m (another) 12 (eigenpair) 14 (of) ks cmmi10.329 @sf 13 r m (H) s cmr10.329 @sf 4 r m (,) 12 (\() ks cmmi10.329 @sf m (x) s cmsy8.300 @sf 591 2113 p m (0) s cmmi10.329 @sf 602 2128 p m (;) 8 (\025) ks cmsy8.300 @sf 650 2113 p m (0) s cmr10.329 @sf 660 2128 p m (\),) 13 (that) 12 (w) 0 (as) 10 (already) 13 (computed.) 20 (There) 13 (will) 14 (b) 1 (e) 13 (a) 12 (need) 14 (then) 13 (to) 12 (do) 12 (t) 0 (w) -1 (o) ks 74 2228 p m (successiv) 0 (e) 16 (pro) 3 (jections) 14 (when) 16 (the) 15 (pro) 1 (cess) 16 (is) 16 (restarted,) 14 (in) 16 (order) 15 (to) 14 (a) 0 (v) -1 (oid) 14 (b) 1 (oth) 15 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 14 (and) 15 (\() ks cmmi10.329 @sf m (x) s cmsy8.300 @sf 1835 2213 p m (0) s cmmi10.329 @sf 1846 2228 p m (;) 8 (\025) ks cmsy8.300 @sf 1894 2213 p m (0) s cmr10.329 @sf 1905 2228 p m (\).) s 124 2369 p m (It) 14 (is) 14 (ob) 0 (vious) 13 (wh) 0 (y) 12 (w) 0 (e) 13 (need) 14 (the) 14 (kno) 0 (wn) 12 (eigenpair) 15 (to) 13 (b) 1 (e) 15 (simple) 15 (for) 13 (the) 13 (algorithm) 14 (just) 13 (outlined) 16 (to) ks 74 2469 p m (w) 0 (ork.) 20 (If) ks cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf 16 r m (is) 16 (m) 0 (ultiple) 16 (then) 16 (left) 16 (eigen) 0 (v) 0 (ectors) 14 (are) 15 (no) 16 (longer) 16 (necessarily) 17 (orthogonal) 15 (to) ks cmmi10.329 @sf 15 r save [ 37 31 -1 0 38] 88 @pc restore cmr10.329 @sf 42 r m (.) 21 (In) 16 (fact,) ks 74 2568 p m (the) 15 (algorithm) 15 (will) 17 (b) 1 (e) 16 (adv) 0 (ersely) 14 (a\013ected) 15 (if) 16 (the) 15 (eigen) 0 (v) -2 (alue) ks cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf 15 r m (is) 15 (ill-c) 1 (onditi) 1 (oned,) 17 (i.e.,) 15 (if) ks cmmi10.329 @sf 15 r m (y) s cmmi8.300 @sf 1759 2553 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 1793 2568 p m (x) s cmr10.329 @sf 15 r m (is) 15 (v) 0 (ery) ks 74 2668 p m (small.) 20 (Indeed,) 16 (in) 14 (this) 15 (case,) 13 (if) 15 (the) 14 (curren) 0 (t) 12 (eigen) 0 (v) 0 (ector) ks cmmi10.329 @sf 12 r save [<80700040F80061FC003F060010030008010004008002000001000000C000006000001000000800 0004000002000801000C1F8007F8C003F04001E020> 19 20 -2 0 21] 122 @pc restore cmr10.329 @sf 36 r m (=) s cmmi10.329 @sf 13 r m (\013) 0 (x) ks cmr10.329 @sf 7 r m (+) s cmmi10.329 @sf 7 r save [ 37 31 -1 0 38] 88 @pc restore 42 r m (v) s cmr10.329 @sf 2 r m (,) 14 (where) ks cmmi10.329 @sf 14 r m (v) s cmr10.329 @sf 16 r m (is) 14 (a) 14 (v) 0 (ector) 12 (of) 13 (length) ks @eop 14 @bop0 14 @bop1 cmr10.329 @sf 1919 -77 p m (14) s 74 67 p m (to) 13 (upp) 1 (er-Hessen) 0 (b) 1 (erg) 15 (form) 13 (increases) 15 (when) ks cmmi10.329 @sf 14 r m (s) s cmr10.329 @sf 14 r m (approac) 0 (hes) 13 (1,) 14 (it) 14 (is) 14 (more) 14 (adv) -2 (an) 0 (t) -1 (ageous) 12 (to) 13 (c) 0 (ho) 1 (ose) 13 (the) ks 74 167 p m (largest) s cmmi10.329 @sf 15 r m (s) s cmr10.329 @sf 16 r m (for) 14 (whic) 0 (h) 15 (the) 16 (ratios) ks cmmi10.329 @sf 15 r m (x) s cmmi8.300 @sf 689 174 p m (i) s cmmi10.329 @sf 703 167 p m (=x) s cmmi8.300 @sf 752 174 p m (s) s cmr10.329 @sf 785 167 p m (are) 15 (mo) 1 (derate.) 20 (W) -3 (e) 14 (wish) 16 (therefore) 15 (to) 15 (de\014ne) 16 (a) 15 (threshold) ks cmmi10.329 @sf 16 r save [<0F00188038403820382038201C101C001C001C000E000E000E000E0007000700070007000380FF F80380038001C001C001C001C000E000C0> 13 28 -1 0 16] 116 @pc restore cmr10.329 @sf 32 r m (for) s 74 266 p m (the) 15 (size) 17 (of) 14 (these) 16 (ratios) 14 (on) 15 (the) 16 (basis) 15 (of) 15 (whic) 0 (h) ks cmmi10.329 @sf 15 r m (s) s cmr10.329 @sf 16 r m (will) 17 (b) 1 (e) 15 (determined.) ks 124 408 p m (Let) s cmex10.300 @sf 220 396 p m (e) s cmmi10.329 @sf 208 409 p m (H) s cmr10.329 @sf 268 408 p m (b) 1 (e) 19 (the) 18 (computed) 18 (form) 18 (of) 17 (the) 19 (matrix) 17 (in) 19 (\(9\).) 28 (In) 19 ([) 0 (17) ks 1297 408 p m (],) 18 (c) 0 (hap.) 27 (9,) 19 (Wilkinson) 19 (established) ks 74 507 p m (that) 15 (if) ks cmsy10.329 @sf 15 r m (k) s cmmi10.329 @sf m (x) s cmsy10.329 @sf m (k) s cmsy8.300 @sf 286 514 p m (1) s cmsy10.329 @sf 336 507 p m (\024) s cmr10.329 @sf 13 r m (1,) 14 (then) 16 (the) 15 (eigen) 0 (v) -2 (alues) 15 (of) ks cmex10.300 @sf 915 495 p m (e) s cmmi10.329 @sf 903 508 p m (H) s cmr10.329 @sf 960 507 p m (are) 14 (the) 16 (exact) 15 (eigen) 0 (v) -2 (alues) 15 (of) 14 (a) 15 (matrix) ks cmex10.300 @sf 1718 495 p m (e) s cmmi10.329 @sf 1706 508 p m (H) s cmsy8.300 @sf 1748 493 p m (0) s cmr10.329 @sf 1774 507 p m (satisfying) s cmsy10.329 @sf 706 629 p m (k) s cmmi10.329 @sf m (H) s cmsy10.329 @sf 14 r m (\000) s cmex10.300 @sf 838 617 p m (e) s cmmi10.329 @sf 826 630 p m (H) s cmsy8.300 @sf 868 612 p m (0) s cmsy10.329 @sf 879 629 p m (k) s cmsy8.300 @sf 902 636 p m (1) s cmsy10.329 @sf 952 629 p m (\024) 13 (k) ks cmmi10.329 @sf m (r) s cmsy10.329 @sf 1 r m (k) s cmsy8.300 @sf 1068 636 p m (1) s cmr10.329 @sf 1115 629 p m (+) 10 (\() ks cmmi10.329 @sf m (n) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 11 r m (1\)) s cmmi10.329 @sf m (\017;) s cmr10.329 @sf 74 752 p m (where) s cmmi10.329 @sf 20 r m (r) s cmr10.329 @sf 20 r m (is) 19 (the) 20 (residual) ks cmmi10.329 @sf 20 r m (\025x) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 13 r m (H) 4 (x) ks cmr10.329 @sf 19 r m (and) s cmmi10.329 @sf 19 r m (\017) s cmr10.329 @sf 20 r m (is) 20 (the) 19 (mac) 0 (hine) 19 (epsilon.) 34 (With) 19 (no) 19 (assumptions) 20 (on) 19 (the) ks 74 851 p m (in\014nit) 0 (y) 16 (norm) 15 (of) ks cmmi10.329 @sf 14 r m (x) s cmr10.329 @sf m (,) 15 (this) 16 (inequalit) 0 (y) 16 (b) 1 (ecomes) ks cmsy10.329 @sf 610 973 p m (k) s cmmi10.329 @sf m (H) s cmsy10.329 @sf 14 r m (\000) s cmex10.300 @sf 742 961 p m (e) s cmmi10.329 @sf 730 974 p m (H) s cmsy8.300 @sf 772 956 p m (0) s cmsy10.329 @sf 783 973 p m (k) s cmsy8.300 @sf 806 980 p m (1) s cmsy10.329 @sf 856 973 p m (\024) 13 (k) ks cmmi10.329 @sf m (r) s cmsy10.329 @sf 1 r m (k) s cmsy8.300 @sf 972 980 p m (1) s cmr10.329 @sf 1019 973 p m (+) 10 (\() ks cmmi10.329 @sf m (n) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 11 r m (1\)) s cmsy10.329 @sf m (k) s cmmi10.329 @sf m (x) s cmsy10.329 @sf m (k) s cmsy8.300 @sf 1278 980 p m (1) s cmmi10.329 @sf 1314 973 p m (\017:) s cmr10.329 @sf 1883 973 p m (\(10\)) s 74 1096 p m (Since) 21 (in) 20 (our) 19 (algorithm,) 20 (our) 19 (computed) 20 (eigenpairs) 21 (ha) 0 (v) -1 (e) 18 (residuals) 21 (on) 19 (the) 19 (order) 19 (of) ks cmmi10.329 @sf 19 r m (n) s cmsy10.329 @sf m (k) s cmmi10.329 @sf m (H) s cmsy10.329 @sf 4 r m (k) s cmsy8.300 @sf 1824 1103 p m (1) s cmmi10.329 @sf 1861 1096 p m (\017) s cmr10.329 @sf m (,) 20 (w) 0 (e) ks 74 1195 p m (prop) 1 (ose) ks cmsy10.329 @sf 15 r m (k) s cmmi10.329 @sf m (H) s cmsy10.329 @sf 4 r m (k) s cmsy8.300 @sf 330 1202 p m (1) s cmr10.329 @sf 382 1195 p m (as) 15 (a) 15 (v) -2 (alue) 15 (for) ks cmmi10.329 @sf 15 r save [<0F00188038403820382038201C101C001C001C000E000E000E000E0007000700070007000380FF F80380038001C001C001C001C000E000C0> 13 28 -1 0 16] 116 @pc restore cmr10.329 @sf 16 r m (.) s 124 1336 p m (In) 13 (addition) 13 (to) 11 (destro) 0 (ying) 11 (the) 12 (structure) 12 (of) 11 (the) 12 (matrix,) 12 (this) 13 (last) 12 (metho) 1 (d) 12 (of) 12 (de\015ation) 12 (su\013ers) 12 (from) ks 74 1436 p m (the) 15 (fact) 14 (that) 14 (in) 15 (the) 15 (case) 15 (when) 15 (the) 15 (eigen) 0 (v) -2 (alue) 14 (to) 14 (b) 1 (e) 16 (de\015ated) 15 (is) 15 (non-real,) 15 (the) 15 (resulting) 16 (matrix) ks cmmi10.329 @sf 14 r m (H) s cmsy8.300 @sf 1953 1421 p m (0) s cmr10.329 @sf 74 1536 p m (is) 17 (complex) 18 (and) 17 (therefore) 16 (will) 19 (considerably) 18 (increase) 18 (the) 17 (cost) 16 (of) 16 (\014nding) 18 (subsequen) 0 (t) 17 (eigenpairs) 18 (if) ks 74 1635 p m (a) 15 (Newton) 15 (pro) 1 (cess) 15 (is) 16 (restarted) 15 (from) 14 (a) 15 (real) 15 (initial) 18 (guess.) ks cmbx12.300 @sf 74 1795 p save [<01FE000FFFC01E07F07801F87E01FCFF00FCFF00FEFF00FEFF00FE7E00FE3C00FE0000FC0000FC 0001F80001F00007C001FF0001FE00001F800007C00003E00003F01F03F01F03F83F81F83F81F8 3F81F83F03F01E03F00F07E007FFC000FE00> 23 32 -2 0 28] 51 @pc restore 28 r m (.2) s 202 1795 p save [ 37 34 -2 0 43] 68 @pc restore 43 r m (e) s save [<7FF0FFE07FF0FFE00F801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F 000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F80 1F00FFFFFF00FFFFFF000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F 803F0007C03F0003E03F0001F83F00007FFF00000FFF00> 27 35 -1 0 31] 13 @pc restore 31 r m (ation) s 18 r save [<001800C000003800E000003C01E000007C01F000007E03F000007E03F00000FE03D80000FB07D8 0001FB079C0001F38F8C0001F18F0C0003E18F060003E0DF060007E0DE070007C0DE030007C07E 03000F807C01800F807C01800F807801801F007800C0FFE7FF07F8FFE7FF07F8> 37 22 -1 0 40] 119 @pc restore 40 r m (ith) 19 (help) ks 18 r save [<7FF8007FF8000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F8000 0F80000F80000F80000F80000F80000F80000F8000FFFC00FFFC000F80000F80000F80000F8000 0F80000F80000F83C00F87E007C7E003C7E001E3E000FFC0003F80> 19 35 -1 0 17] 102 @pc restore 17 r m (rom) 17 (the) 18 (le) ks save [<7FF8007FF8000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F8000 0F80000F80000F80000F80000F80000F80000F8000FFFC00FFFC000F80000F80000F80000F8000 0F80000F80000F83C00F87E007C7E003C7E001E3E000FFC0003F80> 19 35 -1 0 17] 102 @pc restore 17 r m (t) 18 (eigen) ks -1 r save [<000E0000000E0000001F0000001F0000003F8000003F8000007FC000007CC000007CC00000F860 0000F8600001F0300001F0300003E0180003E0180007E01C0007C00C000FC00E000F8006000F80 0600FFE01FE0FFE01FE0> 27 22 -1 0 30] 118 @pc restore 28 r m (ector) s cmr10.329 @sf 74 1965 p m (The) 14 (metho) 1 (d) 13 (w) 0 (e) 13 (in) 0 (tro) 1 (duce) 13 (no) 0 (w) 12 (is) 14 (di\013eren) 0 (t) 12 (in) 15 (spirit) 14 (from) 13 (the) 13 (ones) 14 (in) 14 (the) 13 (previous) 15 (section,) 14 (in) 14 (that) ks 74 2065 p m (no) 15 (attempt) 15 (is) 15 (made) 15 (at) 15 (mo) 1 (difying) 16 (the) 16 (matrix.) ks 124 2206 p m (Assume) 15 (that) 15 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 13 (is) 16 (an) 15 (exact) 15 (eigenpair) 16 (of) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 19 r m (and) 15 (that) ks cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf 14 r m (is) 16 (simple:) ks cmmi10.329 @sf 923 2328 p m (H) 4 (x) ks cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (\025x:) s cmr10.329 @sf 74 2451 p m (No) 15 (assumption) 16 (is) 15 (made) 15 (ab) 1 (out) 15 (the) 16 (remaining) 16 (eigen) 0 (v) -2 (alues) 15 (of) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 4 r m (.) s 124 2592 p m (Let) 15 (\() ks cmmi10.329 @sf m (x;) s 8 r save [ 37 31 -1 0 38] 88 @pc restore cmr10.329 @sf 42 r m (\)) 13 (b) 1 (e) 16 (suc) 0 (h) 15 (that) ks 719 2691 p m (\() s cmmi10.329 @sf m (x;) s 8 r save [ 37 31 -1 0 38] 88 @pc restore cmr10.329 @sf 42 r m (\)) s cmsy8.300 @sf 844 2673 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 889 2691 p m (H) s cmr10.329 @sf 4 r m (\() s cmmi10.329 @sf m (x;) s 8 r save [ 37 31 -1 0 38] 88 @pc restore cmr10.329 @sf 42 r m (\)) 10 (=) ks cmex10.300 @sf 1114 2619 p save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pc restore cmmi10.329 @sf 1168 2664 p m (\025) s cmr10.329 @sf 1239 2664 p m (0) s 1170 2719 p m (0) s cmmi10.329 @sf 1236 2719 p save [<1F000021C00040E000807000F07800F83C00F83C00781E00301E00001E00001E00000F00000F00 000F00000F000007800007800007800007800003C00003C00003C00003C00001E00001E00001E0 0001E00000F00000F00000F00000F8001FFF> 24 32 -3 1 25] 74 @pc restore cmex10.300 @sf 1286 2619 p save [ 21 124 -1 122 33] 33 @pc restore @eop 13 @bop0 13 @bop1 cmr10.329 @sf 1919 -77 p m (13) s 74 67 p m (let) s cmmi10.329 @sf 15 r save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 168 74 p m (ns) s cmr10.329 @sf 223 67 p m (b) 1 (e) 15 (the) 15 (matrix) 14 (obtained) 15 (from) 14 (the) 15 (iden) 0 (tit) 0 (y) 13 (matrix) 14 (b) 0 (y) 14 (p) 1 (erm) 0 (uting) 14 (the) ks cmmi10.329 @sf 15 r m (n) s cmmi8.300 @sf 1581 52 p save [<1E003100310030803080300018001800180018000C000C000C00FFC00600060006000600030003 00> 10 20 -1 0 13] 116 @pc restore 13 r save [ 16 23 -2 0 20] 104 @pc restore cmr10.329 @sf 1631 67 p m (and) s cmmi10.329 @sf 15 r m (s) s cmmi8.300 @sf 1740 52 p save [<1E003100310030803080300018001800180018000C000C000C00FFC00600060006000600030003 00> 10 20 -1 0 13] 116 @pc restore 13 r save [ 16 23 -2 0 20] 104 @pc restore cmr10.329 @sf 1790 67 p m (columns.) s 74 167 p m (Then) 16 (\() ks cmmi10.329 @sf save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 240 174 p m (ns) s cmmi10.329 @sf 280 167 p m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 13 (is) 16 (an) 15 (eigenpair) 16 (of) 15 (the) 15 (matrix) ks cmmi10.329 @sf 15 r save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 995 174 p m (ns) s cmmi10.329 @sf 1035 167 p m (H) s 4 r save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 1106 174 p m (ns) s cmr10.329 @sf 1146 167 p m (,) 15 (since) ks 749 312 p m (\() s cmmi10.329 @sf save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 796 319 p m (ns) s cmmi10.329 @sf 836 312 p m (H) s 4 r save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 907 319 p m (ns) s cmr10.329 @sf 946 312 p m (\)\() s cmmi10.329 @sf save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 1011 319 p m (ns) s cmmi10.329 @sf 1051 312 p m (x) s cmr10.329 @sf m (\)) 12 (=) ks cmmi10.329 @sf 13 r m (\025) s save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 1211 319 p m (ns) s cmmi10.329 @sf 1250 312 p m (x:) s cmr10.329 @sf 74 457 p m (No) 0 (w) 18 (scale) 19 (the) 20 (v) 0 (ector) ks cmmi10.329 @sf 17 r save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 546 464 p m (ns) s cmmi10.329 @sf 586 457 p m (x) s cmr10.329 @sf 19 r m (so) 19 (that) 19 (the) 19 (last) 19 (comp) 1 (onen) 0 (t) 18 (is) 20 (1) 19 (and) 19 (call) 20 (that) 19 (v) 0 (ector) 20 (~) ks cmmi10.329 @sf 1716 457 p m (x) s cmr10.329 @sf 1742 457 p m (.) 32 (Then,) 20 (as) ks 74 557 p m (ab) 1 (o) 0 (v) 0 (e,) 13 (the) 15 (elemen) 0 (tary) 14 (transformation) ks cmmi10.329 @sf 692 733 p m (M) s cmr10.329 @sf 18 r m (=) s cmex10.300 @sf 802 624 p m (0) s 802 697 p m (B) s 802 722 p m (B) s 802 749 p m (@) s cmr10.329 @sf 863 655 p m (1) s 1206 655 p m (~) s cmmi10.329 @sf 1204 655 p m (x) s cmr8.300 @sf 1230 662 p m (1) s cmr10.329 @sf 1018 694 p m (.) s 1035 707 p m (.) s 1053 720 p m (.) s 1220 691 p m (.) s 1220 708 p m (.) s 1220 725 p m (.) s 1193 767 p m (~) s cmmi10.329 @sf 1190 767 p m (x) s cmmi8.300 @sf 1216 774 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmr10.432 @sf 935 811 p m (0) s cmr10.329 @sf 1215 811 p m (1) s cmex10.300 @sf 1310 624 p m (1) s 1310 697 p m (C) s 1310 722 p m (C) s 1310 749 p m (A) s cmr10.329 @sf 74 909 p m (can) 12 (b) 1 (e) 12 (used) 12 (to) 11 (de\015ate) 12 (the) 11 (matrix) ks cmmi10.329 @sf 12 r save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 755 916 p m (ns) s cmmi10.329 @sf 795 909 p m (H) s 4 r save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 866 916 p m (ns) s cmr10.329 @sf 905 909 p m (.) 19 (The) 11 (fact) 11 (that) 11 (here) ks cmmi10.329 @sf 12 r save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 1331 916 p m (ns) s cmmi10.329 @sf 1371 909 p m (H) s 4 r save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 1442 916 p m (ns) s cmr10.329 @sf 1493 909 p m (is) 12 (not) 11 (upp) 1 (er-Hessen) 0 (b) 1 (erg) ks 74 1008 p m (is) 17 (of) 16 (no) 16 (consequence.) 25 (In) 17 (fact,) 16 (w) 0 (e) 15 (can) 16 (mak) 0 (e) 15 (the) 17 (follo) 0 (wing) 16 (general) 16 (statemen) 0 (t:) 21 (Giv) 0 (en) 15 (an) 0 (y) 15 (matrix) ks cmmi10.329 @sf 74 1108 p save [ 30 32 -2 0 34] 65 @pc restore cmr10.329 @sf 49 r m (of) 15 (order) ks cmmi10.329 @sf 15 r m (n) s cmr10.329 @sf m (,) 15 (and) 16 (an) 0 (y) 13 (eigenpair) 17 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 13 (of) ks cmmi10.329 @sf 15 r save [ 30 32 -2 0 34] 65 @pc restore cmr10.329 @sf 34 r m (,) 15 (then) 15 (a) 15 (matrix) ks cmmi10.329 @sf 15 r save [<0000F0000001F8000003FC000003FE000003860000038300000101000001018001FD0080078380 800E81E0001C81700038813C0038811E0070600F00701C070070000380F00003C0F00001C0F000 01E0F00000E0F00000F0F00000F0780000787800007878000078780000783C0000783C0000381E 0000381E0000380F00003807000038078000780380007001C0007000E000E0003000E0001C01C0 000707000001FC00> 29 41 -2 9 36] 81 @pc restore cmr10.329 @sf 51 r m (satisfying) s cmmi10.329 @sf 740 1253 p save [<0000F0000001F8000003FC000003FE000003860000038300000101000001018001FD0080078380 800E81E0001C81700038813C0038811E0070600F00701C070070000380F00003C0F00001C0F000 01E0F00000E0F00000F0F00000F0780000787800007878000078780000783C0000783C0000381E 0000381E0000380F00003807000038078000780380007001C0007000E000E0003000E0001C01C0 000707000001FC00> 29 41 -2 9 36] 81 @pc restore cmsy8.300 @sf 776 1235 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 823 1253 p m (x) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (e) s cmr8.300 @sf 930 1260 p m (1) s cmr10.329 @sf 991 1253 p m (or) s cmmi10.329 @sf 1072 1253 p save [<0000F0000001F8000003FC000003FE000003860000038300000101000001018001FD0080078380 800E81E0001C81700038813C0038811E0070600F00701C070070000380F00003C0F00001C0F000 01E0F00000E0F00000F0F00000F0780000787800007878000078780000783C0000783C0000381E 0000381E0000380F00003807000038078000780380007001C0007000E000E0003000E0001C01C0 000707000001FC00> 29 41 -2 9 36] 81 @pc restore cmsy8.300 @sf 1108 1235 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1155 1253 p m (x) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (e) s cmmi8.300 @sf 1262 1260 p m (n) s cmmi10.329 @sf 1286 1253 p m (;) s cmr10.329 @sf 74 1399 p m (can) 15 (b) 1 (e) 16 (used) 16 (to) 15 (de\015ate) ks cmmi10.329 @sf 15 r save [ 30 32 -2 0 34] 65 @pc restore cmr10.329 @sf 34 r m (,) 15 (in) 16 (the) 15 (sense) 16 (that) ks cmmi10.329 @sf 570 1544 p save [<0000F0000001F8000003FC000003FE000003860000038300000101000001018001FD0080078380 800E81E0001C81700038813C0038811E0070600F00701C070070000380F00003C0F00001C0F000 01E0F00000E0F00000F0F00000F0780000787800007878000078780000783C0000783C0000381E 0000381E0000380F00003807000038078000780380007001C0007000E000E0003000E0001C01C0 000707000001FC00> 29 41 -2 9 36] 81 @pc restore cmsy8.300 @sf 606 1526 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 653 1544 p save [ 30 32 -2 0 34] 65 @pc restore 34 r save [<0000F0000001F8000003FC000003FE000003860000038300000101000001018001FD0080078380 800E81E0001C81700038813C0038811E0070600F00701C070070000380F00003C0F00001C0F000 01E0F00000E0F00000F0F00000F0780000787800007878000078780000783C0000783C0000381E 0000381E0000380F00003807000038078000780380007001C0007000E000E0003000E0001C01C0 000707000001FC00> 29 41 -2 9 36] 81 @pc restore cmr10.329 @sf 48 r m (=) 13 ([) ks cmmi10.329 @sf m (\025e) s cmr8.300 @sf 844 1551 p m (1) s cmmi10.329 @sf 863 1544 p m (;) s 8 r save [ 31 31 -2 0 34] 66 @pc restore cmr8.300 @sf 918 1551 p m (1) s cmr10.329 @sf 938 1544 p m (]) 40 (or) ks cmmi10.329 @sf 1072 1544 p save [<0000F0000001F8000003FC000003FE000003860000038300000101000001018001FD0080078380 800E81E0001C81700038813C0038811E0070600F00701C070070000380F00003C0F00001C0F000 01E0F00000E0F00000F0F00000F0780000787800007878000078780000783C0000783C0000381E 0000381E0000380F00003807000038078000780380007001C0007000E000E0003000E0001C01C0 000707000001FC00> 29 41 -2 9 36] 81 @pc restore cmsy8.300 @sf 1108 1526 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1155 1544 p save [ 30 32 -2 0 34] 65 @pc restore 34 r save [<0000F0000001F8000003FC000003FE000003860000038300000101000001018001FD0080078380 800E81E0001C81700038813C0038811E0070600F00701C070070000380F00003C0F00001C0F000 01E0F00000E0F00000F0F00000F0780000787800007878000078780000783C0000783C0000381E 0000381E0000380F00003807000038078000780380007001C0007000E000E0003000E0001C01C0 000707000001FC00> 29 41 -2 9 36] 81 @pc restore cmr10.329 @sf 48 r m (=) 13 ([) ks cmmi10.329 @sf save [ 31 31 -2 0 34] 66 @pc restore cmr8.300 @sf 1332 1551 p m (2) s cmmi10.329 @sf 1352 1544 p m (;) 8 (\025e) ks cmmi8.300 @sf 1421 1551 p m (n) s cmr10.329 @sf 1444 1544 p m (]) s cmmi10.329 @sf m (;) s cmr10.329 @sf 74 1689 p m (resp) 1 (ectiv) 0 (ely;) 16 (where) ks cmmi10.329 @sf 15 r save [ 31 31 -2 0 34] 66 @pc restore cmr8.300 @sf 500 1696 p m (1) s cmr10.329 @sf 535 1689 p m (and) s cmmi10.329 @sf 16 r save [ 31 31 -2 0 34] 66 @pc restore cmr8.300 @sf 658 1696 p m (2) s cmr10.329 @sf 693 1689 p m (are) s cmmi10.329 @sf 15 r m (n) s cmsy10.329 @sf 10 r m (\002) s cmr10.329 @sf 11 r m (\() s cmmi10.329 @sf m (n) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 10 r m (1\)) 15 (matrices.) ks 124 1830 p m (Ha) 0 (ving) 14 (th) 0 (us) 14 (de\015ated) 16 (the) 15 (matrix) ks cmmi10.329 @sf 15 r save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 806 1837 p m (ns) s cmmi10.329 @sf 846 1830 p m (H) s 4 r save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 917 1837 p m (ns) s cmr10.329 @sf 957 1830 p m (,) 14 (the) 16 (leading) 16 (principal) 18 (submatrix) 15 (of) 15 (order) ks cmmi10.329 @sf 15 r m (n) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 11 r m (1) 14 (of) ks cmmi10.329 @sf 810 1976 p m (M) s cmsy8.300 @sf 859 1958 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 906 1976 p save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 935 1983 p m (ns) s cmmi10.329 @sf 975 1976 p m (H) s 4 r save [ 31 31 -2 0 29] 80 @pc restore cmmi8.300 @sf 1046 1983 p m (ns) s cmmi10.329 @sf 1086 1976 p m (M) 2 (;) ks cmr10.329 @sf 1906 1976 p m (\(9\)) s 74 2121 p m (call) 20 (it) ks cmmi10.329 @sf 20 r m (H) s cmsy8.300 @sf 253 2106 p m (0) s cmr10.329 @sf 264 2121 p m (,) 20 (has) 19 (all) 20 (the) 19 (eigen) 0 (v) -2 (alues) 19 (of) ks cmmi10.329 @sf 19 r m (H) s cmr10.329 @sf 23 r m (except) s cmmi10.329 @sf 19 r m (\025) s cmr10.329 @sf 19 r m (\(if) s cmmi10.329 @sf 19 r m (\025) s cmr10.329 @sf 19 r m (is) 19 (simple\).) 33 (Ho) 0 (w) 0 (ev) -2 (er,) ks cmmi10.329 @sf 18 r m (H) s cmsy8.300 @sf 1669 2106 p m (0) s cmr10.329 @sf 1699 2121 p m (is) 20 (not) 19 (upp) 1 (er-) ks 74 2221 p m (Hessen) 0 (b) 1 (erg) 18 (in) 18 (general) 19 (and) 18 (therefore) 17 (will) 20 (b) 1 (e) 18 (reduced) 19 (bac) 0 (k) 17 (to) 17 (Hessen) 0 (b) 1 (erg) 17 (form) 18 (b) 1 (efore) 18 (applying) ks 74 2320 p m (Newton's) 16 (iterations;) 16 (this) 17 (is) 17 (mean) 0 (t) 14 (to) 16 (sa) 0 (v) -1 (e) 14 (on) 17 (the) 16 (cost) 16 (of) 15 (factorizing) 17 (the) 16 (Jacobian) 18 (when) 16 (solving) ks 74 2420 p m (the) 18 (linear) 18 (systems) 17 (arising) 19 (at) 17 (eac) 0 (h) 16 (step) 18 (of) 17 (Newton's) 17 (iteration.) 27 (Note) 17 (that) 17 (it) 17 (is) 18 (only) 18 (the) 18 (trailing) ks 74 2519 p m (diagonal) 18 (submatrix) 17 (of) 17 (order) ks cmmi10.329 @sf 17 r m (n) s cmsy10.329 @sf 12 r m (\000) s cmmi10.329 @sf 12 r m (s) s cmr10.329 @sf 12 r m (+) 12 (1) ks cmsy10.329 @sf 11 r m (\002) s cmmi10.329 @sf 12 r m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 12 r m (s) s cmr10.329 @sf 12 r m (+) 12 (1) 17 (of) ks cmmi10.329 @sf 17 r m (H) s cmsy8.300 @sf 1199 2504 p m (0) s cmr10.329 @sf 1227 2519 p m (that) 17 (needs) 18 (to) 16 (b) 1 (e) 18 (reduced) 19 (and) 17 (that) 17 (if) ks cmmi10.329 @sf 74 2619 p m (s) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (n) s cmsy10.329 @sf 4 r m (\000) s cmr10.329 @sf 4 r m (1) 13 (or) ks cmmi10.329 @sf 11 r m (s) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (n) s cmr10.329 @sf m (,) 13 (then) ks cmmi10.329 @sf 13 r m (H) s cmsy8.300 @sf 592 2604 p m (0) s cmr10.329 @sf 615 2619 p m (is) 13 (upp) 1 (er-Hessen) 0 (b) 1 (erg.) 19 (Moreo) 0 (v) -1 (er) ks cmmi10.329 @sf 10 r m (s) s cmr10.329 @sf 12 r m (need) 13 (not) 12 (b) 1 (e) 13 (c) 0 (hosen) 11 (so) 12 (that) ks cmmi10.329 @sf 12 r m (x) s cmmi8.300 @sf 1828 2626 p m (s) s cmr10.329 @sf 1858 2619 p m (is) 13 (the) ks 74 2719 p m (largest) 17 (comp) 1 (onen) 0 (t) 16 (of) ks cmmi10.329 @sf 16 r m (x) s cmr10.329 @sf 17 r m (\(in) 17 (absolute) 17 (v) -2 (alue\).) 25 (Indeed,) 18 (since) 18 (the) 17 (size) 18 (of) 16 (the) 17 (matrix) 16 (to) 16 (b) 1 (e) 18 (reduced) ks @eop 12 @bop0 cmr10.329 @sf [ 16 1 -3 -26 23] 22 @dc 12 @bop1 cmr10.329 @sf 1919 -77 p m (12) s 74 67 p m (where) s cmmi10.329 @sf 16 r m (D) s cmr10.329 @sf 16 r m (is) 15 (the) 16 (diagonal) 15 (matrix) 15 (with) 16 (the) 15 (follo) 0 (wing) 15 (en) 0 (tries) ks cmex10.300 @sf 759 126 p m (8) s 759 164 p m (<) s 759 238 p m (:) s cmmi10.329 @sf 849 177 p m (d) s cmmi8.300 @sf 873 184 p m (i) s cmr10.329 @sf 899 177 p m (=) 13 (1) ks cmmi10.329 @sf m (;) s cmr10.329 @sf 32 r m (if) s cmsy8.300 @sf 1076 156 p m (j) s cmmi8.300 @sf m (x) s cmmi6.300 @sf 1106 161 p m (i) s cmsy8.300 @sf 1119 156 p m (j) s 1072 168 p 61 2 ru 1072 195 p m (j) s cmmi8.300 @sf m (x) s cmmi6.300 @sf 1102 199 p m (n) s cmsy8.300 @sf 1123 195 p m (j) s cmsy10.329 @sf 1151 177 p m (\024) s cmr10.329 @sf 13 r m (1) s cmmi10.329 @sf 817 248 p m (d) s cmmi8.300 @sf 841 255 p m (i) s cmr10.329 @sf 867 248 p m (=) s cmsy10.329 @sf 13 r m (\000) s cmmi8.300 @sf 955 231 p m (x) s cmmi6.300 @sf 975 235 p m (n) s 956 238 p 42 2 ru cmmi8.300 @sf 960 264 p m (x) s cmmi6.300 @sf 980 269 p m (i) s cmmi10.329 @sf 1002 248 p m (;) s cmr10.329 @sf 32 r m (if) s cmsy8.300 @sf 1108 227 p m (j) s cmmi8.300 @sf m (x) s cmmi6.300 @sf 1138 232 p m (i) s cmsy8.300 @sf 1151 227 p m (j) s 1104 239 p 61 2 ru 1104 266 p m (j) s cmmi8.300 @sf m (x) s cmmi6.300 @sf 1134 270 p m (n) s cmsy8.300 @sf 1155 266 p m (j) s cmmi10.329 @sf 1182 248 p m (>) s cmr10.329 @sf 13 r m (1) s 74 358 p m (i.e.,) s cmmi10.329 @sf 15 r m (D) s cmr10.329 @sf 16 r m (is) 16 (c) 0 (hosen) 14 (so) 15 (that) 15 (all) 16 (the) 15 (en) 0 (tries) 14 (in) ks cmmi10.329 @sf 17 r m (N) s cmr10.329 @sf 19 r m (are) 15 (less) 16 (than) 15 (or) 15 (equal) 16 (to) 14 (one.) 20 (Then) 16 (w) 0 (e) 14 (ha) 0 (v) -1 (e) ks cmmi10.329 @sf 477 515 p m (N) 5 (H) 4 (M) ks cmr10.329 @sf 16 r m (=) s cmex10.300 @sf 669 418 p m (0) s 669 491 p m (B) s 669 518 p m (@) s cmmi10.329 @sf 741 456 p m (H) s cmsy8.300 @sf 783 441 p m (0) s 829 485 p 2 69 ru cmr10.329 @sf 870 456 p m (0) s 706 487 p 227 2 ru 829 542 p 2 57 ru cmr10.432 @sf 746 582 p m (0) s cmmi10.329 @sf 791 520 p m (\013) s 829 591 p 2 91 ru 868 574 p m (\015) s cmex10.300 @sf 932 418 p m (1) s 932 491 p m (C) s 932 518 p m (A) s cmmi10.329 @sf 976 515 p m (;) 33 (N) 5 (M) ks cmr10.329 @sf 17 r m (=) s cmex10.300 @sf 1173 431 p m (0) s 1173 505 p m (@) s cmmi10.329 @sf 1239 473 p m (D) s cmsy8.300 @sf 1278 458 p m (0) s 1318 502 p 2 69 ru cmr10.329 @sf 1359 473 p m (0) s 1209 504 p 213 2 ru 1318 559 p 2 57 ru cmr10.432 @sf 1249 565 p m (0) s 1318 574 p 2 57 ru cmmi10.329 @sf 1360 557 p m (\016) s cmex10.300 @sf 1422 431 p m (1) s 1422 505 p m (A) s cmmi10.329 @sf 1466 515 p m (;) s cmr10.329 @sf 1906 515 p m (\(7\)) s 74 672 p m (with) s cmmi10.329 @sf 935 772 p m (\025) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (\015) 3 (=\016) 0 (:) ks cmr10.329 @sf 74 898 p m (Also,) s cmmi10.329 @sf 759 998 p m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmsy8.300 @sf 847 980 p m (0) s cmmi10.329 @sf 857 998 p m (;) 8 (D) ks cmsy8.300 @sf 917 980 p m (0) s cmr10.329 @sf 928 998 p m (\)) 12 (=) ks cmmi10.329 @sf 13 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) 1 (;) 8 (I) ks cmr10.329 @sf 4 r m (\)) s cmsy10.329 @sf 8 r m (\000) 10 (f) ks cmmi10.329 @sf m (\025) s cmsy10.329 @sf m (g) s cmr10.329 @sf 74 1125 p m (and) 14 (therefore) 14 (b) 0 (y) 12 (this) 15 (transformation) ks cmmi10.329 @sf 12 r m (\025) s cmr10.329 @sf 13 r m (has) 14 (b) 1 (een) 15 (\\remo) 0 (v) -1 (ed") 12 (from) 13 (the) 14 (sp) 1 (ectrum.) 19 (W) -3 (orking) 13 (on) 14 (the) ks 74 1224 p m (solution) 20 (of) 18 (a) 18 (generalized) 21 (eigen) 0 (v) -2 (alue) 19 (problem) 19 (from) 18 (this) 19 (p) 1 (oin) 0 (t) 18 (on) 19 (will) 20 (not) 19 (in) 19 (general) 19 (cause) 19 (an) 0 (y) ks 74 1324 p m (dramatic) 17 (increase) 19 (in) 18 (the) 17 (cost) 17 (of) 17 (the) 17 (algorithm) 17 (mainly) 19 (b) 1 (ecause) ks cmmi10.329 @sf 18 r m (D) s cmsy8.300 @sf 1379 1309 p m (0) s cmr10.329 @sf 1408 1324 p m (is) 18 (diagonal.) 27 (A) 17 (Newton) 17 (step) ks 74 1423 p m (with) 16 (this) 15 (problem) 16 (in) 0 (v) 0 (olv) 0 (es) 13 (the) 15 (follo) 0 (wing) 15 (computation) ks cmex10.300 @sf 277 1497 p save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pc restore cmmi10.329 @sf 331 1542 p m (H) s cmsy8.300 @sf 373 1526 p m (0) s cmsy10.329 @sf 394 1542 p m (\000) s cmmi10.329 @sf 11 r m (\025) s cmmi8.300 @sf 467 1549 p m (i) s cmmi10.329 @sf 480 1542 p m (D) s cmsy8.300 @sf 519 1526 p m (0) s cmsy10.329 @sf 572 1542 p m (\000) s cmmi10.329 @sf m (D) s cmsy8.300 @sf 646 1526 p m (0) s cmmi10.329 @sf 658 1542 p m (x) s cmmi8.300 @sf 684 1549 p m (i) s cmmi10.329 @sf 407 1597 p m (e) s cmmi8.300 @sf 428 1582 p m (T) s 428 1608 p m (s) s cmr10.329 @sf 624 1597 p m (0) s cmex10.300 @sf 719 1497 p save [ 21 124 -1 122 33] 33 @pc restore 759 1497 p save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pc restore cmmi10.329 @sf 815 1542 p m (y) s 813 1597 p m (\026) s cmex10.300 @sf 861 1497 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 907 1569 p m (=) s cmex10.300 @sf 955 1497 p save [<0000180000300000600000E00000C0000180000380000700000600000E00000C00001C00003800 00380000700000700000E00000E00001E00001C00001C000038000038000038000078000070000 0700000F00000E00000E00001E00001E00001E00001C00001C00003C00003C00003C00003C0000 380000780000780000780000780000780000780000780000780000700000F00000F00000F00000 F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000 F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000700000780000780000 7800007800007800007800007800007800003800003C00003C00003C00003C00001C00001C0000 1E00001E00001E00000E00000E00000F000007000007000007800003800003800003800001C000 01C00001E00000E00000E000007000007000003800003800001C00000C00000E00000600000700 0003800001800000C00000E0000060000030000018> 21 124 -10 122 33] 32 @pc restore cmmi10.329 @sf 1008 1542 p m (r) s cmmi8.300 @sf 1029 1549 p m (i) s cmr10.329 @sf 1014 1597 p m (0) s cmex10.300 @sf 1064 1497 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1104 1569 p m (;) 33 (\025) ks cmmi8.300 @sf 1177 1576 p m (i) s cmsy10.329 @sf 1203 1569 p m ( ) s cmmi10.329 @sf 13 r m (\025) s cmmi8.300 @sf 1288 1576 p m (i) s cmr10.329 @sf 1312 1569 p m (+) s cmmi10.329 @sf 10 r m (\026) s cmr10.329 @sf 26 r m (;) s cmmi10.329 @sf 32 r m (x) s cmmi8.300 @sf 1481 1576 p m (i) s cmsy10.329 @sf 1508 1569 p m ( ) s cmmi10.329 @sf 13 r m (x) s cmmi8.300 @sf 1592 1576 p m (i) s cmr10.329 @sf 1616 1569 p m (+) s cmmi10.329 @sf 11 r m (y) s cmr10.329 @sf 1906 1569 p m (\(8\)) s 74 1714 p m (where) s cmmi10.329 @sf 831 1814 p m (r) s cmmi8.300 @sf 852 1821 p m (i) s cmr10.329 @sf 878 1814 p m (=) s cmmi10.329 @sf 13 r m (\025) s cmmi8.300 @sf 953 1821 p m (i) s cmmi10.329 @sf 967 1814 p m (D) s cmsy8.300 @sf 1006 1796 p m (0) s cmmi10.329 @sf 1017 1814 p m (x) s cmmi8.300 @sf 1043 1821 p m (i) s cmsy10.329 @sf 1068 1814 p m (\000) s cmmi10.329 @sf 10 r m (H) 4 (x) ks cmmi8.300 @sf 1181 1821 p m (i) s cmmi10.329 @sf 1195 1814 p m (:) s cmr10.329 @sf 74 1940 p m (Clearly) 17 (the) 15 (previous) 17 (computation) 15 (in) 0 (v) 0 (olv) 0 (es) 13 (an) ks cmmi10.329 @sf 16 r m (O) s cmr10.329 @sf 1 r m (\() s cmmi10.329 @sf m (n) s cmr10.329 @sf m (\)) 15 (increase) 16 (in) 17 (the) 15 (cost) 16 (of) 15 (one) 15 (step:) 21 (this) 16 (comes) ks 74 2040 p m (from) 12 (the) 12 (m) 0 (ultiplications) 14 (b) 0 (y) ks cmmi10.329 @sf 11 r m (D) s cmsy8.300 @sf 660 2025 p m (0) s cmr10.329 @sf 672 2040 p m (.) 19 (The) 12 (details) 14 (on) 12 (ho) 0 (w) 11 (equation) 13 (\(8\)) 11 (is) 13 (deriv) 0 (ed) 13 (are) 12 (giv) 0 (en) 12 (in) 13 (section) 13 (9.) ks 74 2139 p m (If) s cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf 15 r m (is) 15 (complex,) 16 (then) 15 (after) 15 (de\015ating) ks cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf 15 r m (and) 15 (its) 15 (conjugate) ks 1195 2128 p m (\026) s cmmi10.329 @sf 1193 2140 p m (\025) s cmr10.329 @sf 1234 2139 p m (the) 15 (resulting) 17 (matrices) ks cmmi10.329 @sf 15 r m (H) s cmsy8.300 @sf 1724 2124 p m (0) s cmr10.329 @sf 1750 2139 p m (and) s cmmi10.329 @sf 15 r m (D) s cmsy8.300 @sf 1877 2124 p m (0) s cmr10.329 @sf 1903 2139 p m (are) s 74 2239 p m (complex) 16 (in) 16 (general.) 21 (This) 15 (is) 16 (the) 15 (ma) 3 (jor) 14 (dra) 0 (wbac) -1 (k) 13 (of) 15 (this) 16 (metho) 1 (d.) ks 124 2380 p m (Finally) 21 (w) 0 (e) 17 (men) 0 (tion) 19 (another) 19 (approac) 0 (h) 17 (that) 19 (can) 19 (b) 1 (e) 20 (of) 19 (in) 0 (terest) 18 (when) 20 (the) 19 (similarit) 0 (y) 19 (transfor-) ks 74 2480 p m (mation) 17 (\(6\)) 16 (in) 0 (v) 0 (olv) 0 (es) 15 (a) 17 (v) 0 (ery) 15 (ill-c) 1 (ondi) 1 (tioned) ks cmmi10.329 @sf 19 r m (M) s cmr10.329 @sf 22 r m (\(4\).) 25 (This) 18 (approac) 0 (h) 16 (consists) 17 (of) 17 (in) 0 (terc) 0 (hanging) 15 (t) 0 (w) -1 (o) ks 74 2580 p m (comp) 1 (onen) 0 (ts) 16 (of) ks cmmi10.329 @sf 16 r m (x) s cmr10.329 @sf 16 r m (and) 17 (the) 16 (corresp) 1 (onding) 18 (columns) 17 (and) 17 (ro) 0 (ws) 14 (in) ks cmmi10.329 @sf 17 r m (H) s cmr10.329 @sf 20 r m (so) 16 (that) 16 (the) 17 (last) 16 (comp) 1 (onen) 0 (t) 16 (of) ks cmmi10.329 @sf 74 2679 p m (x) s cmr10.329 @sf 16 r m (is) 16 (large) 16 (enough.) 21 (More) 15 (precisely) -3 (,) 17 (let) ks cmmi10.329 @sf 16 r m (x) s cmmi8.300 @sf 855 2686 p m (s) s cmr10.329 @sf 889 2679 p m (b) 1 (e) 16 (the) 16 (largest) 15 (comp) 1 (onen) 0 (t) 15 (of) ks cmmi10.329 @sf 15 r m (x) s cmr10.329 @sf 16 r m (\(in) 16 (absolute) 16 (v) -2 (alue\)) 16 (and) ks @eop 11 @bop0 11 @bop1 cmr10.329 @sf 1919 -77 p m (11) s 74 67 p m (of) s cmmi10.329 @sf 14 r m (H) s cmsy8.300 @sf 167 52 p m (00) s cmr10.329 @sf 202 67 p m (is) s cmmi10.329 @sf 14 r save [<6003C0E00620700610700E10700E087007083807043803803803803803801C01C01C01C01C01C0 1C01C00E00E00E00E00F00C00E80C0076180071F00070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 22 32 -2 0 26] 104 @pc restore cmsy8.300 @sf 272 52 p m (0) s cmmi8.300 @sf 272 79 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (2) s cmsy10.329 @sf 349 67 p m (\000) s cmmi10.329 @sf 8 r save [<6003C0E00620700610700E10700E087007083807043803803803803803801C01C01C01C01C01C0 1C01C00E00E00E00E00F00C00E80C0076180071F00070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 22 32 -2 0 26] 104 @pc restore cmmi8.300 @sf 418 74 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmmi8.300 @sf m (;n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (2) s cmmi10.329 @sf 563 67 p m (x) s cmsy8.300 @sf 589 52 p m (00) s cmr10.329 @sf 610 67 p m (,) 14 (where) ks cmmi10.329 @sf 14 r save [<6003C0E00620700610700E10700E087007083807043803803803803803801C01C01C01C01C01C0 1C01C00E00E00E00E00F00C00E80C0076180071F00070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 22 32 -2 0 26] 104 @pc restore cmsy8.300 @sf 793 52 p m (0) s cmmi8.300 @sf 793 79 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (2) s cmr10.329 @sf 876 67 p m (is) 15 (the) 14 (last) 14 (column) 15 (of) 13 (the) 15 (leading) 15 (principal) 16 (submatrix) 15 (of) ks cmmi10.329 @sf 74 167 p m (H) s cmsy8.300 @sf 116 152 p m (0) s cmr10.329 @sf 142 167 p m (and) s cmmi10.329 @sf 16 r m (x) s cmsy8.300 @sf 257 152 p m (00) s cmr10.329 @sf 293 167 p m (is) 16 (the) 15 (v) 0 (ector) 14 (whose) 15 (comp) 1 (onen) 0 (ts) 14 (are) 15 (the) 15 (\014rst) ks cmmi10.329 @sf 15 r m (n) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 11 r m (2) 15 (comp) 1 (onen) 0 (ts) 14 (of) 17 (~) ks cmmi10.329 @sf 1609 167 p m (x) s cmr10.329 @sf 1635 167 p m (.) 19 (Since) 17 (all) 16 (of) 15 (the) ks 74 266 p m (quan) 0 (tities) 15 (in) 0 (v) 0 (olv) -1 (ed) 14 (are) 15 (real,) ks cmmi10.329 @sf 15 r m (H) s cmsy8.300 @sf 681 251 p m (00) s cmr10.329 @sf 717 266 p m (is) 16 (real.) ks 124 408 p m (W) -3 (e) 10 (remark) 11 (here,) 13 (as) 11 (can) 11 (b) 1 (e) 12 (readily) 13 (realized,) 13 (that) ks cmmi10.329 @sf 11 r m (H) s cmsy8.300 @sf 1108 393 p m (0) s cmr10.329 @sf 1131 408 p m (\(or) s cmmi10.329 @sf 10 r m (H) s cmsy8.300 @sf 1242 393 p m (00) s cmr10.329 @sf 1263 408 p m (\)) 11 (is) 12 (quite) 12 (c) 0 (heap) 11 (to) 11 (obtain) 11 (in) 12 (practice) ks 74 507 p m (once) 17 (an) 17 (eigenpair) 18 (of) ks cmmi10.329 @sf 16 r m (H) s cmr10.329 @sf 20 r m (is) 17 (a) 0 (v) -2 (ailable.) 24 (It) 17 (requires) ks cmmi10.329 @sf 17 r m (O) s cmr10.329 @sf 1 r m (\() s cmmi10.329 @sf m (n) s cmr10.329 @sf m (\)) 16 (op) 1 (erations) 17 (consisting) 18 (of) 16 (a) 16 (v) 0 (ector) 15 (normal-) ks 74 607 p m (ization,) 19 (a) 17 (scalar-v) 0 (ector) 16 (m) 0 (ultiplication) 20 (and) 17 (a) 18 (v) 0 (ector-v) -1 (ector) 15 (addition.) 29 (Ho) 0 (w) -1 (ev) -1 (er) 15 (the) 18 (conditioning) ks 74 706 p m (of) 15 (the) 15 (matrix) ks cmmi10.329 @sf 15 r m (M) s cmr10.329 @sf 20 r m (migh) 0 (t) 14 (raise) 16 (concern.) 20 (Indeed:) ks cmmi10.329 @sf 479 839 p m (cond) s cmsy8.300 @sf 572 846 p m (1) s cmr10.329 @sf 609 839 p m (\() s cmmi10.329 @sf m (M) s cmr10.329 @sf 5 r m (\)) 12 (=) ks cmsy10.329 @sf 13 r m (k) s cmmi10.329 @sf m (M) s cmsy10.329 @sf 5 r m (k) s cmsy8.300 @sf 849 846 p m (1) s cmsy10.329 @sf 886 839 p m (k) s cmmi10.329 @sf m (M) s cmsy8.300 @sf 958 821 p m (\000) s cmr8.300 @sf m (1) s cmsy10.329 @sf 1005 839 p m (k) s cmsy8.300 @sf 1028 846 p m (1) s cmsy10.329 @sf 1077 839 p m (\031) s cmmi10.329 @sf 13 r m (max) s cmr10.329 @sf m (\() s cmsy10.329 @sf m (j) s cmmi10.329 @sf m (x) s cmmi8.300 @sf 1272 846 p m (i) s cmsy10.329 @sf 1286 839 p m (j) s cmr10.329 @sf m (\)) s cmmi10.329 @sf m (max) s cmex10.300 @sf 1415 779 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmsy10.329 @sf 1454 809 p m (j) s cmmi10.329 @sf m (x) s cmmi8.300 @sf 1493 816 p m (i) s cmsy10.329 @sf 1506 809 p m (j) s 1449 829 p 75 2 ru 1449 870 p m (j) s cmmi10.329 @sf m (x) s cmmi8.300 @sf 1488 877 p m (n) s cmsy10.329 @sf 1511 870 p m (j) s cmex10.300 @sf 1529 779 p save [ 20 99 -1 97 31] 19 @pc restore cmr10.329 @sf 74 971 p m (whic) 0 (h) 12 (can) 13 (b) 1 (e) 13 (large) 12 (if) ks cmmi10.329 @sf 13 r m (x) s cmmi8.300 @sf 514 978 p m (n) s cmsy10.329 @sf 550 971 p save [<000000C00C000003C03C000007007000001C01C000007807800000E00E000003803800000F00F0 00003C03C000007007000001C01C000007807800000E00E000003803800000F00F000000F00F00 000038038000000E00E00000078078000001C01C00000070070000003C03C000000F00F0000003 8038000000E00E00000078078000001C01C00000070070000003C03C000000C00C> 38 30 -3 4 45] 28 @pc restore cmmi10.329 @sf 58 r m (x) s cmmi8.300 @sf 634 978 p m (i) s cmr10.329 @sf 648 971 p m (.) 19 (Ha) 0 (ving) 11 (noted) 13 (this,) 13 (it) 12 (is) 13 (clear) 13 (that) 11 (the) 13 (ill-condi) 1 (tioni) 1 (ng) 14 (of) ks cmmi10.329 @sf 12 r m (M) s cmr10.329 @sf 17 r m (can) 12 (b) 1 (e) ks 74 1071 p m (easily) 15 (detected,) 15 (and) 14 (therefore) 14 (one) 14 (of) 14 (the) 14 (more) 13 (stable) 15 (\(and) 14 (costlier\)) 14 (metho) 1 (ds) 14 (whic) 0 (h) 14 (w) 0 (e) 13 (in) 0 (tro) 1 (duce) ks 74 1170 p m (next) 15 (and) 16 (in) 16 (the) 15 (follo) 0 (wing) 15 (sections) 16 (can) 15 (b) 1 (e) 16 (used.) ks 124 1312 p m (It) 15 (is) 16 (p) 1 (ossible) 17 (to) 15 (prev) 0 (en) 0 (t) 13 (the) 15 (ill-condi) 1 (tioni) 1 (ng) 17 (of) ks cmmi10.329 @sf 15 r m (M) s cmr10.329 @sf 20 r m (from) 15 (b) 1 (earing) 16 (on) 15 (the) 15 (algorithm) 16 (b) 0 (y) 14 (a) 0 (v) -1 (oiding) ks 74 1411 p m (a) 19 (similarit) 0 (y) 20 (transformation.) 30 (More) 19 (precisely) -3 (,) 21 (the) 19 (eigen) 0 (v) -2 (alue) 20 (problem) 20 (w) 0 (e) 18 (w) 0 (an) -1 (t) 17 (to) 19 (solv) 0 (e) 18 (can) 19 (b) 1 (e) ks 74 1511 p m (though) 0 (t) 14 (of) 14 (as) 15 (a) 15 (generalized) 17 (eigen) 0 (v) -2 (alue) 15 (problem,) ks cmmi10.329 @sf 904 1643 p m (H) 4 (x) ks cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (\025) s save [ 31 31 -2 0 34] 66 @pc restore 36 r m (x;) s cmr10.329 @sf 74 1776 p m (with) s cmmi10.329 @sf 18 r save [ 31 31 -2 0 34] 66 @pc restore cmr10.329 @sf 53 r m (=) s cmmi10.329 @sf 16 r m (I) s cmr10.329 @sf 4 r m (.) 26 (W) -3 (e) 16 (w) 0 (an) -1 (t) 15 (to) 17 (\014nd) ks cmmi10.329 @sf 18 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmr10.329 @sf 4 r m (\)) 15 (=) ks cmmi10.329 @sf 16 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) 1 (;) 8 (I) ks cmr10.329 @sf 4 r m (\).) 24 (No) 0 (w) 15 (w) 0 (e) 16 (kno) 0 (w) 16 (that) 17 (giv) 0 (en) 17 (an) 0 (y) 15 (non-singular) ks cmmi10.329 @sf 19 r m (M) s cmr10.329 @sf 74 1875 p m (and) s cmmi10.329 @sf 16 r m (N) s cmr10.329 @sf 5 r m (,) s cmmi10.329 @sf 758 1975 p m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) 1 (;) 8 (I) ks cmr10.329 @sf 4 r m (\)) 10 (=) ks cmmi10.329 @sf 13 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (N) 5 (H) 4 (M) 2 (;) 8 (N) 5 (M) ks cmr10.329 @sf 5 r m (\)) s cmmi10.329 @sf m (:) s cmr10.329 @sf 74 2095 p m (Giv) 0 (en) 21 (a) 21 (particular) 22 (eigenpair) 23 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 19 (w) 0 (e) 20 (w) 0 (ould) 21 (lik) 0 (e) 22 (to) 20 (c) 0 (ho) 1 (ose) ks cmmi10.329 @sf 21 r m (M) s cmr10.329 @sf 26 r m (and) s cmmi10.329 @sf 22 r m (N) s cmr10.329 @sf 26 r m (in) 22 (a) 21 (w) 0 (a) -1 (y) 19 (that) 21 (solv) 0 (es) ks 74 2195 p m (the) 19 (problem) 19 (w) 0 (e) 18 (set) 18 (for) 19 (ourselv) 0 (es) 18 (at) 18 (the) 19 (b) 1 (eginning) 20 (of) 19 (this) 19 (section,) 20 (namely) -3 (,) 19 (w) 0 (e) 17 (w) 0 (an) 0 (t) 16 (to) 18 (reduce) ks 74 2294 p m (the) 23 (problem) 22 (to) 22 (one) 23 (where) ks cmmi10.329 @sf 22 r m (\025) s cmr10.329 @sf 22 r m (is) 23 (no) 22 (longer) 22 (in) 23 (the) 23 (sp) 1 (ectrum.) 41 (A) 23 (closer) 22 (lo) 1 (ok) 23 (at) 22 (the) 22 (similarit) 0 (y) ks 74 2394 p m (transformation) 18 (6,) 18 (rev) 0 (eals) 18 (that) 18 (its) 19 (de\015ating) 20 (prop) 1 (ert) 0 (y) 17 (is) 19 (due) 20 (to) 18 (the) 18 (fact) 19 (that) ks cmmi10.329 @sf 18 r m (M) s cmsy8.300 @sf 1668 2379 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1715 2394 p m (x) s cmr10.329 @sf 18 r m (=) s cmmi10.329 @sf 19 r m (e) s cmmi8.300 @sf 1834 2401 p m (n) s cmmi10.329 @sf 1858 2394 p m (:) s cmr10.329 @sf 18 r m (But) s 74 2494 p m (then) s cmmi10.329 @sf 20 r m (M) s cmsy8.300 @sf 231 2479 p m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 297 2494 p m (is) 20 (not) 19 (the) 20 (only) 20 (matrix) 19 (that) 18 (can) 20 (b) 1 (e) 20 (used) 20 (to) 19 (accomplish) 20 (this.) 33 (In) 20 (fact) 19 (the) 19 (follo) 0 (wing) ks 74 2593 p m (matrix) s cmmi10.329 @sf 15 r m (N) s cmr10.329 @sf 20 r m (can) 15 (b) 1 (e) 16 (c) 0 (hosen) 14 (to) 15 (reduce) ks cmmi10.329 @sf 16 r m (x) s cmr10.329 @sf 15 r m (to) 15 (a) 14 (m) 0 (ultiple) 16 (of) ks cmmi10.329 @sf 15 r m (e) s cmmi8.300 @sf 1154 2600 p m (n) s cmr10.329 @sf 1178 2593 p m (:) s cmmi10.329 @sf 894 2726 p m (N) s cmr10.329 @sf 17 r m (=) s cmmi10.329 @sf 13 r m (D) 1 (M) ks cmsy8.300 @sf 1084 2708 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1131 2726 p m (;) s @eop 10 @bop0 cmsy6.300 @sf [ 18 2 -3 -5 24] 0 @dc cmr8.300 @sf [ 13 1 -2 -18 18] 22 @dc 10 @bop1 cmr10.329 @sf 1919 -77 p m (10) s 74 67 p m (then) 16 (it) 15 (is) 16 (straigh) 0 (tfor) -1 (w) -1 (ard) 13 (to) 14 (v) 0 (erify) 15 (that) 14 (the) 16 (last) 15 (column) 16 (of) ks cmmi10.329 @sf 15 r m (H) s cmsy8.300 @sf 1287 52 p m (0) s cmr10.329 @sf 1313 67 p m (is) s cmmi10.329 @sf 16 r save [<6003C0E00620700610700E10700E087007083807043803803803803803801C01C01C01C01C01C0 1C01C00E00E00E00E00F00C00E80C0076180071F00070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 22 32 -2 0 26] 104 @pc restore cmmi8.300 @sf 1385 74 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmsy10.329 @sf 1463 67 p m (\000) s cmmi10.329 @sf 11 r save [<6003C0E00620700610700E10700E087007083807043803803803803803801C01C01C01C01C01C0 1C01C00E00E00E00E00F00C00E80C0076180071F00070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 22 32 -2 0 26] 104 @pc restore cmmi8.300 @sf 1535 74 p m (n;n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1635 67 p m (x) s cmsy8.300 @sf 1661 52 p m (0) s cmr10.329 @sf 1672 67 p m (,) 15 (where) ks cmmi10.329 @sf 858 241 p m (x) s cmsy8.300 @sf 884 223 p m (0) s cmr10.329 @sf 908 241 p m (=) s cmex10.300 @sf 956 131 p m (0) s 956 204 p m (B) s 956 229 p m (B) s 956 256 p m (@) s cmmi8.300 @sf 1040 153 p m (x) s cmr6.300 @sf 1060 158 p m (1) s 1038 161 p 42 2 ru cmmi8.300 @sf 1038 185 p m (x) s cmmi6.300 @sf 1058 189 p m (n) s cmr10.329 @sf 1052 219 p m (.) s 1052 236 p m (.) s 1052 253 p m (.) s cmmi8.300 @sf 1018 288 p m (x) s cmmi6.300 @sf 1038 293 p m (n) s cmsy6.300 @sf m (\000) s cmr6.300 @sf m (1) s 1018 299 p 81 2 ru cmmi8.300 @sf 1038 324 p m (x) s cmmi6.300 @sf 1058 328 p m (n) s cmex10.300 @sf 1124 131 p m (1) s 1124 204 p m (C) s 1124 229 p m (C) s 1124 256 p m (A) s cmmi10.329 @sf 1168 241 p m (:) s cmr10.329 @sf 74 412 p m (The) 11 (strategy) 9 (w) 0 (e) 8 (ha) 0 (v) 0 (e) 8 (just) 10 (describ) 1 (ed) 12 (is) 11 (giv) 0 (en) 10 (in) 11 ([) 0 (17) ks 1037 412 p m (]) 10 (and) 10 (applies) 12 (regardless) 10 (of) 10 (whether) 10 (the) 11 (eigenpair) ks 74 512 p m (\() s cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 16 (is) 19 (real) 18 (or) 18 (not.) 28 (Ho) 0 (w) 0 (ev) -2 (er,) 17 (when) 19 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 16 (is) 18 (real) 19 (w) 0 (e) 17 (get) 17 (a) 18 (real) 19 (matrix) ks cmmi10.329 @sf 18 r m (H) s cmsy8.300 @sf 1568 497 p m (0) s cmr10.329 @sf 1579 512 p m (.) 28 (In) 19 (the) 18 (case) 19 (when) ks 74 611 p m (\() s cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 12 (is) 15 (not) 14 (real,) 14 (the) 15 (last) 14 (column) 15 (of) ks cmmi10.329 @sf 14 r m (H) s cmsy8.300 @sf 835 596 p m (0) s cmr10.329 @sf 860 611 p m (alone) 14 (is) 15 (not) 14 (real) 15 (since,) 15 (as) 14 (w) 0 (e) 12 (remark) 0 (ed) 13 (earlier,) 15 (the) 14 (other) ks 74 711 p m (columns) 15 (are) 13 (those) 13 (of) 14 (a) 13 (leading) 15 (principal) 16 (submatrix) 14 (of) ks cmmi10.329 @sf 13 r m (H) s cmr10.329 @sf 4 r m (.) 19 (Hence) 14 (the) 14 (leading) 15 (principal) 16 (submatrix) ks 74 811 p m (of) s cmmi10.329 @sf 20 r m (H) s cmsy8.300 @sf 173 796 p m (0) s cmr10.329 @sf 204 811 p m (of) 20 (order) ks cmmi10.329 @sf 20 r m (n) s cmsy10.329 @sf 13 r m (\000) s cmr10.329 @sf 14 r m (2) 20 (is) 20 (real.) 35 (Also) 21 (in) 21 (this) 20 (case) 20 (the) 20 (complex) 21 (conjugate) 20 (of) 20 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\),) 19 (\() 3 (\026) ks cmmi10.329 @sf 1742 811 p m (x) s 1767 811 p m (;) s cmr10.329 @sf 1798 797 p m (\026) s cmmi10.329 @sf 1788 812 p m (\025) s cmr10.329 @sf m (\)) s 1832 811 p m (,) 21 (is) 20 (an) ks 74 910 p m (eigenpair) 17 (of) ks cmmi10.329 @sf 14 r m (H) s cmr10.329 @sf 4 r m (,) 15 (and) 15 (therefore) ks 671 899 p m (\026) s cmmi10.329 @sf 669 911 p m (\025) s cmr10.329 @sf 711 910 p m (is) 15 (an) 16 (eigen) 0 (v) -2 (alue) 15 (of) ks cmex10.300 @sf 1100 898 p m (e) s cmmi10.329 @sf 1088 911 p m (H) s cmr10.329 @sf 1130 910 p m (;) 15 (a) 15 (corresp) 1 (onding) 16 (eigen) 0 (v) 0 (ector) 13 (is) ks cmmi10.329 @sf 713 1109 p m (M) s cmsy8.300 @sf 762 1091 p m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 812 1109 p m (\026) s cmmi10.329 @sf 809 1109 p m (x) s cmr10.329 @sf 848 1109 p m (=) s cmex10.300 @sf 895 974 p m (0) s 895 1047 p m (B) s 895 1072 p m (B) s 895 1097 p m (B) s 895 1122 p m (B) s 895 1149 p m (@) s cmr10.329 @sf 1004 1008 p m (\026) s cmmi10.329 @sf 1001 1008 p m (x) s cmr8.300 @sf 1027 1015 p m (1) s cmsy10.329 @sf 1057 1008 p m (\000) s cmmi10.329 @sf 11 r m (x) s cmr8.300 @sf 1129 1015 p m (1) s 1155 991 p m (\026) s cmmi8.300 @sf 1153 991 p m (x) s cmmi6.300 @sf 1173 995 p m (n) s 1153 998 p 42 2 ru cmmi8.300 @sf 1153 1024 p m (x) s cmmi6.300 @sf 1173 1028 p m (n) s cmr10.329 @sf 1094 1057 p m (.) s 1094 1074 p m (.) s 1094 1091 p m (.) s 955 1147 p m (\026) s cmmi10.329 @sf 953 1147 p m (x) s cmmi8.300 @sf 979 1154 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmsy10.329 @sf 1057 1147 p m (\000) s cmmi10.329 @sf 11 r m (x) s cmmi8.300 @sf 1129 1154 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s 1204 1130 p m (\026) s cmmi8.300 @sf 1202 1130 p m (x) s cmmi6.300 @sf 1222 1134 p m (n) s 1202 1137 p 42 2 ru cmmi8.300 @sf 1202 1163 p m (x) s cmmi6.300 @sf 1222 1167 p m (n) s cmr8.300 @sf 1082 1189 p m (\026) s cmmi8.300 @sf 1080 1189 p m (x) s cmmi6.300 @sf 1100 1193 p m (n) s 1080 1196 p 42 2 ru cmmi8.300 @sf 1080 1222 p m (x) s cmmi6.300 @sf 1100 1226 p m (n) s cmex10.300 @sf 1269 974 p m (1) s 1269 1047 p m (C) s 1269 1072 p m (C) s 1269 1097 p m (C) s 1269 1122 p m (C) s 1269 1149 p m (A) s cmmi10.329 @sf 1313 1109 p m (:) s cmr10.329 @sf 74 1313 p m (Since) s cmmi10.329 @sf 22 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmsy8.300 @sf 286 1298 p m (0) s cmr10.329 @sf 296 1313 p m (\)) 20 (=) ks cmmi10.329 @sf 21 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmr10.329 @sf 4 r m (\)) s cmsy10.329 @sf 11 r m (\000) 14 (f) ks cmmi10.329 @sf m (\025) s cmsy10.329 @sf m (g) s cmr10.329 @sf m (,) s 663 1302 p m (\026) s cmmi10.329 @sf 662 1314 p m (\025) s cmr10.329 @sf 708 1313 p m (is) 20 (an) 20 (eigen) 0 (v) -2 (alue) 20 (of) ks cmmi10.329 @sf 19 r m (H) s cmsy8.300 @sf 1146 1298 p m (0) s cmr10.329 @sf 1177 1313 p m (and) 20 (a) 20 (corresp) 1 (onding) 21 (eigen) 0 (v) 0 (ector) 18 (is) 20 (the) ks 74 1413 p m (v) 0 (ector) 17 (~) ks cmmi10.329 @sf 211 1413 p m (x) s cmr10.329 @sf 252 1413 p m (of) 15 (length) ks cmmi10.329 @sf 16 r m (n) s cmsy10.329 @sf 11 r m (\000) s cmr10.329 @sf 10 r m (1,) 15 (whose) 15 (comp) 1 (onen) 0 (ts) 15 (are) 15 (the) 15 (\014rst) ks cmmi10.329 @sf 15 r m (n) s cmsy10.329 @sf 11 r m (\000) s cmr10.329 @sf 10 r m (1) 15 (comp) 1 (onen) 0 (ts) 15 (of) 15 (a) 15 (scalar) 15 (m) 0 (ultiple) ks 74 1512 p m (of) s cmmi10.329 @sf 15 r m (M) s cmsy8.300 @sf 175 1497 p m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 225 1512 p m (\026) s cmmi10.329 @sf 222 1512 p m (x) s cmr10.329 @sf 248 1512 p m (:) s 703 1624 p m (~) s cmmi10.329 @sf 700 1624 p m (x) s cmr10.329 @sf 739 1624 p m (=) s cmex10.300 @sf 787 1527 p m (0) s 787 1601 p m (B) s 787 1628 p m (@) s cmr10.329 @sf 893 1556 p m (\() 3 (\026) ks cmmi10.329 @sf 911 1556 p m (x) s cmr8.300 @sf 937 1563 p m (1) s cmmi10.329 @sf 956 1556 p m (x) s cmmi8.300 @sf 982 1563 p m (n) s cmsy10.329 @sf 1015 1556 p m (\000) s cmmi10.329 @sf 11 r m (x) s cmr8.300 @sf 1087 1563 p m (1) s cmr10.329 @sf 1109 1556 p m (\026) s cmmi10.329 @sf 1107 1556 p m (x) s cmmi8.300 @sf 1133 1563 p m (n) s cmr10.329 @sf 1156 1556 p m (\)) s cmmi10.329 @sf m (=i) s cmr10.329 @sf 1046 1604 p m (.) s 1046 1621 p m (.) s 1046 1638 p m (.) s 844 1692 p m (\() 3 (\026) ks cmmi10.329 @sf 862 1692 p m (x) s cmmi8.300 @sf 888 1699 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 956 1692 p m (x) s cmmi8.300 @sf 982 1699 p m (n) s cmsy10.329 @sf 1015 1692 p m (\000) s cmmi10.329 @sf 11 r m (x) s cmmi8.300 @sf 1087 1699 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 1158 1692 p m (\026) s cmmi10.329 @sf 1155 1692 p m (x) s cmmi8.300 @sf 1181 1699 p m (n) s cmr10.329 @sf 1205 1692 p m (\)) s cmmi10.329 @sf m (=i) s cmex10.300 @sf 1282 1527 p m (1) s 1282 1601 p m (C) s 1282 1628 p m (A) s cmmi10.329 @sf 1326 1624 p m (;) s cmr10.329 @sf 74 1783 p m (where) s cmmi10.329 @sf 17 r m (i) s cmr8.300 @sf 223 1768 p m (2) s cmr10.329 @sf 257 1783 p m (=) s cmsy10.329 @sf 16 r m (\000) s cmr10.329 @sf m (1.) 24 (This) 17 (is) 17 (due) 17 (to) 16 (the) 17 (sp) 1 (ecial) 18 (structure) 17 (of) ks cmex10.300 @sf 1190 1771 p m (e) s cmmi10.329 @sf 1178 1784 p m (H) s cmr10.329 @sf 1219 1783 p m (.) 24 (No) 0 (w) 15 (recall) 18 (that) ks cmmi10.329 @sf 16 r m (H) s cmsy8.300 @sf 1626 1768 p m (0) s cmr10.329 @sf 1654 1783 p m (has) 16 (no) 17 (zeros) 16 (on) ks 74 1883 p m (the) 16 (sub) 1 (diagonal,) 17 (and) 16 (so) 16 (w) 0 (e) 15 (kno) 0 (w) 14 (that) 16 (the) 16 (last) 15 (comp) 1 (onen) 0 (t) 16 (of) 18 (~) ks cmmi10.329 @sf 1302 1883 p m (x) s cmr10.329 @sf 1344 1883 p m (is) 17 (nonzero.) 22 (Note) 15 (that) 19 (~) ks cmmi10.329 @sf 1790 1883 p m (x) s cmr10.329 @sf 1832 1883 p m (is) 16 (real.) ks 74 1983 p m (W) -3 (e) 14 (can) 16 (carry) 14 (out) 15 (a) 15 (de\015ation) 16 (that) 14 (pro) 1 (duces) 17 (a) 14 (matrix) ks cmmi10.329 @sf 15 r m (H) s cmsy8.300 @sf 1176 1968 p m (00) s cmr10.329 @sf 1212 1983 p m (of) 15 (order) ks cmmi10.329 @sf 15 r m (n) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 11 r m (2) 14 (with) 16 (the) 15 (prop) 1 (ert) 0 (y) 14 (that) ks cmmi10.329 @sf 798 2127 p m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmsy8.300 @sf 886 2109 p m (00) s cmr10.329 @sf 906 2127 p m (\)) 12 (=) ks cmmi10.329 @sf 13 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmsy8.300 @sf 1072 2109 p m (0) s cmr10.329 @sf 1083 2127 p m (\)) s cmsy10.329 @sf 9 r m (\000) 11 (f) ks cmr10.329 @sf 1181 2116 p m (\026) s cmmi10.329 @sf 1179 2128 p m (\025) s cmsy10.329 @sf 1205 2127 p m (g) s cmmi10.329 @sf m (;) s cmr10.329 @sf 74 2272 p m (in) 16 (the) 15 (same) 15 (w) 0 (a) -1 (y) 14 (w) 0 (e) 13 (obtained) ks cmmi10.329 @sf 16 r m (H) s cmsy8.300 @sf 707 2257 p m (0) s cmr10.329 @sf 734 2272 p m (from) s cmmi10.329 @sf 14 r m (H) s cmr10.329 @sf 19 r m (using) 16 (the) 15 (elemen) 0 (tary) 14 (transformation) 14 (of) 15 (order) ks cmmi10.329 @sf 15 r m (n) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 11 r m (1) s cmmi10.329 @sf 676 2447 p m (M) s cmsy8.300 @sf 725 2429 p m (0) s cmr10.329 @sf 749 2447 p m (=) s cmex10.300 @sf 797 2338 p m (0) s 797 2411 p m (B) s 797 2436 p m (B) s 797 2463 p m (@) s cmr10.329 @sf 859 2370 p m (1) s 1202 2370 p m (~) s cmmi10.329 @sf 1199 2370 p m (x) s cmr8.300 @sf 1225 2377 p m (1) s cmr10.329 @sf 1013 2408 p m (.) s 1031 2421 p m (.) s 1049 2434 p m (.) s 1216 2405 p m (.) s 1216 2422 p m (.) s 1216 2439 p m (.) s 1189 2481 p m (~) s cmmi10.329 @sf 1186 2481 p m (x) s cmmi8.300 @sf 1212 2488 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (2) s cmr10.432 @sf 931 2525 p m (0) s cmr10.329 @sf 1178 2525 p m (~) s cmmi10.329 @sf 1175 2525 p m (x) s cmmi8.300 @sf 1201 2532 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmex10.300 @sf 1306 2338 p m (1) s 1306 2411 p m (C) s 1306 2436 p m (C) s 1306 2463 p m (A) s cmmi10.329 @sf 1350 2447 p m (:) s cmr10.329 @sf 74 2626 p m (By) 17 (a) 17 (previous) 18 (remark) 17 (ab) 1 (out) 17 (this) 17 (de\015ation) 18 (strategy) -3 (,) 15 (w) 0 (e) 16 (kno) 0 (w) 16 (that) ks cmmi10.329 @sf 16 r m (H) s cmsy8.300 @sf 1458 2611 p m (00) s cmr10.329 @sf 1496 2626 p m (di\013ers) 17 (from) 16 (the) 18 (leading) ks 74 2726 p m (principal) 16 (submatrix) 13 (of) ks cmmi10.329 @sf 13 r m (H) s cmsy8.300 @sf 568 2711 p m (0) s cmr10.329 @sf 592 2726 p m (of) 13 (order) ks cmmi10.329 @sf 13 r m (n) s cmsy10.329 @sf 6 r m (\000) s cmr10.329 @sf 6 r m (2) 13 (\(whic) 0 (h) 13 (is) 14 (real\)) 13 (in) 14 (the) 13 (last) 14 (column) 14 (only) -3 (.) 19 (The) 13 (last) 13 (column) ks @eop 9 @bop0 9 @bop1 cmr10.329 @sf 1941 -77 p m (9) s 124 67 p m (A) 14 (common) 14 (dra) 0 (wbac) -1 (k) 12 (that) 13 (these) 15 (metho) 1 (ds) 14 (ha) 0 (v) -1 (e) 13 (is) 14 (that) 13 (they) 15 (tend) 14 (to) 13 (serialize) 16 (the) 14 (computation.) ks 74 167 p m (Ho) 0 (w) -1 (ev) -1 (er,) 12 (it) 15 (has) 14 (b) 1 (een) 15 (our) 14 (exp) 1 (erience) 16 (that) 14 (the) 14 (need) 15 (to) 13 (de\015ate) 15 (arises) 14 (infrequen) 0 (tly) -3 (,) 14 (less) 15 (than) 14 (5) ks save [<080000E0180003100C0006080600060406000C0403000C0401801C0201801C0200C01C0200601C 0200601C0200301C0200181C0200180C04000C0C04000606040006060800030310000300E00F01 80001880C0003040C000702060006020300060103000E0101800E0100C00E0100C00E0100600E0 100300E01003006013F980602C06C0703001C030600060188000300F000030> 31 37 -3 3 38] 37 @pc restore 52 r m (of) s 74 266 p m (the) 15 (time) 16 (in) 16 (our) 15 (tests.) ks cmbx12.300 @sf 74 429 p save [<01FE000FFFC01E07F07801F87E01FCFF00FCFF00FEFF00FEFF00FE7E00FE3C00FE0000FC0000FC 0001F80001F00007C001FF0001FE00001F800007C00003E00003F01F03F01F03F83F81F83F81F8 3F81F83F03F01E03F00F07E007FFC000FE00> 23 32 -2 0 28] 51 @pc restore 28 r m (.1) s 202 429 p save [ 37 34 -2 0 43] 68 @pc restore 43 r m (e) s save [<7FF0FFE07FF0FFE00F801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F 000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F80 1F00FFFFFF00FFFFFF000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F 803F0007C03F0003E03F0001F83F00007FFF00000FFF00> 27 35 -1 0 31] 13 @pc restore 31 r m (ation) 18 (using) 19 (elem) -1 (e) -1 (n) -1 (tary) 16 (trans) ks save [<7FF8007FF8000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F8000 0F80000F80000F80000F80000F80000F80000F8000FFFC00FFFC000F80000F80000F80000F8000 0F80000F80000F83C00F87E007C7E003C7E001E3E000FFC0003F80> 19 35 -1 0 17] 102 @pc restore 17 r m (ormations) s cmr10.329 @sf 74 600 p m (W) -3 (e) 12 (no) 0 (w) 11 (describ) 1 (e) 15 (one) 12 (p) 1 (ossible) 15 (de\015ating) 13 (similarit) 0 (y) 13 (transformation.) 18 (W) -3 (e) 12 (assume) 12 (that) ks cmmi10.329 @sf 12 r m (H) s cmr10.329 @sf 17 r m (is) 13 (an) 12 (unre-) ks 74 699 p m (duced) 16 (upp) 1 (er-Hessen) 0 (b) 1 (erg) 16 (matrix,) ks cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf 15 r m (is) 15 (an) 15 (eigen) 0 (v) -2 (alue) 16 (of) ks cmmi10.329 @sf 14 r m (H) s cmr10.329 @sf 19 r m (and) s cmmi10.329 @sf 15 r m (x) s cmr10.329 @sf 15 r m (the) 16 (corresp) 1 (onding) 16 (eigen) 0 (v) 0 (ector.) ks 124 841 p m (Since) 21 (w) 0 (e) 19 (are) 19 (assuming) ks cmmi10.329 @sf 20 r m (H) s cmr10.329 @sf 24 r m (to) 19 (b) 1 (e) 20 (upp) 1 (er-Hessen) 0 (b) 1 (erg) 21 (with) 20 (no) 20 (zeros) 19 (on) 20 (the) 20 (sub) 1 (diagonal,) 22 (then) ks cmmi10.329 @sf 74 940 p m (x) s cmmi8.300 @sf 100 947 p m (n) s cmsy10.329 @sf 136 940 p m (6) s cmr10.329 @sf m (=) 13 (0) 15 (and) 15 (the) 16 (elemen) 0 (tary) 14 (transformation) ks cmmi10.329 @sf 813 1083 p m (M) s cmr10.329 @sf 17 r m (=) 13 ([) ks cmmi10.329 @sf m (e) s cmr8.300 @sf 956 1090 p m (1) s cmmi10.329 @sf 976 1083 p m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 8 (.) ks cmmi10.329 @sf 1057 1083 p m (;) 8 (e) ks cmmi8.300 @sf 1099 1090 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1167 1083 p m (;) 8 (x) ks cmr10.329 @sf m (]) s 74 1226 p m (i.e.,) s cmmi10.329 @sf 640 1400 p m (M) s cmr10.329 @sf 18 r m (=) s cmex10.300 @sf 750 1291 p m (0) s 750 1364 p m (B) s 750 1389 p m (B) s 750 1416 p m (@) s cmr10.329 @sf 815 1322 p m (1) s cmmi10.329 @sf 1152 1322 p m (x) s cmr8.300 @sf 1178 1329 p m (1) s cmr10.329 @sf 943 1361 p m (.) s 961 1374 p m (.) s 979 1387 p m (.) s 1168 1358 p m (.) s 1168 1375 p m (.) s 1168 1392 p m (.) s 1044 1434 p m (1) s cmmi10.329 @sf 1139 1434 p m (x) s cmmi8.300 @sf 1165 1441 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmr10.432 @sf 811 1478 p m (0) s cmmi10.329 @sf 1150 1478 p m (x) s cmmi8.300 @sf 1176 1485 p m (n) s cmex10.300 @sf 1258 1291 p m (1) s 1258 1364 p m (C) s 1258 1389 p m (C) s 1258 1416 p m (A) s cmmi10.329 @sf 1302 1400 p m (;) s cmr10.329 @sf 1906 1400 p m (\(4\)) s 74 1574 p m (is) 16 (non-singular.) 21 (The) 15 (in) 0 (v) 0 (erse) 14 (of) 15 (this) 15 (matrix) 15 (is) ks cmmi10.329 @sf 601 1761 p m (M) s cmsy8.300 @sf 650 1743 p m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 710 1761 p m (=) s cmex10.300 @sf 758 1639 p m (0) s 758 1712 p m (B) s 758 1737 p m (B) s 758 1762 p m (B) s 758 1789 p m (@) s cmr10.329 @sf 823 1670 p m (1) s cmsy10.329 @sf 1155 1670 p m (\000) s cmmi8.300 @sf 1197 1653 p m (x) s cmr6.300 @sf 1217 1658 p m (1) s 1196 1661 p 42 2 ru cmmi8.300 @sf 1196 1685 p m (x) s cmmi6.300 @sf 1216 1689 p m (n) s cmr10.329 @sf 951 1711 p m (.) s 969 1724 p m (.) s 987 1737 p m (.) s 1192 1708 p m (.) s 1192 1725 p m (.) s 1192 1742 p m (.) s 1052 1784 p m (1) s cmsy10.329 @sf 1147 1784 p m (\000) s cmmi8.300 @sf 1187 1763 p m (x) s cmmi6.300 @sf 1207 1768 p m (n) s cmsy6.300 @sf m (\000) s cmr6.300 @sf m (1) s 1187 1774 p 81 2 ru cmmi8.300 @sf 1207 1800 p m (x) s cmmi6.300 @sf 1227 1804 p m (n) s cmr10.432 @sf 819 1849 p m (0) s cmr8.300 @sf 1190 1832 p m (1) s 1178 1839 p 42 2 ru cmmi8.300 @sf 1178 1865 p m (x) s cmmi6.300 @sf 1198 1869 p m (n) s cmex10.300 @sf 1297 1639 p m (1) s 1297 1712 p m (C) s 1297 1737 p m (C) s 1297 1762 p m (C) s 1297 1789 p m (A) s cmmi10.329 @sf 1341 1761 p m (:) s cmr10.329 @sf 1906 1761 p m (\(5\)) s 74 1954 p m (It) 15 (is) 16 (easy) 15 (to) 15 (see) 15 (that) ks cmmi10.329 @sf 15 r m (M) s cmsy8.300 @sf 546 1939 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 593 1954 p m (x) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (e) s cmmi8.300 @sf 700 1961 p m (n) s cmmi10.329 @sf 724 1954 p m (:) s cmr10.329 @sf 15 r m (No) 0 (w) 13 (w) 0 (e) 14 (let) ks cmex10.300 @sf 840 2085 p m (e) s cmmi10.329 @sf 828 2098 p m (H) s cmr10.329 @sf 882 2097 p m (=) s cmmi10.329 @sf 13 r m (M) s cmsy8.300 @sf 979 2079 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1026 2097 p m (H) 4 (M) 2 (:) ks cmr10.329 @sf 1906 2097 p m (\(6\)) s 74 2240 p m (Then) 18 (it) 18 (is) 18 (easy) 18 (to) 16 (v) 0 (erify) 17 (that) 17 (the) 18 (last) 17 (column) 19 (of) ks cmex10.300 @sf 1078 2228 p m (e) s cmmi10.329 @sf 1066 2241 p m (H) s cmr10.329 @sf 1125 2240 p m (is) s cmmi10.329 @sf 18 r m (\025e) s cmmi8.300 @sf 1221 2247 p m (n) s cmr10.329 @sf 1244 2240 p m (.) 27 (F) -3 (urthermore) 16 (the) 18 (leading) 19 (principal) ks 74 2340 p m (submatrix) 14 (of) 12 (order) ks cmmi10.329 @sf 13 r m (n) s cmsy10.329 @sf 6 r m (\000) s cmr10.329 @sf 6 r m (1) 14 (of) ks cmex10.300 @sf 628 2328 p m (e) s cmmi10.329 @sf 616 2341 p m (H) s cmr10.329 @sf 658 2340 p m (,) 13 (whic) 0 (h) 13 (w) 0 (e) 12 (will) 15 (call) ks cmmi10.329 @sf 14 r m (H) s cmsy8.300 @sf 1084 2325 p m (0) s cmr10.329 @sf 1095 2340 p m (,) 14 (is) 13 (upp) 1 (er) 15 (Hessen) 0 (b) 1 (erg,) 12 (has) 14 (the) 13 (prop) 1 (ert) 0 (y) 12 (that) ks cmmi10.329 @sf 815 2483 p m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmsy8.300 @sf 903 2465 p m (0) s cmr10.329 @sf 913 2483 p m (\)) 13 (=) ks cmmi10.329 @sf 12 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmr10.329 @sf 4 r m (\)) s cmsy10.329 @sf 9 r m (\000) 10 (f) ks cmmi10.329 @sf m (\025) s cmsy10.329 @sf m (g) s cmr10.329 @sf 74 2626 p m (and) 15 (di\013ers) 16 (from) 14 (the) 15 (leading) ks cmmi10.329 @sf 17 r m (n) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 10 r m (1) s cmsy10.329 @sf 9 r m (\002) s cmmi10.329 @sf 10 r m (n) s cmsy10.329 @sf 11 r m (\000) s cmr10.329 @sf 10 r m (1) 14 (principal) 18 (submatrix) 15 (of) ks cmmi10.329 @sf 14 r m (H) s cmr10.329 @sf 19 r m (in) 16 (the) 15 (last) 15 (column) 16 (only) -3 (.) 19 (In) ks 74 2726 p m (fact,) 16 (if) 17 (w) 0 (e) 16 (let) ks cmmi10.329 @sf 17 r save [<6003C0E00620700610700E10700E087007083807043803803803803803801C01C01C01C01C01C0 1C01C00E00E00E00E00F00C00E80C0076180071F00070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 22 32 -2 0 26] 104 @pc restore cmmi8.300 @sf 383 2733 p m (n) s cmsy8.300 @sf m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 468 2726 p m (b) 1 (e) 18 (the) 16 (last) 17 (column) 17 (of) 17 (the) 16 (leading) 18 (principal) 19 (submatrix) 17 (of) ks cmmi10.329 @sf 16 r m (H) s cmr10.329 @sf 20 r m (of) 17 (order) ks cmmi10.329 @sf 16 r m (n) s cmsy10.329 @sf 11 r m (\000) s cmr10.329 @sf 12 r m (1,) s @eop 8 @bop0 8 @bop1 cmr10.329 @sf 1941 -77 p m (8) s 124 67 p m (Lastly) 16 (when) 16 (starting) 15 (from) 15 (a) 15 (real) 16 (initial) 18 (guess,) 15 (only) ks cmti10.329 @sf 17 r m (r) -1 (e) -2 (al) ks cmr10.329 @sf 13 r m (corrections) 16 (are) 16 (computed.) 21 (Therefore) ks 74 167 p m (the) 15 (imaginary) 15 (part) 13 (of) 14 (the) 15 (eigen) 0 (v) -2 (alue) 14 (should) 16 (b) 1 (e) 15 (p) 1 (erturb) 1 (ed) 16 (if) 15 (con) 0 (v) -1 (ergence) 13 (to) 14 (a) 14 (complex) 16 (eigenpair) ks 74 266 p m (is) 23 (to) 22 (b) 1 (e) 23 (made) 22 (p) 1 (ossible.) 43 (In) 23 (practice) 23 (w) 0 (e) 21 (ha) 0 (v) -1 (e) 21 (done) 23 (this) 22 (when) 23 (real) 23 (arithmetic) 23 (do) 1 (es) 22 (not) 22 (lead) ks 74 366 p m (to) 20 (con) 0 (v) 0 (ergence) 20 (after) 20 (a) 20 (pre-sp) 1 (eci\014e) 1 (d) 23 (n) 0 (um) 0 (b) 1 (er) 19 (of) 20 (corrections.) 38 (T) -3 (o) 19 (illustrate) 22 (the) 21 (situation) 22 (when) ks 74 466 p m (p) 1 (erturbing) 15 (the) 15 (imaginary) 14 (part) 14 (of) 13 (the) 14 (eigen) 0 (v) -2 (alue) 15 (is) 14 (necessary) 14 (w) 0 (e) 13 (men) 0 (tion) 14 (the) 14 (v) 0 (ery) 13 (simple) 15 (case) 15 (of) ks 74 565 p m (a) 15 (2) ks cmsy10.329 @sf 10 r m (\002) s cmr10.329 @sf 10 r m (2) 15 (real) 16 (matrix) 15 (whose) 15 (eigen) 0 (v) -2 (alues) 15 (are) 15 (complex.) ks cmbx10.432 @sf 74 750 p save [<00FF800007FFF0001FFFFC003F01FE007C007F007E007F80FF007FC0FF003FC0FF003FE0FF003F E07E003FE03C003FE000003FE000003FE000003FC000003FC000007F8000007F0000007E000001 FC0000FFF00000FFC0000007F0000001F8000001FC000000FE000000FF000000FF000F007F801F 807F803F807F803F807F803F807F803F80FF001F00FF000F81FE0007FFFC0003FFF000007F8000> 27 39 -3 0 34] 51 @pc restore 177 750 p m (De\015ation) s cmr10.329 @sf 74 936 p m (When) 19 (Newton's) 17 (metho) 1 (d) 18 (is) 19 (applied) 20 (to) 18 (solv) 0 (e) 17 (the) 18 (eigensystem) 19 (of) 17 (a) 18 (matrix) 18 (H,) 18 (it) 18 (is) 19 (p) 1 (ossible) 20 (that) ks 74 1036 p m (starting) 18 (from) 17 (distinct) 19 (initial) 20 (guesses) 18 (w) 0 (e) 17 (con) 0 (v) 0 (erge) 16 (to) 17 (the) 18 (same) 18 (eigenpair) 19 (of) ks cmmi10.329 @sf 18 r m (H) s cmr10.329 @sf 4 r m (.) 28 (In) 18 (fact) 18 (a) 18 (naiv) 0 (e) ks 74 1135 p m (implemen) 0 (tation) 11 (of) 10 (the) 11 (algorithm) 11 (in) 11 (section) 11 (2) 10 (ma) 0 (y) 9 (result) 11 (in) 12 (man) 0 (y) 9 (eigen) 0 (v) -2 (alues) 10 (b) 1 (eing) 12 (found) 11 (m) 0 (ultiple) ks 74 1235 p m (times) 11 (and) 11 (consequen) 0 (tly) 11 (some) 10 (eigen) 0 (v) -2 (alues) 11 (not) 10 (b) 1 (eing) 12 (found) 11 (at) 10 (all) 11 (since) 12 (the) 11 (n) 0 (um) 0 (b) 1 (er) 9 (of) 10 (initial) 13 (guesses) ks 74 1335 p m (is) s cmmi10.329 @sf 16 r m (n) s cmr10.329 @sf 16 r m (\(at) 14 (most\).) 19 (T) -3 (o) 14 (a) 0 (v) -1 (oid) 14 (this) 16 (un) 0 (w) 0 (an) -1 (t) -1 (ed) 14 (situation,) 15 (w) 0 (e) 14 (includ) 1 (ed) 17 (a) 15 (de\015ation) 16 (step) 16 (in) 16 (our) 15 (algorithm) ks 74 1434 p m (whic) 0 (h) 18 (is) 19 (designed) 19 (to) 18 (obtain) 18 (further) 18 (zeros) 18 (using) 19 (Newton's) 18 (metho) 1 (d.) 29 (In) 19 (this) 18 (section) 19 (w) 0 (e) 17 (prop) 1 (ose) ks 74 1534 p m (v) -2 (arious) 15 (metho) 1 (ds) 15 (for) 15 (doing) 15 (this.) 21 (Basically) -3 (,) 15 (these) 16 (metho) 1 (ds) 15 (fall) 16 (in) 0 (to) 14 (t) 0 (w) -1 (o) 13 (classes.) ks 124 1675 p m (Assume) 11 (that) 11 (when) 11 (algorithm) 11 (2.1) 10 (is) 12 (applied) 13 (to) 10 (the) ks cmmi10.329 @sf 11 r m (n) s cmsy10.329 @sf 2 r m (\002) s cmmi10.329 @sf 2 r m (n) s cmr10.329 @sf 11 r m (matrix) s cmmi10.329 @sf 11 r m (H) s cmr10.329 @sf 15 r m (\(w) 0 (e) 9 (will) 13 (assume) 11 (for) 10 (simplici) 1 (t) 0 (y) ks 74 1775 p m (that) 12 (it) 12 (has) 12 (no) 12 (m) 0 (ultiple) 13 (eigen) 0 (v) -2 (alues\)) 12 (the) 12 (eigenpair) 13 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 11 (of) ks cmmi10.329 @sf 11 r m (H) s cmr10.329 @sf 16 r m (is) 12 (obtained) 13 (more) 12 (than) 12 (once,) 13 (i.e.,) 12 (the) ks 74 1874 p m (algorithm) 17 (con) 0 (v) -1 (erges) 15 (to) 16 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 14 (from) 16 (sev) 0 (eral) 16 (distinct) 18 (initial) 19 (guesses) 16 (\() ks cmmi10.329 @sf m (x) s cmr8.300 @sf 1430 1851 p save [<0102040C1818303070606060E0E0E0E0E0E0E0E0E0E060606070303018180C040201> 8 34 -3 9 14] 40 @pc restore cmmi8.300 @sf 14 r m (i) s cmr8.300 @sf save [<8040203018180C0C0E060606070707070707070707070606060E0C0C181830204080> 8 34 -2 9 14] 41 @pc restore 1430 1887 p m (0) s cmmi10.329 @sf 1471 1874 p m (;) 8 (\025) ks cmr8.300 @sf 1519 1851 p save [<0102040C1818303070606060E0E0E0E0E0E0E0E0E0E060606070303018180C040201> 8 34 -3 9 14] 40 @pc restore cmmi8.300 @sf 14 r m (i) s cmr8.300 @sf save [<8040203018180C0C0E060606070707070707070707070606060E0C0C181830204080> 8 34 -2 9 14] 41 @pc restore 1519 1887 p m (0) s cmr10.329 @sf 1560 1874 p m (\)) s cmmi10.329 @sf m (;) 8 (i) ks cmr10.329 @sf 13 r m (=) 16 (1) ks cmmi10.329 @sf m (;) s cmr10.329 @sf 8 r m (.) 8 (.) 7 (.) ks cmmi10.329 @sf 1782 1874 p m (;) 8 (r) -1 (;) 8 (r) 13 (>) ks cmr10.329 @sf 16 r m (1.) s 74 1974 p m (Then) 13 (the) 12 (metho) 1 (ds) 12 (of) 12 (one) 12 (class) 13 (pro) 1 (duce) 13 (an) ks cmmi10.329 @sf 12 r m (n) s cmsy10.329 @sf 4 r m (\000) s cmr10.329 @sf 4 r m (1) s cmsy10.329 @sf 4 r m (\002) s cmmi10.329 @sf 4 r m (n) s cmsy10.329 @sf 4 r m (\000) s cmr10.329 @sf 4 r m (1) 13 (matrix) ks cmmi10.329 @sf 12 r m (H) s cmsy8.300 @sf 1337 1959 p m (0) s cmr10.329 @sf 1360 1974 p m (suc) 0 (h) 12 (that) ks cmmi10.329 @sf 11 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmsy8.300 @sf 1643 1959 p m (0) s cmr10.329 @sf 1653 1974 p m (\)) 13 (=) ks cmmi10.329 @sf 13 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmr10.329 @sf 4 r m (\)) s cmsy10.329 @sf 4 r m (\000) 4 (f) ks cmmi10.329 @sf m (\025) s cmsy10.329 @sf m (g) s cmr10.329 @sf -1 r m (.) s 74 2074 p m (Algorithm) 16 (2.1) 15 (is) 17 (then) 16 (applied) 18 (to) ks cmmi10.329 @sf 15 r m (H) s cmsy8.300 @sf 776 2059 p m (0) s cmr10.329 @sf 803 2074 p m (starting) 15 (from) ks cmmi10.329 @sf 15 r m (r) s cmsy10.329 @sf 12 r m (\000) s cmr10.329 @sf 11 r m (1) 15 (of) 16 (these) 16 (initial) 18 (guesses;) 16 (indeed,) 17 (w) 0 (e) 15 (can) ks 74 2173 p m (exp) 1 (ect) ks cmmi10.329 @sf 16 r m (r) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 9 r m (1) 15 (eigenpairs) 16 (of) ks cmmi10.329 @sf 14 r m (H) s cmr10.329 @sf 19 r m (to) 14 (ha) 0 (v) -1 (e) 13 (b) 1 (een) 16 (missed.) 20 (If) 16 (the) 14 (algorithm) 15 (con) 0 (v) 0 (erges,) 12 (then) 15 (it) 15 (will) 17 (do) 14 (so) ks 74 2273 p m (to) 15 (eigenpairs) 16 (di\013eren) 0 (t) 15 (from) 14 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 13 (since) ks cmmi10.329 @sf 17 r m (\025) s cmr10.329 @sf 14 r m (is) 16 (no) 15 (longer) 16 (in) 16 (the) 15 (sp) 1 (ectrum.) ks 124 2414 p m (The) 15 (other) 14 (class) 15 (of) 15 (metho) 1 (ds) 14 (will) 17 (reapply) 15 (algorithm) 15 (2.1) 14 (to) 14 (the) 15 (original) 15 (matrix) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 18 r m (starting) 14 (from) ks cmmi10.329 @sf 74 2514 p m (r) s cmsy10.329 @sf 14 r m (\000) s cmr10.329 @sf 14 r m (1) 19 (of) 19 (the) 20 (initial) 22 (guesses) 20 (men) 0 (tioned) 19 (ab) 1 (o) 0 (v) 0 (e,) 18 (but) 20 (will) 22 (force) 19 (con) 0 (v) 0 (ergence) 18 (a) 0 (w) -1 (a) -1 (y) 17 (from) 19 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 18 (b) 0 (y) ks 74 2613 p m (ensuring) 16 (at) 15 (all) 16 (steps) 15 (that) 15 (the) 15 (curren) 0 (t) 14 (eigen) 0 (v) 0 (ector) 13 (forms) 15 (a) 15 (non) 15 (zero) 15 (angle) 16 (with) ks cmmi10.329 @sf 15 r m (x) s cmr10.329 @sf m (.) s @eop 7 @bop0 7 @bop1 cmr10.329 @sf 1941 -77 p m (7) s 74 67 p m (pro) 1 (cessors.) 24 (Ho) 0 (w) 0 (ev) -1 (er,) 14 (care) 17 (m) 0 (ust) 15 (b) 1 (e) 18 (exercised) 18 (if) 17 (the) 17 (algorithm) 17 (is) 17 (to) 16 (b) 1 (e) 17 (k) 0 (ept) 16 (e\016cien) 0 (t.) 24 (More) 16 (will) ks 74 167 p m (b) 1 (e) 18 (said) 18 (ab) 1 (out) 17 (this) 18 (in) 18 (section) 18 (6) 17 (\(w) 0 (ork) 15 (estimate\).) 26 (In) 18 (practice,) 18 (the) 17 (original) 18 (matrix) 17 (will) 19 (b) 1 (e) 18 (dense) ks 74 266 p m (and) 18 (w) 0 (e) 17 (will) 20 (need) 18 (to) 18 (reduce) 18 (it) 19 (to) 17 (upp) 1 (er-Hessen) 0 (b) 1 (erg) 18 (form) 18 (as) 17 (a) 18 (\014rst) 17 (step;) 19 (this) 19 (can) 18 (b) 1 (e) 18 (done) 19 (in) 18 (a) ks 74 366 p m (stable) 13 (fashion) 13 (through) 13 (a) 12 (sequence) 14 (of) 13 (orthogonal) 11 (similarit) 0 (y) 13 (transformations,) 12 (although) 13 (elemen) 0 (tary) ks 74 466 p m (transformations) 14 (can) 15 (also) 15 (b) 1 (e) 16 (used) 16 (with) 16 (con\014dence) 16 (as) 15 (in) 16 (R) 0 (G) 14 ([) 0 (15) ks 1315 466 p m (].) s 124 607 p m (A) 12 (brief) 13 (study) 12 (of) 12 (some) 12 (su\016cien) 0 (t) 12 (conditions) 13 (guaran) 0 (teeing) 11 (the) 12 (con) 0 (v) 0 (ergence) 11 (of) 11 (our) 12 (metho) 1 (d) 13 (will) 13 (b) 1 (e) ks 74 706 p m (touc) 0 (hed) 11 (up) 1 (on) 13 (in) 13 (section) 12 (4.) 19 (No) 0 (w) 10 (assuming) 12 (that) 12 (the) 12 (algorithm) 12 (con) 0 (v) -1 (erges,) 10 (it) 13 (could) 13 (happ) 1 (en) 13 (that) 11 (the) ks 74 806 p m (same) 14 (eigenpair) 15 (of) ks cmmi10.329 @sf 13 r m (H) s cmr10.329 @sf 18 r m (is) 14 (obtained) 15 (more) 13 (than) 14 (once:) 19 (i.e.,starting) 13 (from) 13 (t) 0 (w) -1 (o) 12 (\(or) 13 (more\)) 13 (distinct) 15 (initial) ks 74 906 p m (appro) 0 (ximations) 15 (Newton's) 16 (metho) 1 (d) 16 (con) 0 (v) 0 (erg) -1 (es) 15 (to) 15 (the) 16 (same) 16 (eigenpair) 18 (of) ks cmmi10.329 @sf 16 r m (H) s cmr10.329 @sf 4 r m (.) 22 (W) -3 (e) 15 (ha) 0 (v) -1 (e) 15 (in) 0 (v) 0 (estigated) ks 74 1005 p m (metho) 1 (ds) 15 (to) 15 (obtain) 15 (further) 15 (eigenpairs) 17 (of) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 18 r m (should) 17 (this) 15 (happ) 1 (en) 17 (\(see) 15 (section) 15 (3\).) ks 124 1146 p m (W) -3 (e) 19 (end) 20 (this) 20 (section) 20 (with) 20 (some) 19 (implemen) 0 (tational) 20 (details.) 34 (Our) 20 (algorithm) 19 (will) 21 (accept) 20 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) s 74 1246 p m (as) 17 (an) 17 (eigenpair) 18 (of) ks cmmi10.329 @sf 17 r m (H) s cmr10.329 @sf 20 r m (when) s cmsy10.329 @sf 18 r m (k) s cmmi10.329 @sf m (H) 4 (x) ks cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 12 r m (\025x) s cmsy10.329 @sf m (k) s cmmi10.329 @sf m (=) s cmsy10.329 @sf m (k) s cmmi10.329 @sf m (x) s cmsy10.329 @sf m (kk) s cmmi10.329 @sf m (H) s cmsy10.329 @sf 3 r m (k) s cmmi10.329 @sf 14 r save [<000001C00000078000001E00000078000001E00000078000000E00000038000000F0000003C000 000F0000003C000000F0000000F00000003C0000000F00000003C0000000F0000000380000000E 0000000780000001E0000000780000001E0000000780000001C0> 26 26 -4 2 35] 60 @pc restore 51 r save [<0F00188038403820382038201C101C001C001C000E000E000E000E0007000700070007000380FF F80380038001C001C001C001C000E000C0> 13 28 -1 0 16] 116 @pc restore 16 r m (o) s save [<38006400E200E200E200E200710070007000700038003800380038001C001C001C001C000E000E 000E000E00070007000700070003800380038003801FC003C0> 10 32 -2 0 14] 108 @pc restore cmr10.329 @sf 15 r m (,) 17 (where) ks cmmi10.329 @sf 17 r save [<0F00188038403820382038201C101C001C001C000E000E000E000E0007000700070007000380FF F80380038001C001C001C001C000E000C0> 13 28 -1 0 16] 116 @pc restore 16 r m (o) s save [<38006400E200E200E200E200710070007000700038003800380038001C001C001C001C000E000E 000E000E00070007000700070003800380038003801FC003C0> 10 32 -2 0 14] 108 @pc restore cmr10.329 @sf 32 r m (is) 17 (some) 17 (sp) 1 (eci\014ed) 19 (tolerance) 18 (of) ks 74 1346 p m (order) s cmmi10.329 @sf 16 r m (\017) s cmr10.329 @sf m (,) 15 (the) 16 (mac) 0 (hine) 16 (unit) 16 (roundo\013.) 21 (Under) 16 (these) 16 (conditions) 17 (\([) 0 (8) ks 1320 1346 p m (]\),) 15 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 13 (is) 16 (an) 16 (exact) 15 (eigenpair) 18 (of) ks 74 1445 p m (a) 15 (matrix) 15 (obtained) 16 (from) ks cmmi10.329 @sf 14 r m (H) s cmr10.329 @sf 19 r m (b) 0 (y) 14 (a) 15 (sligh) 0 (t) 15 (p) 1 (erturbation:) 20 (Indeed,) ks 789 1581 p m (\() s cmmi10.329 @sf m (H) s cmr10.329 @sf 13 r m (+) s 940 1551 p m (1) s 908 1571 p 86 2 ru cmmi10.329 @sf 908 1612 p m (x) s cmmi8.300 @sf 934 1600 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 968 1612 p m (x) s 999 1581 p m (r) 1 (x) ks cmmi8.300 @sf 1047 1563 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 1080 1581 p m (\)) s cmmi10.329 @sf m (x) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (\025x;) s cmr10.329 @sf 74 1716 p m (where) s cmmi10.329 @sf 16 r m (r) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (\025x) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (H) 4 (x) ks cmr10.329 @sf m (.) s 124 1857 p m (Starting) 15 (from) 14 (t) 0 (w) -1 (o) 13 (complex) 16 (conjugate) 15 (initial) 18 (appro) 0 (ximations,) 14 (Newton's) 14 (metho) 1 (d) 16 (will) 17 (con) 0 (v) -1 (erge) ks 74 1957 p m (to) 15 (t) 0 (w) -1 (o) 13 (complex) 16 (conjugate) 15 (zeros) 15 (of) ks cmmi10.329 @sf 14 r save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 794 1964 p m (s) s cmr10.329 @sf 813 1957 p m (,) 15 (or) 15 (the) 15 (same) 15 (real) 15 (zero.) 20 (T) -3 (o) 14 (pro) 0 (v) -1 (e) 14 (this) 16 (it) 15 (su\016ces) 16 (to) 14 (lo) 1 (ok) 16 (at) ks 74 2056 p m (one) 15 (iteration) 14 (and) 15 (sho) 0 (w) 13 (that) 14 (when) 14 (the) 15 (curren) 0 (t) 13 (appro) 0 (ximations) 14 (are) 14 (complex) 15 (conjugate,) 14 (Newton's) ks 74 2156 p m (metho) 1 (d) 17 (yields) 18 (t) 0 (w) -1 (o) 14 (complex) 18 (conjugate) 16 (corrections,) 17 (or) 16 (the) 17 (same) 16 (real) 17 (correction.) 24 (The) 17 (system) 16 (w) 0 (e) ks 74 2256 p m (ha) 0 (v) 0 (e) 13 (to) 15 (solv) 0 (e) 14 (starting) 14 (from) 15 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 13 (is) 16 (\(1\).) 19 (F) -3 (or) 13 (\() 3 (\026) ks cmmi10.329 @sf 982 2256 p m (x) s 1008 2256 p m (;) s cmr10.329 @sf 1030 2245 p m (\026) s cmmi10.329 @sf 1029 2257 p m (\025) s cmr10.329 @sf 1055 2256 p m (\)) 14 (this) 16 (b) 1 (ecomes) ks cmex10.300 @sf 658 2319 p save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pc restore cmmi10.329 @sf 712 2364 p m (H) s cmsy10.329 @sf 13 r m (\000) s cmr10.329 @sf 811 2353 p m (\026) s cmmi10.329 @sf 809 2365 p m (\025) s 835 2364 p m (I) s cmsy10.329 @sf 900 2364 p m (\000) s cmr10.329 @sf 3 r m (\026) s cmmi10.329 @sf 935 2364 p m (x) s 761 2419 p m (e) s cmmi8.300 @sf 782 2404 p m (T) s 782 2430 p m (s) s cmr10.329 @sf 920 2419 p m (0) s cmex10.300 @sf 983 2319 p save [ 21 124 -1 122 33] 33 @pc restore 1023 2319 p save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pc restore cmmi10.329 @sf 1078 2364 p m (y) s cmsy8.300 @sf 1102 2348 p m (0) s cmmi10.329 @sf 1077 2419 p m (\026) s cmsy8.300 @sf 1104 2404 p m (0) s cmex10.300 @sf 1136 2319 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1182 2391 p m (=) s cmex10.300 @sf 1230 2319 p save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pc restore cmr10.329 @sf 1286 2364 p m (\026) s cmmi10.329 @sf 1284 2364 p m (r) s cmr10.329 @sf 1283 2419 p m (0) s cmex10.300 @sf 1327 2319 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1367 2391 p m (:) s cmr10.329 @sf 74 2526 p m (But) 18 (this) 18 (is) 19 (the) 18 (same) 17 (linear) 19 (system) 18 (obtained) 18 (when) 18 (the) 18 (conjugate) 18 (of) 17 (b) 1 (oth) 18 (sides) 19 (in) 19 (\(1\)) 17 (is) 18 (tak) 0 (en,) ks 74 2626 p m (kno) 0 (wing) 17 (that) 17 (the) 18 (matrix) 18 (is) 18 (real) 19 (and) 18 (hence) ks 961 2616 p m (\026) s cmmi10.329 @sf 949 2627 p m (H) s cmr10.329 @sf 1007 2626 p m (=) s cmmi10.329 @sf 18 r m (H) s cmr10.329 @sf 4 r m (.) 27 (Therefore:) ks cmmi10.329 @sf 26 r m (y) s cmsy8.300 @sf 1396 2611 p m (0) s cmr10.329 @sf 1424 2626 p m (=) 21 (\026) ks cmmi10.329 @sf 1477 2626 p m (y) s cmr10.329 @sf 1519 2626 p m (and) s cmmi10.329 @sf 18 r m (\026) s cmsy8.300 @sf 1637 2611 p m (0) s cmr10.329 @sf 1666 2626 p m (=) 21 (\026) ks cmmi10.329 @sf 1718 2626 p m (\026) s cmr10.329 @sf 1746 2626 p m (.) 28 (This) 18 (will) ks 74 2726 p m (allo) 0 (w) 15 (signi\014can) 0 (t) 15 (sa) 0 (vings) 14 (in) 16 (the) 15 (computations.) ks @eop 6 @bop0 1.000000 /cmmi9.300 @newfont cmmi9.300 @sf [<8040202010101070F0F060> 4 11 -3 7 11] 59 @dc 6 @bop1 cmr10.329 @sf 1941 -77 p m (6) s 74 67 p m (The) 15 (quan) 0 (tities) 15 (that) 14 (v) -2 (ary) 14 (with) ks cmmi10.329 @sf 15 r m (k) s cmr10.329 @sf 16 r m (in) 15 (this) 15 (expression) 16 (for) 14 (the) 15 (rate) 14 (of) 15 (c) 0 (hange) 14 (of) ks cmmi10.329 @sf 14 r m (\025) s cmr10.329 @sf m (,) 14 (are) 15 (the) 15 (factors) 13 (in) ks 74 167 p m (the) 15 (n) 0 (umerator.) 18 (Ho) 0 (w) -1 (ev) -1 (er,) ks cmsy10.329 @sf 13 r m (j) s cmmi10.329 @sf m (\013) s cmsy10.329 @sf m (j) s cmmi10.329 @sf m (;) s cmsy10.329 @sf 8 r m (j) s cmmi10.329 @sf m (y) s cmmi8.300 @sf 698 174 p m (k) s cmr8.300 @sf 1 r m (+1) s cmsy10.329 @sf 763 167 p m (j) s cmr10.329 @sf 14 r m (and) s cmsy10.329 @sf 15 r m (j) s cmmi10.329 @sf m (x) s cmmi8.300 @sf 917 174 p m (k) s cmsy10.329 @sf 938 167 p m (j) s cmr10.329 @sf 15 r m (are) 14 (not) 15 (really) 16 (indep) 1 (enden) 1 (t) 15 (of) 14 (one) 15 (another:) 20 (indeed,) ks 74 266 p m (if) s cmmi10.329 @sf 17 r m (\013) s cmr10.329 @sf 14 r m (=) 15 (0,) 16 (then) 16 (at) 16 (least) 16 (one) 17 (of) ks cmmi10.329 @sf 15 r m (y) s cmmi8.300 @sf 689 273 p m (k) s cmr8.300 @sf 1 r m (+1) s cmr10.329 @sf 772 266 p m (or) s cmmi10.329 @sf 16 r m (x) s cmmi8.300 @sf 855 273 p m (k) s cmr10.329 @sf 893 266 p m (is) 16 (zero.) 23 (Hence) 17 (for) ks cmmi10.329 @sf 16 r m (\013) s cmr10.329 @sf 16 r m (small,) 17 (w) 0 (e) 15 (can) 16 (exp) 1 (ect) 17 (one) 17 (of) ks cmmi10.329 @sf 15 r m (y) s cmmi8.300 @sf 1897 273 p m (k) s cmr8.300 @sf 1 r m (+1) s cmr10.329 @sf 74 366 p m (and) s cmmi10.329 @sf 14 r m (x) s cmmi8.300 @sf 187 373 p m (k) s cmr10.329 @sf 222 366 p m (to) 12 (b) 1 (e) 15 (corresp) 1 (ondingly) 15 (small,) 14 (since) 15 (the) 13 (comp) 1 (onen) 0 (ts) 13 (of) 13 (the) 13 (eigen) 0 (v) 0 (ectors) 12 (v) -2 (ary) 12 (con) 0 (tin) 0 (uously) -3 (.) ks 74 466 p m (Therefore,) 14 (w) 0 (e) 13 (ha) 0 (v) 0 (e) 12 (found) 15 (it) 15 (su\016cien) 0 (t) 14 (in) 15 (practice) 15 (to) 14 (lo) 1 (ok) 15 (for) 14 (the) 14 (smallest) 15 (sub) 1 (diagonal) 16 (en) 0 (try) 13 (in) 15 (a) ks 74 565 p m (pre-sp) 1 (eci\014ed) 16 (range,) 13 (and) 13 (accept) 14 (it) 13 (as) 13 (the) 14 (sub) 1 (diagonal) 14 (en) 0 (try) 12 (\(in) 14 (that) 13 (range\)) 12 (with) 14 (resp) 1 (ect) 14 (to) 12 (whic) 0 (h) ks 74 665 p m (the) 15 (eigen) 0 (v) -2 (alues) 16 (of) 14 (the) 16 (matrix) 14 (are) 15 (least) 16 (sensitiv) 0 (e,) 15 (and) 15 (set) 15 (it) 15 (equal) 16 (to) 15 (zero.) ks 124 806 p m (An) 15 (outline) 17 (of) 15 (the) 15 (algorithm) 15 (follo) 0 (ws:) ks cmbx10.329 @sf 74 985 p save [ 35 31 -2 0 40] 65 @pc restore 40 r save [ 11 32 -2 0 14] 108 @pc restore 14 r save [<01FF000FFFE03F01F878003C78003CF0001EF0001EF0001E70003E3C007C1FFFFC07FFF80FFFF0 1FFF801C000018000018000009FC000FFF000F07801E03C03E03E03E03E03E03E03E03E03E03E0 1E03DE0F079E07FFFE01FC3C> 23 30 -1 10 26] 103 @pc restore 26 r save [<01FF0007FFC01F83F03E00F83E00F87C007C7C007CFC007EFC007EFC007EFC007EFC007EFC007E 7C007C7C007C3E00F83E00F81F83F007FFC001FF00> 23 20 -1 0 26] 111 @pc restore 26 r save [ 18 20 -2 0 22] 114 @pc restore 22 r save [ 11 33 -2 0 14] 105 @pc restore 14 r save [<01F003F807CC0F860F860F860F860F860F800F800F800F800F800F800F800F800F800F80FFFCFF FC3F800F800780038003800380018001800180> 15 29 -1 0 20] 116 @pc restore 20 r save [ 24 32 -3 0 29] 104 @pc restore 29 r save [ 39 20 -3 0 46] 109 @pc restore 62 r save [ 19 29 -3 0 26] 50 @pc restore 26 r m (.) s save [ 17 29 -4 0 26] 49 @pc restore cmti10.329 @sf 416 985 p m (Given) 21 (an) 21 (upp) -1 (er-Hessenb) -2 (er) -2 (g) 19 (matrix) ks cmmi10.329 @sf 22 r m (H) s cmti10.329 @sf 4 r m (,) 22 (the) 22 (fol) 2 (lowing) 20 (algorithm) 22 (c) -1 (omputes) 21 (the) ks 74 1084 p m (eigensystems) 21 (of) 22 (two) 23 (submatric) -1 (es) 21 (of) ks cmmi10.329 @sf 22 r m (H) s cmti10.329 @sf 26 r m (and) 22 (uses) 22 (them) 23 (as) 22 (initial) 22 (guesses) 21 (for) 22 (starting) 22 (Newton) ks 74 1184 p m (iter) -1 (ations) 15 (for) 16 (determining) 16 (the) 17 (eigensystem) 15 (of) ks cmmi10.329 @sf 16 r m (H) s cmti10.329 @sf 4 r m (.) s 313 1375 p save [ 24 26 -2 0 29] 68 @pc restore 29 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [ 29 16 -1 0 32] 109 @pc restore 32 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 31 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [<07CFC00C2E001C1E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E00 1C0E001C0E00FC7E00> 18 16 -1 0 21] 117 @pc restore 21 r save [<10F0001B0C001E07001C03001C03801C01C01C01C01C01C01C01C01C01C01C01C01C01801C0380 1E07001F0E001CF8001C00001C00001C00001C00001C00001C00001C00001C00001C0000FC0000> 18 26 -1 0 21] 98 @pc restore 22 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore 21 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<07E0381C6006C003C003C003C003600F1FFE3FFC3FF07000600020002FC0186030307038703870 387038303018730FCE> 16 24 -1 8 19] 103 @pc restore 19 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 20 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 9 26 0 0 10] 108 @pc restore 26 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 9 26 0 0 10] 108 @pc restore 10 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 29 16 -1 0 32] 109 @pc restore 32 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore cmmi9.300 @sf 27 r save [<1F038020C640603E00E00E00C00E00E00E00E00F00E00E80E00E80600E40700E40300E20381C20 1C182006381003E000> 20 16 -2 0 25] 11 @pc restore 38 r save [<010040000180C0000380E0000380E00003C1E0000741D000074190000F2398000E2388000E2308 001E170C001C1704001C160400380E06003C0E0700FF3F9F80> 25 16 -1 0 28] 119 @pc restore 28 r save [ 18 26 -1 0 21] 104 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore cmmi9.300 @sf 30 r save [ 30 26 -2 0 32] 72 @pc restore 45 r save [ 25 10 -2 -4 30] 61 @pc restore cmex10.300 @sf 1089 1305 p save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pc restore cmmi9.300 @sf 1148 1337 p save [ 30 26 -2 0 32] 72 @pc restore cmr6.300 @sf 1180 1341 p m (11) s 1238 1363 p 2 59 ru cmmi9.300 @sf 1277 1337 p save [ 30 26 -2 0 32] 72 @pc restore cmr6.300 @sf 1309 1341 p m (12) s 1122 1365 p 257 2 ru 1238 1409 p 2 46 ru cmr10.432 @sf 1159 1420 p m (0) s cmmi9.300 @sf 1202 1384 p save [<1F038020C640603E00E00E00C00E00E00E00E00F00E00E80E00E80600E40700E40300E20381C20 1C182006381003E000> 20 16 -2 0 25] 11 @pc restore 1238 1426 p 2 59 ru 1277 1412 p save [ 30 26 -2 0 32] 72 @pc restore cmr6.300 @sf 1309 1416 p m (22) s cmex10.300 @sf 1379 1305 p save [ 21 124 -1 122 33] 33 @pc restore cmmi9.300 @sf 1418 1375 p m (;) s 34 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [ 18 26 -1 0 21] 104 @pc restore 21 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [<07CFC00C2E001C1E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E00 1C0E001C0E00FC7E00> 18 16 -1 0 21] 117 @pc restore 21 r save [ 9 26 0 0 10] 108 @pc restore 10 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore 35 r save [<10F0001B0C001E07001C03001C03801C01C01C01C01C01C01C01C01C01C01C01C01C01801C0380 1E07001F0E001CF8001C00001C00001C00001C00001C00001C00001C00001C00001C0000FC0000> 18 26 -1 0 21] 98 @pc restore 22 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 31 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [ 18 23 -1 7 21] 112 @pc restore 21 r save [ 9 26 0 0 10] 108 @pc restore 10 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [<8040202010101070F0F060000000000000000060F0F060> 4 23 -3 7 11] 59 @pc restore 313 1474 p save [ 24 26 -2 0 29] 68 @pc restore 29 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [ 29 16 -1 0 32] 109 @pc restore 32 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 31 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 20 r save [ 9 26 0 0 10] 108 @pc restore 25 r save [<07E0381C6006C003C003C003C003600F1FFE3FFC3FF07000600020002FC0186030307038703870 387038303018730FCE> 16 24 -1 8 19] 103 @pc restore 19 r save [<07CFC00C2E001C1E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E00 1C0E001C0E00FC7E00> 18 16 -1 0 21] 117 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 29 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFC00E000E000E000E 000E000E000E100738031801F0> 13 26 0 0 12] 102 @pc restore 12 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 29 16 -1 0 32] 109 @pc restore 45 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<07E0381C6006C003C003C003C003600F1FFE3FFC3FF07000600020002FC0186030307038703870 387038303018730FCE> 16 24 -1 8 19] 103 @pc restore 19 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [<780000E40000E20000E1000001000001000000800000800001C00001C00001C00003A00003A000 0790000710000710000E08000E08001E0C001C04001C04003C0600FF1F80> 17 23 -1 7 20] 121 @pc restore 20 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 29 16 -1 0 32] 109 @pc restore 32 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 30 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFC00E000E000E000E 000E000E000E100738031801F0> 13 26 0 0 12] 102 @pc restore 24 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 18 26 -1 0 21] 104 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 30 r save [ 14 24 -2 0 19] 50 @pc restore 32 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore 21 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<07E0381C6006C003C003C003C003600F1FFE3FFC3FF07000600020002FC0186030307038703870 387038303018730FCE> 16 24 -1 8 19] 103 @pc restore 19 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 20 r save [ 9 26 0 0 10] 108 @pc restore 25 r save [<10F0001B0C001E07001C03001C03801C01C01C01C01C01C01C01C01C01C01C01C01C01801C0380 1E07001F0E001CF8001C00001C00001C00001C00001C00001C00001C00001C00001C0000FC0000> 18 26 -1 0 21] 98 @pc restore 21 r save [ 9 26 0 0 10] 108 @pc restore 10 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 20 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [ 18 26 -1 0 20] 107 @pc restore 20 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore cmmi9.300 @sf 28 r save [ 30 26 -2 0 32] 72 @pc restore cmr6.300 @sf 1506 1478 p m (11) s 1552 1474 p save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore cmmi9.300 @sf 34 r save [ 30 26 -2 0 32] 72 @pc restore cmr6.300 @sf 1658 1478 p m (22) s 1690 1474 p save [<8040202010101070F0F060000000000000000060F0F060> 4 23 -3 7 11] 59 @pc restore 313 1574 p save [ 20 26 -2 0 25] 70 @pc restore 23 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 27 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [ 18 26 -1 0 21] 104 @pc restore 33 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 20 r save [ 9 26 0 0 10] 108 @pc restore 25 r save [<07E0381C6006C003C003C003C003600F1FFE3FFC3FF07000600020002FC0186030307038703870 387038303018730FCE> 16 24 -1 8 19] 103 @pc restore 19 r save [<07CFC00C2E001C1E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E00 1C0E001C0E00FC7E00> 18 16 -1 0 21] 117 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 29 r save [<00800100020004000C00080018003000300030006000600060006000E000E000E000E000E000E0 00E000E000E000E0006000600060006000300030003000180008000C000400020001000080> 9 38 -3 10 15] 40 @pc restore cmmi9.300 @sf 15 r save [ 18 26 -2 0 22] 21 @pc restore cmmi6.300 @sf 717 1578 p m (i) s cmmi9.300 @sf 730 1574 p m (;) s 6 r save [<70F0CB08EB04C70207020702038003800380038041C041C041C321E711A30F1E> 16 16 -2 0 22] 120 @pc restore cmmi6.300 @sf 769 1578 p m (i) s 782 1574 p save [<8000400020001000180008000C0006000600060003000300030003000380038003800380038003 80038003800380038003000300030003000600060006000C00080018001000200040008000> 9 38 -2 10 15] 41 @pc restore 28 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 31 r save [<07CFC00C2E001C1E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E00 1C0E001C0E00FC7E00> 18 16 -1 0 21] 117 @pc restore 21 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [ 9 26 0 0 10] 108 @pc restore 23 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<00800001C00001C00001C00003A00003A0000790000710000710000E08000E08001E0C001C0400 1C04003C0600FF1F80> 17 16 -1 0 20] 118 @pc restore 20 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<07E0381C6006C003C003C003C003600F1FFE3FFC3FF07000600020002FC0186030307038703870 387038303018730FCE> 16 24 -1 8 19] 103 @pc restore 19 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<60F0F060000000000000000060F0F060> 4 16 -3 0 11] 58 @pc restore cmex10.300 @sf 454 1788 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmmi9.300 @sf 505 1822 p save [ 30 26 -2 0 32] 72 @pc restore 43 r save [ 23 2 -3 -8 30] 0 @pc restore cmmi9.300 @sf 39 r save [ 18 26 -2 0 22] 21 @pc restore cmmi6.300 @sf 609 1826 p m (i) s cmmi9.300 @sf 622 1822 p save [ 17 26 -1 0 17] 73 @pc restore 683 1822 p save [ 23 2 -3 -8 30] 0 @pc restore cmmi9.300 @sf 30 r save [<70F0CB08EB04C70207020702038003800380038041C041C041C321E711A30F1E> 16 16 -2 0 22] 120 @pc restore cmmi6.300 @sf 735 1826 p m (i) s cmmi9.300 @sf 552 1868 p save [<1F0030C06020E010E008E000E000E000E000FFC070207010381018100E1003E0> 13 16 -2 0 18] 101 @pc restore cmmi6.300 @sf 570 1853 p save [<7FE00006000003000003000003000003000001800001800001800001800000C00080C04080C040 40C0404060403060C03FFFC0> 18 17 -2 0 18] 84 @pc restore 570 1875 p m (s) s 706 1868 p save [<078018603030703860186018E01CE01CE01CE01CE01CE01CE01CE01CE01CE01CE01CE01C601860 183030303018600780> 14 24 -2 0 19] 48 @pc restore cmex10.300 @sf 769 1788 p save [ 20 99 -1 97 31] 19 @pc restore 806 1788 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmmi9.300 @sf 859 1823 p save [<3C004300C180E0C060E0006000700FF01C7018383838383838381C1C1C1C1C1C0E1C8E0E8E0E87 0E470E26071C06> 16 23 -2 7 19] 121 @pc restore 857 1868 p save [ 18 23 -2 7 23] 22 @pc restore cmex10.300 @sf 901 1788 p save [ 20 99 -1 97 31] 19 @pc restore 942 1845 p save [ 25 10 -2 -4 30] 61 @pc restore cmex10.300 @sf 983 1788 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmmi9.300 @sf 1034 1823 p save [<3000700038003800380038001C001C001C001C008E008E008E188F384D983870> 13 16 -2 0 17] 114 @pc restore cmmi6.300 @sf 1051 1827 p m (i) s 1040 1868 p save [<078018603030703860186018E01CE01CE01CE01CE01CE01CE01CE01CE01CE01CE01CE01C601860 183030303018600780> 14 24 -2 0 19] 48 @pc restore cmex10.300 @sf 1085 1788 p save [ 20 99 -1 97 31] 19 @pc restore 1122 1845 p save [<8040202010101070F0F060000000000000000060F0F060> 4 23 -3 7 11] 59 @pc restore cmmi9.300 @sf 17 r save [ 18 26 -2 0 22] 21 @pc restore cmr6.300 @sf 1161 1849 p save [ 6 18 0 0 8] 105 @pc restore 1183 1845 p save [<0400000004000000080000001000000020000000FFFFFFFFFFFFFFFF2000000010000000080000 000400000004000000> 32 12 -3 -3 38] 32 @pc restore cmmi9.300 @sf 49 r save [ 18 26 -2 0 22] 21 @pc restore cmr6.300 @sf 1254 1849 p save [ 6 18 0 0 8] 105 @pc restore 1274 1845 p save [<000C0000000C0000000C0000000C0000000C0000000C0000000C0000000C0000000C0000000C00 00000C0000000C0000FFFFFF80FFFFFF80000C0000000C0000000C0000000C0000000C0000000C 0000000C0000000C0000000C0000000C0000000C0000000C0000> 25 26 -2 4 30] 43 @pc restore cmmi9.300 @sf 39 r save [ 18 23 -2 7 23] 22 @pc restore 44 r save [<8040202010101070F0F060000000000000000060F0F060> 4 23 -3 7 11] 59 @pc restore 28 r save [ 18 16 -1 0 20] 120 @pc restore cmr6.300 @sf 1405 1849 p save [ 6 18 0 0 8] 105 @pc restore 1427 1845 p save [<0400000004000000080000001000000020000000FFFFFFFFFFFFFFFF2000000010000000080000 000400000004000000> 32 12 -3 -3 38] 32 @pc restore 49 r save [ 18 16 -1 0 20] 120 @pc restore cmr6.300 @sf 1496 1849 p save [ 6 18 0 0 8] 105 @pc restore 1515 1845 p save [<000C0000000C0000000C0000000C0000000C0000000C0000000C0000000C0000000C0000000C00 00000C0000000C0000FFFFFF80FFFFFF80000C0000000C0000000C0000000C0000000C0000000C 0000000C0000000C0000000C0000000C0000000C0000000C0000> 25 26 -2 4 30] 43 @pc restore 39 r save [<780000E40000E20000E1000001000001000000800000800001C00001C00001C00003A00003A000 0790000710000710000E08000E08001E0C001C04001C04003C0600FF1F80> 17 23 -1 7 20] 121 @pc restore 20 r save [<8040202010101070F0F060000000000000000060F0F060> 4 23 -3 7 11] 59 @pc restore 313 2024 p save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore 21 r save [<8040202010101070F0F060000000000000000060F0F060> 4 23 -3 7 11] 59 @pc restore 313 2123 p save [<003F0001C0C00300300E00081C00081C0004380004780002700002700002F00000F00000F00000 F00000F00000F000007000027000027800023800061C00061C000E0E001E03002E01C0C6003F02> 23 26 -2 0 28] 67 @pc restore 28 r save [ 18 26 -1 0 21] 104 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [ 18 26 -1 0 20] 107 @pc restore 32 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFC00E000E000E000E 000E000E000E100738031801F0> 13 26 0 0 12] 102 @pc restore 12 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 28 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore 21 r save [<07CFC00C2E001C1E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E00 1C0E001C0E00FC7E00> 18 16 -1 0 21] 117 @pc restore 21 r save [ 18 23 -1 7 21] 112 @pc restore 21 r save [ 9 26 0 0 10] 108 @pc restore 10 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 30 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore 35 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<7F9FE00E07000E07000E07000E07000E07000E07000E07000E07000E07000E07000E07000E0700 0E07000E0700FFFF000E07000E07000E07000E07000E07000E070006070007070003870000FF00> 19 26 0 0 21] 13 @pc restore 21 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 31 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFC00E000E000E000E 000E000E000E100738031801F0> 13 26 0 0 12] 102 @pc restore 25 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<780000E40000E20000E1000001000001000000800000800001C00001C00001C00003A00003A000 0790000710000710000E08000E08001E0C001C04001C04003C0600FF1F80> 17 23 -1 7 20] 121 @pc restore 20 r save [<8040202010101070F0F060000000000000000060F0F060> 4 23 -3 7 11] 59 @pc restore cmr10.329 @sf 124 2302 p m (More) 14 (will) 17 (b) 1 (e) 15 (said) 16 (ab) 1 (out) 15 (the) 15 (last) 14 (step,) 15 (de\015ation,) 15 (in) 16 (section) 16 (3.) 19 (The) 15 (algorithm) 15 (just) 15 (describ) 1 (ed) 17 (is) ks 74 2401 p m (inheren) 0 (tly) 14 (parallel.) 21 (Indeed,) 15 (the) 13 (eigensystems) 14 (of) ks cmmi10.329 @sf 12 r m (H) s cmr8.300 @sf 1056 2408 p m (11) s cmr10.329 @sf 1107 2401 p m (and) s cmmi10.329 @sf 13 r m (H) s cmr8.300 @sf 1231 2408 p m (22) s cmr10.329 @sf 1282 2401 p m (can) 13 (b) 1 (e) 14 (computed) 14 (in) 14 (parallel.) 20 (After) ks 74 2501 p m (whic) 0 (h) 21 (Newton's) 20 (metho) 1 (d) 21 (can) 21 (b) 1 (e) 22 (started) 20 (with) 21 (di\013eren) 0 (t) 20 (initial) 23 (guesses) 21 (on) 21 (di\013eren) 0 (t) 20 (pro) 1 (cessors.) ks 74 2601 p m (F) -3 (urthermore,) 12 (the) 14 (dividing) 16 (pro) 1 (cess) 13 (can) 14 (b) 1 (e) 14 (applied) 16 (recursiv) 0 (ely) 13 (to) 13 (obtain) 14 (y) 0 (et) 12 (smaller) 14 (subproblems,) ks 74 2700 p m (i.e.,) s cmmi10.329 @sf 23 r m (H) s cmr8.300 @sf 206 2707 p m (11) s cmr10.329 @sf 264 2700 p m (and) s cmmi10.329 @sf 21 r m (H) s cmr8.300 @sf 396 2707 p m (22) s cmr10.329 @sf 454 2700 p m (can) 22 (b) 1 (e) 22 (divided) 23 (eac) 0 (h) 20 (in) 0 (to) 20 (subproblems.) 39 (This) 22 (will) 23 (p) 1 (ermit) 22 (the) 21 (use) 22 (of) 21 (more) ks @eop 5 @bop0 5 @bop1 cmr10.329 @sf 1941 -77 p m (5) s 74 67 p m (should) 16 (satisfy) 15 (the) 16 (same) 14 (condition,) 17 (then) 15 (\() ks cmmi10.329 @sf m (y) 2 (;) 8 (\026) ks cmr10.329 @sf m (\)) 14 (is) 16 (the) 15 (solution) 16 (of) ks cmex10.300 @sf 664 140 p save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pc restore cmmi10.329 @sf 718 185 p m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (\025I) s cmsy10.329 @sf 906 185 p m (\000) s cmmi10.329 @sf m (x) s 767 241 p m (e) s cmmi8.300 @sf 788 226 p m (T) s 788 252 p m (s) s cmr10.329 @sf 926 241 p m (0) s cmex10.300 @sf 988 140 p save [ 21 124 -1 122 33] 33 @pc restore 1029 140 p save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pc restore cmmi10.329 @sf 1084 185 p m (y) s 1082 241 p m (\026) s cmex10.300 @sf 1131 140 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1176 212 p m (=) s cmex10.300 @sf 1224 140 p save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pc restore cmmi10.329 @sf 1278 185 p m (r) s cmr10.329 @sf 1278 241 p m (0) s cmex10.300 @sf 1321 140 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1362 212 p m (;) s cmr10.329 @sf 74 358 p m (with) s cmmi10.329 @sf 20 r m (r) s cmr10.329 @sf 21 r m (as) 19 (ab) 1 (o) 0 (v) -1 (e.) 32 (But,) 20 (this) 20 (is) 20 (the) 20 (same) 19 (equation) 21 (that) 19 (w) 0 (e) 18 (obtain) 20 (when) 20 (a) 19 (Newton) 20 (iteration) 20 (is) ks 74 457 p m (applied) 19 (to) 15 (the) 17 (function) ks cmmi10.329 @sf 17 r save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 579 464 p m (s) s cmr10.329 @sf 614 457 p m (to) 16 (\014nd) 17 (a) 17 (correction) 16 (to) 16 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\),) 15 (as) 16 (w) 0 (e) 15 (can) 16 (see) 17 (from) 16 (\(1\).) 23 (W) -3 (e) 15 (note) 17 (here) ks 74 557 p m (a) 19 (result) 19 (from) 18 ([) 0 (4) ks 393 557 p m (],) 19 (where) 19 (the) 19 (author) 18 (studied) 20 (an) 19 (iterativ) 0 (e) 18 (re\014nemen) 0 (t) 18 (tec) 0 (hnique) 20 (to) 18 (compute) 19 (the) ks 74 657 p m (correction) 17 (\() ks cmmi10.329 @sf m (y) 2 (;) 8 (\026) ks cmr10.329 @sf m (\)) 15 (to) 16 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 14 (from) 16 (equation) 17 (\(2\)) 15 (\(i.e.,) 16 (without) 17 (ignoring) 17 (the) 16 (second) 17 (order) 16 (term\)) 16 (and) ks 74 756 p m (pro) 0 (v) -1 (ed) 20 (that) 20 (in) ks cmti10.329 @sf 21 r m (exact) s cmr10.329 @sf 21 r m (arithmetic,) 23 (that) 20 (metho) 1 (d) 21 (and) 21 (Newton's) 20 (metho) 1 (d) 21 (pro) 1 (duce) 22 (the) 21 (same) 20 (\014nal) ks 74 856 p m (iteration.) s 124 997 p m (So) 13 (far) 13 (w) 0 (e) 13 (ha) 0 (v) -1 (e) 12 (not) 13 (attempted) 13 (to) 13 (answ) 0 (er) 12 (the) 14 (question) 14 (of) 13 (whic) 0 (h) 13 (sub) 1 (diagonal) 15 (en) 0 (try) 12 (to) 13 (in) 0 (tro) 1 (duce) ks 74 1097 p m (the) 17 (zero.) 23 (W) -3 (e) 16 (will) 18 (use) 17 (\014rst) 16 (order) 16 (p) 1 (erturbation) 17 (theory) 16 (in) 18 (order) 16 (to) 16 (shed) 17 (some) 16 (ligh) 0 (t) 16 (on) 17 (this) 17 (issue.) ks 74 1196 p m (Let) s cmmi10.329 @sf 18 r save [ 32 31 -2 0 34] 69 @pc restore cmr10.329 @sf 53 r m (=) s cmsy10.329 @sf 17 r m (\000) s cmmi10.329 @sf m (\013) 0 (e) ks cmmi8.300 @sf 348 1203 p m (k) s cmr8.300 @sf 1 r m (+1) s cmmi10.329 @sf 415 1196 p m (e) s cmmi8.300 @sf 436 1181 p m (T) s 436 1209 p m (k) s cmr10.329 @sf 464 1196 p m (,) 17 (where) 18 (as) 18 (ab) 1 (o) 0 (v) -1 (e:) ks cmmi10.329 @sf 23 r m (\013) s cmr10.329 @sf 17 r m (=) s cmmi10.329 @sf 17 r save [<6003C0E00620700610700E10700E087007083807043803803803803803801C01C01C01C01C01C0 1C01C00E00E00E00E00F00C00E80C0076180071F00070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 22 32 -2 0 26] 104 @pc restore cmmi8.300 @sf 962 1203 p m (k) s cmr8.300 @sf 1 r m (+1) s cmmi8.300 @sf m (;k) s cmr10.329 @sf 1075 1196 p m (\(note) 17 (that) ks cmmi10.329 @sf 17 r m (H) s cmr10.329 @sf 15 r m (+) s cmmi10.329 @sf 12 r save [ 32 31 -2 0 34] 69 @pc restore cmr10.329 @sf 53 r m (=) s cmmi10.329 @sf 17 r m (H) s cmr8.300 @sf 1540 1203 p m (0) s cmr10.329 @sf 1560 1196 p m (,) 17 (in) 0 (tro) 1 (duced) 18 (ab) 1 (o) 0 (v) 0 (e\)) -1 (.) ks 74 1296 p m (Then) 17 (classical) 18 (results) 16 (from) 16 (function) 17 (theory) 16 (\([) 0 (12) ks 1023 1296 p m (],) 15 (v.) 16 (2,) 16 (pp.) 23 (119-134\)) 15 (allo) 0 (w) 15 (us) 17 (to) 15 (state) 16 (that) 15 (in) 17 (a) ks 74 1395 p m (small) 16 (neigh) 0 (b) 1 (orho) 1 (o) 1 (d) 16 (of) 14 (zero,) 15 (w) 0 (e) 14 (ha) 0 (v) -1 (e) ks 769 1541 p m (\() s cmmi10.329 @sf m (H) s cmr10.329 @sf 13 r m (+) s cmmi10.329 @sf 11 r m (\017) s save [ 32 31 -2 0 34] 69 @pc restore cmr10.329 @sf 37 r m (\)) s cmmi10.329 @sf m (x) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (\017) s cmr10.329 @sf m (\)) 11 (=) ks cmmi10.329 @sf 13 r m (\025) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (\017) s cmr10.329 @sf m (\)) s cmmi10.329 @sf m (x) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (\017) s cmr10.329 @sf m (\)) s cmmi10.329 @sf m (;) s cmr10.329 @sf 74 1686 p m (for) 13 (all) ks cmmi10.329 @sf 15 r m (\017) s cmr10.329 @sf 15 r m (in) 14 (that) 13 (neigh) 0 (b) 1 (orho) 1 (o) 1 (d) 15 (and) 14 (for) 13 (di\013eren) 0 (tiable) 14 (\() ks cmmi10.329 @sf m (x) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (\017) s cmr10.329 @sf m (\)) s cmmi10.329 @sf m (;) 8 (\025) ks cmr10.329 @sf m (\() s cmmi10.329 @sf m (\017) s cmr10.329 @sf m (\)\)) 12 (corresp) 1 (onding) 15 (to) 13 (a) 14 (simple) 15 (eigen-) ks 74 1786 p m (pair) 23 (\() ks cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 20 (of) ks cmmi10.329 @sf 22 r m (H) s cmr10.329 @sf 4 r m (.) 41 (Clearly:) ks cmmi10.329 @sf 34 r m (x) s cmr10.329 @sf m (\(0\)) 24 (=) ks cmmi10.329 @sf 25 r m (x) s cmr10.329 @sf 22 r m (and) s cmmi10.329 @sf 23 r m (\025) s cmr10.329 @sf m (\(0\)) 23 (=) ks cmmi10.329 @sf 24 r m (\025) s cmr10.329 @sf m (.) 41 (Let) ks cmmi10.329 @sf 23 r m (y) s cmmi8.300 @sf 1324 1771 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 1379 1786 p m (b) 1 (e) 23 (the) 23 (left) 22 (eigen) 0 (v) 0 (ector) 21 (of) ks cmmi10.329 @sf 22 r m (H) s cmr10.329 @sf 74 1885 p m (corresp) 1 (onding) 16 (to) ks cmmi10.329 @sf 15 r m (\025) s cmr10.329 @sf m (.) 19 (Then) 16 (di\013eren) 0 (tiating) 15 (b) 1 (oth) 15 (sides) 16 (w) 0 (e) 14 (ha) 0 (v) 0 (e,) ks cmmi10.329 @sf 445 2031 p m (H) 4 (D) ks cmmi8.300 @sf 525 2038 p save [<1F0030C04000C000C000C000C000C000FF006000600030001C0007C0> 10 14 -2 0 14] 15 @pc restore cmmi10.329 @sf 541 2031 p m (x) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (\017) s cmr10.329 @sf m (\)) 10 (+) ks cmmi10.329 @sf 10 r save [ 32 31 -2 0 34] 69 @pc restore 37 r m (x) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (\017) s cmr10.329 @sf m (\)) 9 (+) ks cmmi10.329 @sf 11 r m (\017) s save [ 32 31 -2 0 34] 69 @pc restore 37 r m (D) s cmmi8.300 @sf 941 2038 p save [<1F0030C04000C000C000C000C000C000FF006000600030001C0007C0> 10 14 -2 0 14] 15 @pc restore cmmi10.329 @sf 956 2031 p m (x) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (\017) s cmr10.329 @sf m (\)) 13 (=) ks cmmi10.329 @sf 13 r m (D) s cmmi8.300 @sf 1135 2038 p save [<1F0030C04000C000C000C000C000C000FF006000600030001C0007C0> 10 14 -2 0 14] 15 @pc restore cmmi10.329 @sf 1151 2031 p m (\025) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (\017) s cmr10.329 @sf m (\)) s cmmi10.329 @sf m (x) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (\017) s cmr10.329 @sf m (\)) 9 (+) ks cmmi10.329 @sf 10 r m (\025) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (\017) s cmr10.329 @sf m (\)) s cmmi10.329 @sf m (D) s cmmi8.300 @sf 1485 2038 p save [<1F0030C04000C000C000C000C000C000FF006000600030001C0007C0> 10 14 -2 0 14] 15 @pc restore cmmi10.329 @sf 1501 2031 p m (x) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (\017) s cmr10.329 @sf m (\)) s cmmi10.329 @sf m (;) s cmr10.329 @sf 74 2176 p m (where,) s cmmi10.329 @sf 17 r m (D) s cmmi8.300 @sf 258 2183 p save [<1F0030C04000C000C000C000C000C000FF006000600030001C0007C0> 10 14 -2 0 14] 15 @pc restore cmr10.329 @sf 290 2176 p m (denotes) 17 (the) 17 (di\013enren) 0 (tiation) 17 (with) 16 (resp) 1 (ect) 18 (to) ks cmmi10.329 @sf 15 r m (\017) s cmr10.329 @sf m (.) 25 (Multiplyin) 1 (g) 18 (b) 0 (y) ks cmmi10.329 @sf 15 r m (y) s cmmi8.300 @sf 1567 2161 p save [ 29 23 -1 0 29] 72 @pc restore cmr10.329 @sf 1617 2176 p m (and) 17 (setting) ks cmmi10.329 @sf 17 r m (\017) s cmr10.329 @sf 15 r m (=) 15 (0) ks 74 2276 p m (w) 0 (e) 14 (get) ks cmmi10.329 @sf 812 2375 p m (y) s cmmi8.300 @sf 836 2357 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 869 2375 p save [ 32 31 -2 0 34] 69 @pc restore 37 r m (x) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (D) s cmmi8.300 @sf 1030 2382 p save [<1F0030C04000C000C000C000C000C000FF006000600030001C0007C0> 10 14 -2 0 14] 15 @pc restore cmmi10.329 @sf 1046 2375 p m (\025) s cmr10.329 @sf m (\(0\)) s cmmi10.329 @sf m (y) s cmmi8.300 @sf 1156 2357 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 1188 2375 p m (x;) s cmr10.329 @sf 74 2502 p m (and) 16 (therefore) ks cmsy10.329 @sf 626 2647 p m (j) s cmmi10.329 @sf m (D) s cmmi8.300 @sf 677 2654 p save [<1F0030C04000C000C000C000C000C000FF006000600030001C0007C0> 10 14 -2 0 14] 15 @pc restore cmmi10.329 @sf 692 2647 p m (\025) s cmr10.329 @sf m (\(0\)) s cmsy10.329 @sf m (j) s cmr10.329 @sf 11 r m (=) s cmsy10.329 @sf 855 2617 p m (j) s cmmi10.329 @sf m (y) s cmmi8.300 @sf 892 2602 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 925 2617 p save [ 32 31 -2 0 34] 69 @pc restore 37 r m (x) s cmsy10.329 @sf m (j) s 855 2637 p 145 2 ru 873 2678 p m (j) s cmmi10.329 @sf m (y) s cmmi8.300 @sf 910 2666 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 944 2678 p m (x) s cmsy10.329 @sf m (j) s cmr10.329 @sf 1018 2647 p m (=) s cmsy10.329 @sf 1071 2617 p m (j) s cmmi10.329 @sf m (\013) s cmsy10.329 @sf m (jj) s cmmi10.329 @sf m (y) s cmmi8.300 @sf 1161 2624 p m (k) s cmr8.300 @sf 1 r m (+1) s cmsy10.329 @sf 1227 2617 p m (jj) s cmmi10.329 @sf m (x) s cmmi8.300 @sf 1279 2624 p m (k) s cmsy10.329 @sf 1299 2617 p m (j) s 1071 2637 p 242 2 ru 1137 2678 p m (j) s cmmi10.329 @sf m (y) s cmmi8.300 @sf 1174 2666 p save [ 29 23 -1 0 29] 72 @pc restore cmmi10.329 @sf 1207 2678 p m (x) s cmsy10.329 @sf m (j) s cmmi10.329 @sf 1317 2647 p m (:) s cmr10.329 @sf 1906 2647 p m (\(3\)) s @eop 4 @bop0 4 @bop1 cmr10.329 @sf 1941 -77 p m (4) s cmmi10.329 @sf 74 67 p m (H) s cmr8.300 @sf 112 74 p m (0) s cmr10.329 @sf 143 67 p m (corresp) 1 (onding) 12 (to) ks cmmi10.329 @sf 11 r m (\025) s cmr10.329 @sf m (.) 18 (On) 12 (the) 11 (other) 11 (hand,) 12 (if) ks cmmi10.329 @sf 12 r m (\025) s cmr10.329 @sf 11 r m (is) 11 (an) 12 (eigen) 0 (v) -2 (alue) 11 (of) ks cmmi10.329 @sf 11 r m (H) s cmr8.300 @sf 1401 74 p m (22) s cmr10.329 @sf 1449 67 p m (and) s cmmi10.329 @sf 12 r m (x) s cmr10.329 @sf 11 r m (is) 12 (the) 11 (corresp) 1 (onding) ks 74 167 p m (eigen) 0 (v) 0 (ector,) 12 (then) ks cmex10.300 @sf 423 95 p save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pc restore cmr10.329 @sf 478 140 p m (0) s cmmi10.329 @sf 477 195 p m (x) s cmex10.300 @sf 524 95 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 556 167 p m (,) 14 (where) ks cmmi10.329 @sf 13 r m (k) s cmr10.329 @sf 15 r m (zeros) 13 (are) 13 (pre\014xed) 14 (to) ks cmmi10.329 @sf 13 r m (x) s cmr10.329 @sf 13 r m (is) 14 (tak) 0 (en) 12 (as) 13 (an) 13 (appro) 0 (ximate) 12 (eigen) 0 (v) 0 (ector) ks 74 266 p m (of) s cmmi10.329 @sf 11 r m (H) s cmr10.329 @sf 14 r m (corresp) 1 (onding) 12 (to) 11 (the) 11 (appro) 0 (ximate) 9 (eigen) 0 (v) -2 (alue) ks cmmi10.329 @sf 11 r m (\025) s cmr10.329 @sf m (.) 18 (If) ks cmmi10.329 @sf 11 r m (\025) s cmr10.329 @sf 11 r m (is) 11 (not) 11 (an) 11 (eigen) 0 (v) -2 (alue) 11 (of) ks cmmi10.329 @sf 11 r m (H) s cmr8.300 @sf 1672 273 p m (11) s cmr10.329 @sf 1720 266 p m (then) 11 (the) 11 (last) ks cmmi10.329 @sf 74 366 p m (n) s cmsy10.329 @sf 7 r m (\000) s cmmi10.329 @sf 7 r m (k) s cmr10.329 @sf 16 r m (comp) 1 (onen) 0 (ts) 13 (of) ks cmex10.300 @sf 489 294 p save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pc restore cmr10.329 @sf 545 339 p m (0) s cmmi10.329 @sf 543 394 p m (x) s cmex10.300 @sf 590 294 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 623 366 p m (,) 13 (i.e.,) 14 (those) 13 (of) ks cmmi10.329 @sf 14 r m (x) s cmr10.329 @sf m (,) 13 (are) 14 (the) 14 (trailing) 15 (comp) 1 (onen) 0 (ts) 12 (of) 14 (an) 14 (exact) 13 (eigen) 0 (v) 0 (ector) ks 74 495 p m (of) s cmmi10.329 @sf 19 r m (H) s cmr8.300 @sf 168 502 p m (0) s cmr10.329 @sf 206 495 p m (corresp) 1 (onding) 21 (to) ks cmmi10.329 @sf 18 r m (\025) s cmr10.329 @sf m (,) 19 (namely:) ks cmex10.300 @sf 805 423 p save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pc restore cmr10.329 @sf 858 468 p m (\() s cmmi10.329 @sf m (H) s cmr8.300 @sf 914 475 p m (11) s cmsy10.329 @sf 961 468 p m (\000) s cmmi10.329 @sf 11 r m (\025) s cmr10.329 @sf m (\)) s cmsy8.300 @sf 1052 452 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1098 468 p m (H) s cmr8.300 @sf 1136 475 p m (12) s cmmi10.329 @sf 1173 468 p m (x) s 1016 523 p m (x) s cmex10.300 @sf 1220 423 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1253 495 p m (.) 32 (Ho) 0 (w) -1 (ev) -1 (er,) 17 (if) ks cmmi10.329 @sf 20 r m (\025) s cmr10.329 @sf 19 r m (is) 19 (an) 19 (eigen) 0 (v) -2 (alue) 20 (of) ks cmmi10.329 @sf 74 594 p m (H) s cmr8.300 @sf 112 601 p m (11) s cmr10.329 @sf 149 594 p m (,) 14 (and) 14 (hence) 14 (a) 13 (necessarily) 15 (m) 0 (ultiple) 15 (eigen) 0 (v) -2 (alue) 13 (of) ks cmmi10.329 @sf 13 r m (H) s cmr8.300 @sf 1128 601 p m (0) s cmr10.329 @sf 1148 594 p m (,) 13 (then) 14 (if) ks cmmi10.329 @sf 14 r m (\025) s cmr10.329 @sf 13 r m (has) 14 (geometric) 13 (m) 0 (ultiplicit) 0 (y) 14 (one,) ks 74 694 p m (no) 15 (eigen) 0 (v) 0 (ector) 14 (of) ks cmmi10.329 @sf 14 r m (H) s cmr8.300 @sf 463 701 p m (0) s cmr10.329 @sf 498 694 p m (will) 17 (ha) 0 (v) -1 (e) 14 (the) 15 (comp) 1 (onen) 0 (ts) 14 (of) ks cmmi10.329 @sf 15 r m (x) s cmr10.329 @sf 15 r m (as) 15 (its) 15 (trailing) 16 (comp) 1 (onen) 0 (ts.) ks 124 835 p m (Ha) 0 (ving) 18 (constructed) 19 (these) 19 (initial) 22 (guesses,) 19 (w) 0 (e) 18 (no) 0 (w) 18 (use) 19 (them) 19 (as) 19 (starting) 18 (p) 1 (oin) 0 (ts) 18 (for) 19 (Newton's) ks 74 935 p m (metho) 1 (d) 20 (to) 19 (\014nd) 20 (the) 20 (zeros) 19 (of) ks cmmi10.329 @sf 20 r save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 686 942 p m (s) s cmr10.329 @sf 704 935 p m (,) 20 (i.e.,) 21 (the) 20 (eigenpairs) 20 (of) ks cmmi10.329 @sf 20 r m (H) s cmr10.329 @sf 4 r m (.) 32 (Hence,) 21 (giv) 0 (en) 19 (an) 20 (appro) 0 (ximate) 18 (zero) ks 74 1034 p m (\() s cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 13 (of) ks cmmi10.329 @sf 15 r save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 278 1041 p m (s) s cmr10.329 @sf 312 1034 p m (the) 15 (next) 15 (appro) 0 (ximation) 15 (is) ks cmmi10.329 @sf 797 1163 p m (x) s cmsy8.300 @sf 823 1145 p m (0) s cmr10.329 @sf 847 1163 p m (=) s cmmi10.329 @sf 13 r m (x) s cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 11 r m (y) s cmr10.329 @sf 2 r m (;) s cmmi10.329 @sf 8 r m (\025) s cmsy8.300 @sf 1049 1145 p m (0) s cmr10.329 @sf 1071 1163 p m (=) s cmmi10.329 @sf 13 r m (\025) s cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 10 r m (\026;) s cmr10.329 @sf 74 1293 p m (where) 16 (\() ks cmmi10.329 @sf m (y) 2 (;) 8 (\026) ks cmr10.329 @sf m (\)) 14 (is) 15 (the) 16 (solution) 16 (of) 14 (the) 16 (system) ks cmex10.300 @sf 626 1350 p save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pc restore cmmi10.329 @sf 680 1395 p m (H) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 10 r m (\025I) s cmsy10.329 @sf 869 1395 p m (\000) s cmmi10.329 @sf m (x) s 729 1450 p m (e) s cmmi8.300 @sf 750 1435 p m (T) s 750 1461 p m (s) s cmr10.329 @sf 888 1450 p m (0) s cmex10.300 @sf 951 1350 p save [ 21 124 -1 122 33] 33 @pc restore 991 1350 p save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pc restore cmmi10.329 @sf 1046 1395 p m (y) s 1045 1450 p m (\026) s cmex10.300 @sf 1093 1350 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1138 1422 p m (=) s cmex10.300 @sf 1186 1350 p save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pc restore cmmi10.329 @sf 1240 1395 p m (r) s cmr10.329 @sf 1240 1450 p m (0) s cmex10.300 @sf 1283 1350 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1324 1422 p m (;) s cmr10.329 @sf 1906 1422 p m (\(1\)) s 74 1551 p m (where) s cmmi10.329 @sf 16 r m (r) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (\025x) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (H) 4 (x) ks cmr10.329 @sf m (.) s 124 1692 p m (Newton's) 17 (metho) 1 (d) 17 (comes) 17 (in) 0 (to) 16 (this) 18 (problem) 18 (in) 18 (a) 17 (rather) 17 (\\natural") 17 (w) 0 (a) -1 (y) -4 (.) 24 (Indeed,) 19 (supp) 1 (ose) 18 (that) ks 74 1792 p m (\() s cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 13 (is) 16 (an) 15 (appro) 0 (ximate) 14 (eigenpair) 17 (of) ks cmmi10.329 @sf 14 r m (H) s cmr10.329 @sf 4 r m (,) s cmmi10.329 @sf 923 1921 p m (H) 4 (x) ks cmsy10.329 @sf 12 r m (\031) s cmmi10.329 @sf 13 r m (\025x;) s cmr10.329 @sf 74 2050 p m (and) 20 (let) 20 (us) 20 (\014nd) 20 (a) 19 (w) 0 (a) -1 (y) 17 (to) 19 (compute) 20 (a) 19 (correction) 20 (\() ks cmmi10.329 @sf m (y) 2 (;) 8 (\026) ks cmr10.329 @sf m (\)) 18 (to) 19 (this) 20 (appro) 0 (ximate) 18 (eigenpair.) 34 (Clearly) -3 (,) ks 74 2150 p m (\() s cmmi10.329 @sf m (y) 2 (;) 8 (\026) ks cmr10.329 @sf m (\)) 14 (should) 16 (satisfy) ks cmmi10.329 @sf 749 2249 p m (H) s cmr10.329 @sf 4 r m (\() s cmmi10.329 @sf m (x) s cmr10.329 @sf 9 r m (+) s cmmi10.329 @sf 10 r m (y) s cmr10.329 @sf 2 r m (\)) 12 (=) 13 (\() ks cmmi10.329 @sf m (\025) s cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 10 r m (\026) s cmr10.329 @sf m (\)\() s cmmi10.329 @sf m (x) s cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 10 r m (y) s cmr10.329 @sf 2 r m (\)) s cmmi10.329 @sf m (:) s cmr10.329 @sf 74 2368 p m (Rearranging) 16 (the) 15 (latter) 15 (equation) 15 (yields) ks 654 2497 p m (\() s cmmi10.329 @sf m (H) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (\025) s cmr10.329 @sf m (\)) s cmmi10.329 @sf m (y) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (\026x) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (\025x) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (H) 4 (x) ks cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 10 r m (\026y) 2 (:) ks cmr10.329 @sf 1906 2497 p m (\(2\)) s 74 2626 p m (No) 0 (w) 16 (w) 0 (e) 16 (ignore) 18 (the) 17 (second) 18 (order) 18 (term) ks cmmi10.329 @sf 17 r m (\026y) s cmr10.329 @sf 2 r m (,) 17 (and) 18 (w) 0 (e) 16 (imp) 1 (ose) 19 (a) 17 (normalization) 18 (condition) 19 (on) ks cmmi10.329 @sf 17 r m (x) s cmr10.329 @sf m (,) 18 (sa) 0 (y) ks cmmi10.329 @sf 74 2726 p m (x) s cmmi8.300 @sf 100 2733 p m (s) s cmr10.329 @sf 138 2726 p m (=) 19 (1,) 20 (where) ks cmmi10.329 @sf 19 r m (x) s cmmi8.300 @sf 409 2733 p m (s) s cmr10.329 @sf 447 2726 p m (is) 20 (the) ks cmmi10.329 @sf 19 r m (s) s cmmi8.300 @sf 600 2711 p save [<1E003100310030803080300018001800180018000C000C000C00FFC00600060006000600030003 00> 10 20 -1 0 13] 116 @pc restore cmmi10.329 @sf 615 2726 p save [<6003C0E00620700610700E10700E087007083807043803803803803803801C01C01C01C01C01C0 1C01C00E00E00E00E00F00C00E80C0076180071F00070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 22 32 -2 0 26] 104 @pc restore cmr10.329 @sf 45 r m (comp) 1 (onen) 0 (t) 19 (of) ks cmmi10.329 @sf 18 r m (x) s cmr10.329 @sf m (.) 32 (If) 20 (w) 0 (e) 18 (also) 19 (assume) 19 (that) 18 (the) 20 (desired) 20 (eigen) 0 (v) 0 (ector) ks @eop 3 @bop0 3 @bop1 cmr10.329 @sf 1941 -77 p m (3) s cmbx10.432 @sf 74 67 p save [ 27 39 -3 0 34] 50 @pc restore 177 67 p save [<007FFFFFE000007FFFFFE000007FFFFFE00000003FC0000000003FC0000000003FC0000000003F C0000000003FC0000000003FC0000000003FC0000000003FC0000000003FC0000000003FC00000 00003FC0000000003FC0000000003FC0000000003FC0000000003FC0000000003FC0000000003F C0000000003FC0000000003FC0000000003FC0000000003FC0000000003FC00000E0003FC000E0 E0003FC000E0E0003FC000E0E0003FC000E0E0003FC000E0F0003FC001E0F0003FC001E070003F C001C078003FC003C078003FC003C07E003FC007C07F803FC03FC07FFFFFFFFFC07FFFFFFFFFC0 7FFFFFFFFFC0> 43 40 -2 0 48] 84 @pc restore 48 r m (he) s 23 r save [ 47 41 -2 0 52] 65 @pc restore 52 r m (lgorithm) s cmr10.329 @sf 74 253 p m (Giv) 0 (en) 16 (a) 17 (matrix) ks cmmi10.329 @sf 17 r m (H) s cmr10.329 @sf 4 r m (,) 16 (an) 17 (eigenpair) 18 (\() ks cmmi10.329 @sf m (x) s cmr8.300 @sf 773 260 p m (0) s cmmi10.329 @sf 792 253 p m (;) 8 (\025) ks cmr8.300 @sf 840 260 p m (0) s cmr10.329 @sf 859 253 p m (\)) 16 (of) ks cmmi10.329 @sf 17 r m (H) s cmr10.329 @sf 20 r m (can) 17 (b) 1 (e) 18 (though) 0 (t) 15 (of) 16 (as) 17 (a) 16 (solution) 18 (to) 16 (the) 17 (follo) 0 (wing) ks 74 353 p m (p) 1 (olynomial) 17 (system) ks 813 453 p m (\() s cmmi10.329 @sf save [<81F80000C60E0000E8030000700180006001C0006000C0006000E0002000600020007000200070 000000700000007000000070000000F0000003F000003FF00000FFE00001FFC00003FF800003F8 000003C0000003800000038000000380020003800200038002000180020001C0030000C0070000 60070000300B00001811800007E080> 25 33 -3 1 28] 83 @pc restore cmr10.329 @sf 31 r m (\)) s cmex10.300 @sf 888 381 p save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pc restore cmmi10.329 @sf 941 426 p m (H) 4 (x) ks cmsy10.329 @sf 9 r m (\000) s cmmi10.329 @sf 11 r m (\025x) s cmr10.329 @sf 12 r m (=) 13 (0) ks cmmi10.329 @sf 941 481 p m (L) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (x) s cmr10.329 @sf m (\)) 12 (=) 13 (1) ks 74 579 p m (where) s cmmi10.329 @sf 16 r m (L) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (x) s cmr10.329 @sf m (\)) 14 (is) 16 (a) 15 (scalar) 15 (equation.) 20 (Here,) 15 (w) 0 (e) 14 (set) ks cmmi10.329 @sf 15 r m (L) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (x) s cmr10.329 @sf m (\)) 12 (=) ks cmmi10.329 @sf 13 r m (e) s cmmi8.300 @sf 1161 564 p m (T) s 1161 590 p m (s) s cmmi10.329 @sf 1189 579 p m (x) s cmr10.329 @sf m (,) 14 (where) ks cmmi10.329 @sf 16 r m (e) s cmmi8.300 @sf 1395 586 p m (s) s cmr10.329 @sf 1428 579 p m (is) 16 (the) ks cmmi10.329 @sf 15 r m (s) s 1573 564 p save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 18 26 -1 0 21] 104 @pc restore cmr10.329 @sf 1627 579 p m (unit) 16 (v) 0 (ector.) 18 (Let) ks cmmi10.329 @sf 760 723 p save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 789 730 p m (s) s cmr10.329 @sf 807 723 p m (\() s cmmi10.329 @sf m (x;) 8 (\025) ks cmr10.329 @sf m (\)) 11 (=) ks cmex10.300 @sf 976 651 p save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pc restore cmmi10.329 @sf 1029 696 p m (H) 4 (x) ks cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (\025x) s 1041 751 p m (e) s cmmi8.300 @sf 1062 736 p m (T) s 1062 762 p m (s) s cmmi10.329 @sf 1089 751 p m (x) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 11 r m (1) s cmex10.300 @sf 1226 651 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1266 723 p m (:) s cmr10.329 @sf 74 867 p m (Then,) 19 (\014nding) 20 (an) 18 (eigenpair) 19 (of) ks cmmi10.329 @sf 18 r m (H) s cmr10.329 @sf 22 r m (reduces) 19 (to) 17 (\014nding) 20 (a) 18 (zero) 18 (of) ks cmmi10.329 @sf 18 r save [ 32 31 -2 0 29] 70 @pc restore cmmi8.300 @sf 1344 874 p m (s) s cmr10.329 @sf 1362 867 p m (.) 29 (In) 19 (what) 17 (follo) 0 (ws,) 18 (unless) 19 (oth-) ks 74 967 p m (erwise) 17 (men) 0 (tioned,) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 19 r m (is) 17 (assumed) 16 (to) 15 (b) 1 (e) 16 (a) 16 (real,) 16 (unreduced) 17 (\(no) 16 (zeros) 16 (on) 15 (the) 16 (sub) 1 (diagonal\),) 17 (upp) 1 (er-) ks 74 1066 p m (Hessen) 0 (b) 1 (erg) 16 (matrix) 15 (of) 15 (order) ks cmmi10.329 @sf 16 r m (n) s cmr10.329 @sf m (.) 22 (This) 16 (is) 17 (no) 15 (restriction) 17 (on) 15 (the) 16 (t) 0 (yp) 1 (e) 15 (of) 15 (problems) 17 (w) 0 (e) 14 (w) 0 (an) 0 (t) 13 (to) 15 (solv) 0 (e,) ks 74 1166 p m (since) 19 (if) ks cmmi10.329 @sf 19 r m (H) s cmr10.329 @sf 21 r m (has) 18 (a) 18 (zero) 18 (on) 18 (the) 18 (sub) 1 (diagonal) 20 (then) 18 (\014nding) 19 (its) 19 (eigen) 0 (v) -2 (alues) 18 (reduces) 19 (to) 17 (\014nding) 19 (those) ks 74 1266 p m (of) 15 (the) 16 (blo) 1 (c) 0 (ks) 15 (on) 15 (the) 15 (diagonal.) 21 (W) -3 (e) 15 (note) 15 (also) 15 (that) 15 (as) 15 (a) 15 (consequence) 17 (of) 14 (our) 16 (assumption) 15 (that) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 19 r m (is) s 74 1365 p m (unreduced,) 20 (an) 17 (eigen) 0 (v) -2 (alue) 18 (of) ks cmmi10.329 @sf 17 r m (H) s cmr10.329 @sf 21 r m (can) 18 (only) 18 (ha) 0 (v) -1 (e) 16 (geometric) 18 (m) 0 (ultiplicit) 0 (y) 18 (one:) 25 (this) 18 (is) 18 (quite) 18 (easy) 18 (to) ks 74 1465 p m (see) 18 (since) 18 (the) 17 (\014rst) ks cmmi10.329 @sf 17 r m (n) s cmsy10.329 @sf 11 r m (\000) s cmr10.329 @sf 12 r m (1) 17 (columns) 18 (of) ks cmmi10.329 @sf 16 r m (H) s cmsy10.329 @sf 15 r m (\000) s cmmi10.329 @sf 12 r m (\025I) s cmr10.329 @sf 20 r m (are) 17 (linearly) 18 (indep) 1 (en) 1 (den) 0 (t.) 26 (W) -3 (e) 16 (will) 19 (assume) 17 (for) 17 (no) 0 (w) ks 74 1564 p m (that) s cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 18 r m (has) 15 (a) 15 (simple) 17 (sp) 1 (ectrum.) 20 (W) -3 (e) 14 (can) 16 (write) ks cmmi10.329 @sf 15 r m (H) s cmr10.329 @sf 19 r m (as) s cmmi10.329 @sf 715 1709 p m (H) s cmr10.329 @sf 798 1709 p m (=) s cmex10.300 @sf 875 1637 p save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pc restore cmmi10.329 @sf 993 1669 p m (H) s cmr8.300 @sf 1031 1676 p m (11) s 1152 1686 p 2 57 ru cmmi10.329 @sf 1177 1669 p m (H) s cmr8.300 @sf 1215 1676 p m (12) s 908 1688 p 370 2 ru cmmi10.329 @sf 933 1751 p m (\013) 0 (e) ks cmr8.300 @sf 983 1728 p save [<0102040C1818303070606060E0E0E0E0E0E0E0E0E0E060606070303018180C040201> 8 34 -3 9 14] 40 @pc restore cmmi8.300 @sf 14 r m (k) s cmr8.300 @sf 1 r save [<8040203018180C0C0E060606070707070707070707070606060E0C0C181830204080> 8 34 -2 9 14] 41 @pc restore 983 1763 p m (1) s cmmi10.329 @sf 1032 1751 p m (e) s cmr8.300 @sf 1053 1728 p save [<0102040C1818303070606060E0E0E0E0E0E0E0E0E0E060606070303018180C040201> 8 34 -3 9 14] 40 @pc restore cmmi8.300 @sf 14 r m (k) s cmr8.300 @sf 1 r save [<8040203018180C0C0E060606070707070707070707070606060E0C0C181830204080> 8 34 -2 9 14] 41 @pc restore cmmi8.300 @sf 14 r m (T) s 1053 1765 p m (k) s 1152 1765 p 2 79 ru cmmi10.329 @sf 1177 1751 p m (H) s cmr8.300 @sf 1215 1758 p m (22) s cmex10.300 @sf 1277 1637 p save [ 21 124 -1 122 33] 33 @pc restore cmmi10.329 @sf 1331 1709 p m (;) s cmr10.329 @sf 74 1853 p m (where) s cmmi10.329 @sf 16 r m (H) s cmr8.300 @sf 244 1860 p m (11) s cmr10.329 @sf 297 1853 p m (and) s cmmi10.329 @sf 16 r m (H) s cmr8.300 @sf 424 1860 p m (22) s cmr10.329 @sf 477 1853 p m (are) 15 (upp) 1 (er-Hessen) 0 (b) 1 (erg) 16 (of) 16 (dimensions) ks cmmi10.329 @sf 17 r m (k) s cmsy10.329 @sf 12 r m (\002) s cmmi10.329 @sf 10 r m (k) s cmr10.329 @sf 17 r m (and) s cmmi10.329 @sf 16 r m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (k) s cmsy10.329 @sf 12 r m (\002) s cmmi10.329 @sf 11 r m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (k) s cmr10.329 @sf 1 r m (,) 16 (resp) 1 (ectiv) 0 (ely;) ks cmmi10.329 @sf 74 1952 p m (\013) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r save [<6003C0E00620700610700E10700E087007083807043803803803803803801C01C01C01C01C01C0 1C01C00E00E00E00E00F00C00E80C0076180071F00070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 22 32 -2 0 26] 104 @pc restore cmmi8.300 @sf 190 1959 p m (k) s cmr8.300 @sf 1 r m (+1) s cmmi8.300 @sf m (;k) s cmr10.329 @sf 286 1952 p m (,) 14 (and) ks cmmi10.329 @sf 16 r m (e) s cmr8.300 @sf 423 1929 p save [<0102040C1818303070606060E0E0E0E0E0E0E0E0E0E060606070303018180C040201> 8 34 -3 9 14] 40 @pc restore cmmi8.300 @sf 14 r m (k) s cmr8.300 @sf 1 r save [<8040203018180C0C0E060606070707070707070707070606060E0C0C181830204080> 8 34 -2 9 14] 41 @pc restore cmmi8.300 @sf 423 1965 p m (i) s cmr10.329 @sf 487 1952 p m (is) 16 (the) ks cmmi10.329 @sf 15 r m (i) s 627 1937 p save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 18 26 -1 0 21] 104 @pc restore cmr10.329 @sf 680 1952 p m (unit) 16 (v) 0 (ector) 13 (of) 15 (length) ks cmmi10.329 @sf 16 r m (k) s cmr10.329 @sf 1 r m (.) s 124 2094 p m (Let) s cmmi10.329 @sf 15 r m (H) s cmr8.300 @sf 243 2101 p m (0) s cmr10.329 @sf 275 2094 p m (=) s cmmi10.329 @sf 13 r m (H) s cmsy10.329 @sf 12 r m (\000) s cmmi10.329 @sf 9 r m (\013) 0 (e) ks cmr8.300 @sf 467 2071 p save [<0102040C1818303070606060E0E0E0E0E0E0E0E0E0E060606070303018180C040201> 8 34 -3 9 14] 40 @pc restore cmmi8.300 @sf 14 r m (n) s cmr8.300 @sf save [<8040203018180C0C0E060606070707070707070707070606060E0C0C181830204080> 8 34 -2 9 14] 41 @pc restore cmmi8.300 @sf 467 2108 p m (k) s cmr8.300 @sf 1 r m (+1) s cmmi10.329 @sf 534 2094 p m (e) s cmr8.300 @sf 555 2071 p save [<0102040C1818303070606060E0E0E0E0E0E0E0E0E0E060606070303018180C040201> 8 34 -3 9 14] 40 @pc restore cmmi8.300 @sf 14 r m (n) s cmr8.300 @sf save [<8040203018180C0C0E060606070707070707070707070606060E0C0C181830204080> 8 34 -2 9 14] 41 @pc restore cmmi8.300 @sf 14 r m (T) s 555 2108 p m (k) s cmr10.329 @sf 632 2094 p m (,) 14 (then) ks cmmi10.329 @sf 15 r m (H) s cmr8.300 @sf 800 2101 p m (0) s cmr10.329 @sf 832 2094 p m (=) s cmex10.300 @sf 880 2022 p save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pc restore cmmi10.329 @sf 938 2067 p m (H) s cmr8.300 @sf 976 2074 p m (11) s 1037 2084 p 2 57 ru cmmi10.329 @sf 1063 2067 p m (H) s cmr8.300 @sf 1101 2074 p m (12) s 913 2086 p 250 2 ru cmr10.329 @sf 964 2130 p m (0) s 1037 2139 p 2 57 ru cmmi10.329 @sf 1063 2130 p m (H) s cmr8.300 @sf 1101 2137 p m (22) s cmex10.300 @sf 1163 2022 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1196 2094 p m (,) 14 (and) ks cmmi10.329 @sf 15 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmr8.300 @sf 1395 2101 p m (0) s cmr10.329 @sf 1413 2094 p m (\)) 13 (=) ks cmmi10.329 @sf 13 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmr8.300 @sf 1576 2101 p m (11) s cmr10.329 @sf 1612 2094 p m (\)) s cmsy10.329 @sf 8 r save [<00FE0003FF800F01E01C007030001860000C60000CC00006C00006C00006C00006C00006C00006 C00006C00006C00006C00006C00006C00006C00006C00006C00006C00006C00006C00006C00006 C00006400002> 23 28 -3 1 30] 91 @pc restore cmmi10.329 @sf 40 r m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (H) s cmr8.300 @sf 1762 2101 p m (22) s cmr10.329 @sf 1798 2094 p m (\)) 14 (\(where) ks cmmi10.329 @sf 74 2193 p m (\033) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (M) s cmr10.329 @sf 5 r m (\)) 14 (is) 15 (the) 14 (sp) 1 (ectrum) 15 (of) ks cmmi10.329 @sf 14 r m (M) s cmr10.329 @sf 5 r m (\).) 20 (The) 14 (algorithm) 15 (can) 15 (then) 14 (b) 1 (e) 16 (describ) 1 (ed) 16 (as) 14 (follo) 0 (ws.) 19 (W) -3 (e) 14 (\014rst) 14 (\014nd) 15 (the) ks cmmi10.329 @sf 74 2293 p m (k) s cmr10.329 @sf 14 r m (eigenpairs) 15 (of) ks cmmi10.329 @sf 12 r m (H) s cmr8.300 @sf 410 2300 p m (11) s cmr10.329 @sf 460 2293 p m (and) 14 (the) ks cmmi10.329 @sf 13 r m (n) s cmsy10.329 @sf 6 r m (\000) s cmmi10.329 @sf 6 r m (k) s cmr10.329 @sf 14 r m (eigenpairs) 15 (of) ks cmmi10.329 @sf 12 r m (H) s cmr8.300 @sf 1033 2300 p m (22) s cmr10.329 @sf 1084 2293 p m (b) 0 (y) 12 (some) 12 (metho) 1 (d,) 14 (p) 1 (erhaps) 13 (the) 14 (QR) 13 (algorithm.) ks 74 2392 p m (These) 15 (eigenpairs) 15 (are) 14 (then) 14 (used) 15 (to) 14 (construct) 13 (initial) 17 (appro) 0 (ximations) 13 (to) 13 (the) 14 (eigenpairs) 16 (of) ks cmmi10.329 @sf 13 r m (H) s cmr10.329 @sf 18 r m (in) 15 (the) ks 74 2492 p m (follo) 0 (wing) 19 (w) 0 (a) -1 (y:) 25 (if) ks cmmi10.329 @sf 19 r m (\025) s cmr10.329 @sf 18 r m (is) 20 (an) 19 (eigen) 0 (v) -2 (alue) 18 (of) ks cmmi10.329 @sf 19 r m (H) s cmr8.300 @sf 908 2499 p m (11) s cmr10.329 @sf 964 2492 p m (and) s cmmi10.329 @sf 19 r m (x) s cmr10.329 @sf 19 r m (is) 19 (the) 19 (corresp) 1 (onding) 20 (eigen) 0 (v) 0 (ector,) 17 (then) ks cmmi10.329 @sf 19 r m (\025) s cmr10.329 @sf 19 r m (is) s 74 2592 p m (view) 0 (ed) 11 (as) 11 (an) 11 (appro) 0 (ximate) 10 (eigen) 0 (v) -2 (alue) 11 (of) ks cmmi10.329 @sf 11 r m (H) s cmr10.329 @sf 14 r m (with) 12 (the) 11 (corresp) 1 (onding) 13 (appro) 0 (ximate) 9 (eigen) 0 (v) 0 (ector) 10 (tak) 0 (en) ks 74 2691 p m (to) 14 (b) 1 (e) ks cmex10.300 @sf 190 2619 p save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pc restore cmmi10.329 @sf 244 2664 p m (x) s cmr10.329 @sf 246 2719 p m (0) s cmex10.300 @sf 291 2619 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 324 2691 p m (,) 14 (where) ks cmmi10.329 @sf 15 r m (n) s cmsy10.329 @sf 9 r m (\000) s cmmi10.329 @sf 9 r m (k) s cmr10.329 @sf 16 r m (zeros) 15 (are) 14 (app) 1 (ended) 16 (to) ks cmmi10.329 @sf 14 r m (x) s cmr10.329 @sf m (.) 20 (Note) 14 (that) ks cmex10.300 @sf 1317 2619 p save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pc restore cmmi10.329 @sf 1371 2664 p m (x) s cmr10.329 @sf 1372 2719 p m (0) s cmex10.300 @sf 1417 2619 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1465 2691 p m (is) 15 (an) 14 (exact) 15 (eigen) 0 (v) 0 (ector) 12 (of) ks @eop 2 @bop0 2 @bop1 cmr10.329 @sf 1941 -77 p m (2) s 74 67 p m (nal) 17 (form\).) 23 (This) 17 (approac) 0 (h) 15 (in) 17 (turn) 17 (enables) 17 (rapid) 17 (and) 17 (accurate) 16 (determination,) 18 (in) 17 (parallel,) 18 (of) 16 (the) ks 74 167 p m (eigen) 0 (v) -2 (alues) 15 (and) 16 (the) 15 (asso) 1 (ciated) 15 (eigen) 0 (v) 0 (ectors.) ks 124 308 p m (In) 13 (this) 13 (pap) 1 (er) 13 (w) 0 (e) 12 (prop) 1 (ose) 12 (a) 12 (parallel) 15 (algorithm) 12 (for) 12 (the) 13 (solution) 13 (of) 12 (the) 13 (non-symmetric) 13 (eigen) 0 (v) -2 (alue) ks 74 408 p m (problem.) 27 (The) 17 (approac) 0 (h) 16 (uses) 18 (some) 17 (of) 17 (the) 17 (features) 17 (of) 17 (the) 17 (divide-and-c) 1 (onquer) 19 (algorithm) 17 (for) 17 (the) ks 74 507 p m (symmetric) 13 (case) 13 (men) 0 (tioned) 12 (earlier.) 20 (In) 14 (particular,) 13 (the) 13 (original) 14 (problem) 13 (is) 13 (divided) 15 (in) 0 (to) 12 (t) 0 (w) -1 (o) 10 (smaller) ks 74 607 p m (and) 23 (indep) 1 (enden) 1 (t) 22 (subproblems) 23 (b) 0 (y) 22 (a) 21 (rank-one) 23 (mo) 1 (di\014cation) 23 (of) 22 (the) 22 (matrix.) 41 (\(W) -3 (e) 21 (assume) 22 (that) ks 74 706 p m (the) 19 (matrix) 18 (has) 19 (already) 19 (b) 1 (een) 20 (reduced) 20 (to) 18 (Hessen) 0 (b) 1 (erg) 18 (form) 18 (and) 19 (that) 18 (the) 19 (rank-one) 19 (mo) 1 (di\014cation) ks 74 806 p m (remo) 0 (v) -1 (es) 13 (a) 14 (sub) 1 (diagonal) 16 (elemen) 0 (t\).) 19 (Once) 15 (the) 15 (eigensystems) 15 (of) 14 (the) 15 (smaller) 15 (subproblems) 16 (are) 14 (kno) 0 (wn,) ks 74 906 p m (it) 16 (is) 16 (p) 1 (ossible) 17 (to) 15 (compute) 16 (those) 15 (of) 15 (the) 16 (original) 16 (matrix.) 21 (In) 16 (the) 15 (non-symmetric) 16 (case,) 16 (ho) 0 (w) -1 (ev) -1 (er,) 13 (the) ks 74 1005 p m (eigen) 0 (v) -2 (alues) 18 (of) 17 (the) 17 (mo) 1 (di\014ed) 19 (matrix) 17 (do) 18 (not) 17 (in) 0 (terlace) 17 (with) 18 (those) 17 (of) 17 (the) 18 (original) 19 (matrix.) 26 (Indeed,) ks 74 1105 p m (the) 15 (eigen) 0 (v) -2 (alues) 16 (can) 15 (scatter) 14 (an) 0 (ywhere) 14 (in) 16 (the) 16 (complex) 16 (plane.) ks 124 1246 p m (In) 15 (our) 14 (algorithm) 15 (for) 13 (the) 15 (non-symmetric) 15 (case,) 14 (the) 15 (eigensystem) 15 (of) 14 (the) 14 (subproblem) 16 (is) 15 (used) 15 (only) ks 74 1346 p m (to) 18 (construct) 19 (initial) 21 (guesses) 18 (for) 19 (an) 18 (iterativ) 0 (e) 18 (pro) 1 (cess) 19 (that) 18 (yields) 21 (the) 18 (desired) 20 (eigensystem) 20 (of) 18 (the) ks 74 1445 p m (original) 19 (problem.) 30 (Under) 19 (suitable) 19 (conditions,) 20 (Newton's) 18 (metho) 1 (d) 18 (or) 18 (a) 18 (con) 0 (tin) 0 (uation) 16 (metho) 1 (d) 19 (can) ks 74 1545 p m (b) 1 (e) 16 (used) 16 (to) 15 (\014nd) 16 (the) 16 (eigenpairs) 17 (of) 15 (the) 15 (original) 17 (problem.) 21 (W) -3 (e) 14 (rep) 1 (ort) 16 (here) 15 (on) 16 (our) 15 (application) 17 (of) 15 (an) ks 74 1645 p m (iterativ) 0 (e) 14 (re\014nemen) 0 (t) 15 (approac) 0 (h) 14 (based) 15 (on) 15 (Newton's) 14 (metho) 1 (d;) 15 (w) 0 (e) 14 (shall) 16 (not) 15 (pursue) 16 (the) 15 (con) 0 (tin) 0 (uation) ks 74 1744 p m (metho) 1 (d) 16 (in) 16 (this) 15 (pap) 1 (er.) 21 (W) -3 (ork) 13 (on) 15 (the) 16 (con) 0 (tin) 0 (uat) -1 (ion) 14 (approac) 0 (h) 14 (has) 15 (b) 1 (een) 16 (rep) 1 (orted) 16 (b) 0 (y) 14 ([) 0 (13) ks 1742 1744 p m (].) s 124 1885 p m (In) 14 (section) 14 (2) 14 (w) 0 (e) 12 (describ) 1 (e) 15 (the) 14 (algorithm) 13 (using) 15 (an) 13 (iterativ) 0 (e) 13 (re\014nemen) 0 (t) 13 (pro) 1 (cedure) 14 (based) 14 (on) 14 (New-) ks 74 1985 p m (ton's) 12 (metho) 1 (d.) 19 (Section) 13 (3) 12 (co) 0 (v) -1 (ers) 11 (the) 12 (de\015ation) 13 (step) 12 (required) 14 (to) 12 (o) 0 (v) -1 (ercome) 10 (m) 0 (ultiple) 13 (con) 0 (v) 0 (ergence) 11 (to) 11 (a) ks 74 2085 p m (particular) 14 (eigen) 0 (v) -2 (alue.) 19 (In) 13 (section) 14 (4) 13 (the) 13 (con) 0 (v) -1 (ergence) 12 (b) 1 (eha) 0 (vior) 12 (is) 14 (discussed.) 21 (In) 13 (section) 14 (5) 12 (w) 0 (e) 12 (discuss) ks 74 2184 p m (the) 18 (case) 18 (when) 18 (the) 18 (matrix) 18 (or) 17 (its) 19 (rank) 17 (one) 18 (mo) 1 (di\014cation) 19 (has) 18 (a) 18 (defectiv) 0 (e) 18 (system) 17 (of) 17 (eigen) 0 (v) 0 (ectors.) ks 74 2284 p m (Section) 20 (6) 18 (estimates) 19 (the) 19 (amoun) 0 (t) 17 (of) 18 (w) 0 (ork) 17 (the) 19 (parallel) 21 (algorithm) 18 (requires) 20 (and) 19 (compares) 18 (this) 20 (to) ks 74 2383 p m (the) 19 (standard) 19 (tec) 0 (hniques.) 31 (Section) 19 (7) 19 (describ) 1 (es) 20 (the) 19 (parallel) 21 (algorithm) 18 (and) 20 (the) 18 (di\013eren) 0 (t) 19 (parallel) ks 74 2483 p m (implemen) 0 (tations) 14 (of) 13 (the) 14 (new) 14 (algorithm,) 14 (and) 14 (giv) 0 (es) 13 (n) 0 (umerical) 14 (results.) 20 (Section) 14 (9) 14 (describ) 1 (es) 15 (ho) 0 (w) 12 (our) ks 74 2583 p m (ideas) 16 (extend) 16 (to) 14 (the) 16 (generalized) 17 (eigen) 0 (v) -2 (alue) 15 (problem.) ks @eop 1 @bop0 1 @bop1 cmr10.329 @sf 1941 -77 p m (1) s cmbx10.432 @sf 167 67 p save [ 47 41 -2 0 52] 65 @pc restore 75 r save [ 39 41 -3 0 47] 80 @pc restore 46 r m (arallel) s 20 r save [ 47 41 -2 0 52] 65 @pc restore 52 r m (lgorithm) 19 (for) 24 (the) ks 22 r save [ 47 41 -3 0 54] 78 @pc restore 54 r m (on) s save [ 17 6 -1 -11 23] 45 @pc restore 23 r save [ 29 41 -4 0 38] 83 @pc restore 38 r save [<0FC00000003FE00000007C78000000FE3C000000FE1E000000FE0E000000FE0F0000007C070000 003807800000000380000000038000000001C000000001C000000003E000000003E000000007F0 00000007F00000000FF80000000FF80000000FF80000001FDC0000001FDC0000003FDE0000003F 8E0000007F8F0000007F070000007F07000000FE03800000FE03800001FC01C00001FC01C00003 FC01E00003F800E00007F800F00007F000700007F0007000FFFE03FF80FFFE03FF80FFFE03FF80> 33 39 -1 12 36] 121 @pc restore 36 r m (mm) -2 (e) -1 (tri) -1 (c) ks 21 r save [ 39 41 -3 0 45] 69 @pc restore 45 r m (igen) -1 (v) -3 (al) -1 (ue) ks 868 142 p save [ 39 41 -3 0 47] 80 @pc restore 47 r m (roblem) s 1147 121 p save [<01800180018001804182F18F399C0FF003C003C00FF0399CF18F41820180018001800180> 16 18 -2 -1 21] 3 @pc restore 834 259 p save [<1F80000021E000004070000040380000F03C0000F81E0000F81E0000780F0000380F0000000F00 00000F0000000780000007800000078000000780000003C0000003C0000003C0000003C0000001 E0000001E0000001E0000001E0000000F0000000F0000000F0000000F000000078000000780000 0078000000780000003C0000003C0000003C000007FFC0> 26 35 -4 1 26] 74 @pc restore 26 r save [<0F0780308C40305C40703C20701C20F01C20F00E10F00E00F00E00F00E00780700780700780700 3807003C03801C03800E03800E03800705C00185C000F8C0> 20 21 -5 0 25] 97 @pc restore 25 r save [<0FC000183000300C00700200700100F00100F00000F00000F00000F00000780000780000780000 3800003C00001C07800E078007038003018001C100007E00> 17 21 -5 0 22] 99 @pc restore 22 r save [<600F00E01880701880703840703840703840381C20381C003838003838001C70001FC0001E0000 1D80000E40000E20600E10F00E10F0070C700702100701E0070000038000038000038000038000 01C00001C00001C00001C00000E00000E00000E0000FE00000F000> 20 35 -3 0 22] 107 @pc restore 40 r save [<1F80000021E000004070000040380000F03C0000F81E0000F81E0000780F0000380F0000000F00 00000F0000000780000007800000078000000780000003C0000003C0000003C0000003C0000001 E0000001E0000001E0000001E0000000F0000000F0000000F0000000F000000078000000780000 0078000000780000003C0000003C0000003C000007FFC0> 26 35 -4 1 26] 74 @pc restore 26 r save [ 5 5 -6 0 15] 46 @pc restore 32 r save [ 35 34 -3 0 37] 68 @pc restore 37 r save [<07C000187000301800700C00700E00700700F00780F00380F003C0F003C07801E07801E07801E0 3801E03C01E01C01E00E01C00701C003818001C300007E00> 19 21 -5 0 25] 111 @pc restore 25 r save [<3003C0700620380610380E10380E083807081C07041C03801C03801C03800E01C00E01C00E01C0 0E01C08700E08700E08780E08780E04740C02631C01C0F00> 22 21 -5 0 27] 110 @pc restore 27 r save [<3F800060E000F03000F01800701C00000E00000E00000E0000070000070001E700061700060B80 0E07800E03801E03801E01C01E01C01E01C01E01C00F00E00F00E00F00E00700E0078070038070 01C07001C07000E0B80030B8001F18> 21 31 -2 10 22] 103 @pc restore 22 r save [<0F0780308C40305C40703C20701C20F01C20F00E10F00E00F00E00F00E00780700780700780700 3807003C03801C03800E03800E03800705C00185C000F8C0> 20 21 -5 0 25] 97 @pc restore 25 r save [<3000007000003800003800003800003800001C00001C00001C00001C00000E00000E00000E0000 0E00008700008701808703C08783C04741C02620801C1F00> 18 21 -5 0 21] 114 @pc restore 21 r save [<3000007000003800003800003800003800001C00001C00001C00001C00000E00000E00000E0000 0E00008700008701808703C08783C04741C02620801C1F00> 18 21 -5 0 21] 114 @pc restore 20 r save [<0F0780308C40305C40703C20701C20F01C20F00E10F00E00F00E00F00E00780700780700780700 3807003C03801C03800E03800E03800705C00185C000F8C0> 20 21 -5 0 25] 97 @pc restore 981 329 p save [<0F0780308C40305C40703C20701C20F01C20F00E10F00E00F00E00F00E00780700780700780700 3807003C03801C03800E03800E03800705C00185C000F8C0> 20 21 -5 0 25] 97 @pc restore 25 r save [<3003C0700620380610380E10380E083807081C07041C03801C03801C03800E01C00E01C00E01C0 0E01C08700E08700E08780E08780E04740C02631C01C0F00> 22 21 -5 0 27] 110 @pc restore 27 r save [<0F0780308C40305C40703C20701C20F01C20F00E10F00E00F00E00F00E00780700780700780700 3807003C03801C03800E03800E03800705C00185C000F9C00001C00000E00000E00000E00000E0 0000700000700000700000700000380000380000380003F800003C> 22 35 -5 0 25] 100 @pc restore 879 399 p save [ 46 34 -3 0 44] 77 @pc restore 44 r save [<0F0780308C40305C40703C20701C20F01C20F00E10F00E00F00E00F00E00780700780700780700 3807003C03801C03800E03800E03800705C00185C000F8C0> 20 21 -5 0 25] 97 @pc restore 25 r save [<3C0000630000F18000F0C00070E000007000007000007000003800003800003800003800001C00 001C00001C00001C00000E00000E00000E00000E00000700000700000700000700010380010380 008380008380004380002300001E00000000000000000000000000000000000000000000000000 0000C00001E00001E00000E0> 19 43 2 10 15] 106 @pc restore 15 r save [<0F80306070186004E002E002E000E000E000E000F000F000FFE0F018780438023C021C020E0203 8400F8> 15 21 -6 0 22] 101 @pc restore 21 r save [<0F0780308C40305C40703C20701C20F01C20F00E10F00E00F00E00F00E00780700780700780700 3807003C03801C03800E03800E03800705C00185C000F9C00001C00000E00000E00000E00000E0 0000700000700000700000700000380000380000380003F800003C> 22 35 -5 0 25] 100 @pc restore 41 r save [<81FC0000C6070000C80180007000C0007000600060003000600038002000180020001C0020001C 0020001C0000001E0000001E0000001E0000003C0000007C000003FC00001FF800007FF00000FF E00001FF000001F8000003E0000003C0000003C0000003C0010003C0010001C0018001C0018000 C0018000E00180006001C0003001C0001802C0000E0C400001F020> 27 36 -3 1 27] 83 @pc restore 27 r save [<1C00320071007080708070803840380038001C001C001C000E000E008700870087004300430023 001C000000000000000000000000000000000001C001C001E000C0> 11 33 -5 0 15] 105 @pc restore 15 r save [<0F0780308C40305C40703C20701C20F01C20F00E10F00E00F00E00F00E00780700780700780700 3807003C03801C03800E03800E03800705C00185C000F9C00001C00000E00000E00000E00000E0 0000700000700000700000700000380000380000380003F800003C> 22 35 -5 0 25] 100 @pc restore 25 r save [<0F0780308C40305C40703C20701C20F01C20F00E10F00E00F00E00F00E00780700780700780700 3807003C03801C03800E03800E03800705C00185C000F8C0> 20 21 -5 0 25] 97 @pc restore 25 r save [<3003C0700620380610380E10380E083807081C07041C03801C03801C03800E01C00E01C00E01C0 0E01C08700E08700E08780E08780E04740C02631C01C0F00> 22 21 -5 0 27] 110 @pc restore 27 r save [<1C00320071007080708070803840380038001C001C001C000E000E008700870087004300430023 001C000000000000000000000000000000000001C001C001E000C0> 11 33 -5 0 15] 105 @pc restore cmr10.329 @sf 713 467 p m (Computer) 15 (Science) 17 (Departmen) 0 (t) ks 786 524 p m (Univ) 0 (ersit) 0 (y) 14 (of) 14 (T) -3 (ennessee) ks 760 580 p m (Kno) 0 (xville,) 16 (TN) 15 (37996-1301) ks 983 690 p m (and) s 714 777 p m (Mathematical) 15 (Sciences) 17 (Section) ks 701 833 p m (Oak) 16 (Ridge) 16 (National) 16 (Lab) 1 (oratory) ks 802 890 p m (Oak) 15 (Ridge,) 16 (TN) 15 (37831) ks 825 976 p m (Septem) 0 (b) 1 (er) 15 (13,) 14 (1991) ks 928 1174 p save [ 31 28 -2 0 36] 65 @pc restore 36 r save [<1C3F001EC1E01F80701F00781F003C1F003C1F003E1F003E1F003E1F003E1F003E1F003E1F003C 1F003C1F00781F80701FE1E01F3F801F00001F00001F00001F00001F00001F00001F00001F0000 1F0000FF0000FF0000> 23 29 -1 0 27] 98 @pc restore 27 r save [ 14 18 -2 0 19] 115 @pc restore 19 r save [<03F007980F081F0C1F0C1F0C1F0C1F001F001F001F001F001F001F001F001F00FFFC3FFC0F000F 00070007000300030003000300> 14 26 -1 0 19] 116 @pc restore 19 r save [ 17 18 -1 0 20] 114 @pc restore 20 r save [<0FE1F83E13F8780BC0F807C0F807C0F807C07C07C03C07C01F07C007E7C0007FC00007C01C07C0 3E07C03E07803E0F801C1E000FF800> 21 18 -1 0 23] 97 @pc restore 23 r save [<03F8000E0E001C03003C0180780180780000F80000F80000F80000F80000F80000F80000780E00 781F003C1F001C1F000E0E0003FC00> 17 18 -2 0 21] 99 @pc restore 21 r save [<03F007980F081F0C1F0C1F0C1F0C1F001F001F001F001F001F001F001F001F00FFFC3FFC0F000F 00070007000300030003000300> 14 26 -1 0 19] 116 @pc restore 250 1278 p save [<03FFFC00001F8000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F00 00000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000800F 0020800F0020800F0020C00F0020400F0040400F0040600F00C0700F01C07FFFFFC0> 27 28 -1 0 30] 84 @pc restore 30 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 29 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 19 26 -1 8 23] 112 @pc restore 24 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 13 18 -1 0 16] 114 @pc restore 29 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<10F8001906001E03001C01801C01C01C00C01C00E01C00E01C00E01C00E01C00E01C00E01C00C0 1C01C01C01801E03001D86001C7C001C00001C00001C00001C00001C00001C00001C00001C0000 1C00001C0000FC0000> 19 29 -1 0 23] 98 @pc restore 24 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 31 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 33 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 9 29 -1 0 12] 108 @pc restore 24 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [ 33 18 -1 0 36] 109 @pc restore 46 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 28 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 32 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 31 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<00400000E00000E00000E00001D00001D00003D8000388000388000704000704000704000E0200 0E02001C01001C01003C0380FF07E0> 19 18 -1 0 22] 118 @pc restore 21 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 9 29 -1 0 12] 108 @pc restore 11 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 28 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 35 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<00400000E00000E00000E00001D00001D00003D8000388000388000704000704000704000E0200 0E02001C01001C01003C0380FF07E0> 19 18 -1 0 22] 118 @pc restore 22 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 188 1328 p save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 26 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 35 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [ 11 2 0 -8 14] 45 @pc restore 14 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<3C0000660000F30000F10000F0800000800000800000400000400000E00000E00000E00001D000 01D00003D8000388000388000704000704000704000E02000E02001C01001C01003C0380FF07E0> 19 26 -1 8 22] 121 @pc restore 22 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [ 33 18 -1 0 36] 109 @pc restore 35 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 31 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 21 18 0 0 22] 120 @pc restore 22 r save [<60F0F060> 4 4 -4 0 12] 46 @pc restore 29 r save [<03FFFC00001F8000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F00 00000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000800F 0020800F0020800F0020C00F0020400F0040400F0040600F00C0700F01C07FFFFFC0> 27 28 -1 0 30] 84 @pc restore 30 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 33 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [ 33 18 -1 0 36] 109 @pc restore 47 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 30 r save [<10F8001906001E03001C01801C01C01C00C01C00E01C00E01C00E01C00E01C00E01C00E01C00C0 1C01C01C01801E03001D86001C7C001C00001C00001C00001C00001C00001C00001C00001C0000 1C00001C0000FC0000> 19 29 -1 0 23] 98 @pc restore 23 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 38 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 37 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 34 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<00400000E00000E00000E00001D00001D00003D8000388000388000704000704000704000E0200 0E02001C01001C01003C0380FF07E0> 19 18 -1 0 22] 118 @pc restore 22 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 11 2 0 -8 14] 45 @pc restore 14 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [ 11 2 0 -8 14] 45 @pc restore 14 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<003FE000070000070000070000070000070000070000070007C7000C3700180F00300F00700700 600700E00700E00700E00700E00700E00700E00700700700700700300F00180B000C330003C100> 19 26 -2 8 22] 113 @pc restore 22 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 13 18 -1 0 16] 114 @pc restore 31 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 22 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 34 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 188 1378 p save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 31 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 37 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<00400000E00000E00000E00001D00001D00003D8000388000388000704000704000704000E0200 0E02001C01001C01003C0380FF07E0> 19 18 -1 0 22] 118 @pc restore 22 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 30 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<7F87F80E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C0 0E01C00E01C00E01C00E01C0FFFFC00E00000E00000E00000E00000E00000E01800E03C00703C0 03018001C180007E00> 21 29 0 0 23] 12 @pc restore 23 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 30 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<003FE000070000070000070000070000070000070000070007C7000C3700180F00300F00700700 600700E00700E00700E00700E00700E00700E00700700700700700300F00180B000C330003C100> 19 26 -2 8 22] 113 @pc restore 22 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<60F0F060> 4 4 -4 0 12] 46 @pc restore cmbx10.432 @sf 74 1563 p m (1) s 177 1563 p save [ 22 41 -2 0 26] 73 @pc restore 26 r m (n) -1 (tro) 2 (duction) ks cmr10.329 @sf 74 1749 p m (The) 16 (algebraic) 16 (eigen) 0 (v) -2 (alue) 15 (problem) 16 (is) 16 (one) 15 (of) 15 (the) 16 (fundamen) 0 (tal) 15 (problems) 15 (in) 17 (computational) 15 (mathe-) ks 74 1848 p m (matics.) 19 (It) 14 (arises) 14 (in) 14 (man) 0 (y) 12 (applications) 15 (and) 13 (therefore) 14 (represen) 0 (ts) 12 (an) 13 (imp) 1 (ortan) 0 (t) 12 (area) 13 (of) 13 (algorithmic) ks 74 1948 p m (researc) 0 (h.) 17 (The) 12 (problem) 12 (has) 10 (receiv) 0 (ed) 12 (considerable) 13 (atten) 0 (t) -1 (ion) 10 (whic) 0 (h) 11 (has) 11 (resulted) 12 (in) 12 (reliable) 13 (metho) 1 (ds) ks 74 2048 p m ([) 0 (17) ks 132 2048 p m (,) 16 (16) ks 206 2048 p m (,) 16 (15) ks 280 2048 p m (].) 22 (Ho) 0 (w) 0 (ev) -2 (er) 15 (it) 16 (is) 16 (reasonable) 17 (to) 15 (exp) 1 (ect) 17 (that) 15 (calculations) 18 (migh) 0 (t) 15 (b) 1 (e) 17 (accelerated) 16 (through) ks 74 2147 p m (the) 16 (use) 16 (of) 15 (parallel) 17 (algorithms.) 22 (A) 15 (fully) 17 (parallel) 17 (algorithm) 16 (for) 15 (the) 16 (symmetric) 16 (eigen) 0 (v) -2 (alue) 15 (problem) ks 74 2247 p m (w) 0 (as) 16 (recen) 0 (tly) 17 (prop) 1 (osed) 18 (in) 18 ([) 0 (6) ks 624 2247 p m (].) 26 (This) 18 (algorithm) 18 (is) 18 (based) 17 (on) 18 (a) 17 (divide-and-conqu) 1 (er) 19 (pro) 1 (cedure) 18 (out-) ks 74 2347 p m (lined) 15 (in) 14 ([) 0 (3) ks 269 2347 p m (].) 19 (The) 13 (latter) 13 (w) 0 (as) 11 (based) 13 (on) 13 (w) 0 (ork) 11 (in) 14 ([) 0 (10) ks 1015 2347 p m (]) 12 (and) 13 ([) 0 (1) ks 1162 2347 p m (].) 18 (The) 14 (fundamen) 0 (tal) 12 (principl) 1 (e) 15 (b) 1 (ehind) 15 (this) ks 74 2446 p m (algorithm) 15 (is) 14 (that) 14 (the) 15 (partitioning) 15 (b) 0 (y) 13 (rank-one) 15 (tearing) 14 (in) 0 (terlaces) 14 (the) 15 (eigen) 0 (v) -2 (alues) 14 (of) 14 (the) 15 (mo) 1 (di\014ed) ks 74 2546 p m (problem) 19 (with) 19 (the) 19 (eigen) 0 (v) -2 (alues) 19 (of) 18 (the) 18 (original) 20 (problem) 19 (\(the) 19 (matrix) 18 (is) 19 (\014rst) 18 (reduced) 20 (to) 18 (tridiago-) ks 74 2588 p 756 2 ru cmsy6.300 @sf 125 2616 p save [<0C000C008C40EDC07F800C007F80EDC08C400C000C00> 10 11 -3 -1 16] 3 @pc restore 143 2631 p save [<03FFE000001C0000001C0000001C0000001C0000001C0000001C0000001C0000001C0000001C00 00001C0000001C0000001C0000001C0000001C0000001C0000001C0000001C0000801C0080801C 0080801C0080C01C0180401C0100401C0100701C07007FFFFF00> 25 26 -1 0 28] 84 @pc restore 28 r save [ 18 26 -1 0 21] 104 @pc restore 21 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 27 r save [<010040000180C0000380E0000380E00003C1E0000741D000074190000F2398000E2388000E2308 001E170C001C1704001C160400380E06003C0E0700FF3F9F80> 25 16 -1 0 28] 119 @pc restore 28 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [ 18 26 -1 0 20] 107 @pc restore 30 r save [<010040000180C0000380E0000380E00003C1E0000741D000074190000F2398000E2388000E2308 001E170C001C1704001C160400380E06003C0E0700FF3F9F80> 25 16 -1 0 28] 119 @pc restore 28 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 25 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [<07CFC00C2E001C1E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E00 1C0E001C0E00FC7E00> 18 16 -1 0 21] 117 @pc restore 21 r save [ 18 23 -1 7 21] 112 @pc restore 21 r save [ 18 23 -1 7 21] 112 @pc restore 22 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore 34 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [ 18 16 -1 0 21] 110 @pc restore 33 r save [ 18 23 -1 7 21] 112 @pc restore 21 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 26 r save [<10F0001B0C001E07001C03001C03801C01C01C01C01C01C01C01C01C01C01C01C01C01801C0380 1E07001F0E001CF8001C00001C00001C00001C00001C00001C00001C00001C00001C0000FC0000> 18 26 -1 0 21] 98 @pc restore 21 r save [<780000E40000E20000E1000001000001000000800000800001C00001C00001C00003A00003A000 0790000710000710000E08000E08001E0C001C04001C04003C0600FF1F80> 17 23 -1 7 20] 121 @pc restore 31 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 18 26 -1 0 21] 104 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 28 r save [ 24 26 -2 0 29] 78 @pc restore 29 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 9 26 0 0 10] 108 @pc restore 23 r save [<87E0D818E004C006C00280038003800300030007000E003E07FC1FF83FE07E007000E000C002C0 02C002C0066006200E18360FC2> 16 26 -2 0 21] 83 @pc restore 21 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 30 r save [ 20 26 -2 0 25] 70 @pc restore 23 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [<07CFC00C2E001C1E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E00 1C0E001C0E00FC7E00> 18 16 -1 0 21] 117 @pc restore 21 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore 21 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 18 16 -1 0 21] 110 @pc restore 33 r save [<87E0D818E004C006C00280038003800300030007000E003E07FC1FF83FE07E007000E000C002C0 02C002C0066006200E18360FC2> 16 26 -2 0 21] 83 @pc restore 21 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 30 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore 33 r save [<03FFE000001C0000001C0000001C0000001C0000001C0000001C0000001C0000001C0000001C00 00001C0000001C0000001C0000001C0000001C0000001C0000001C0000001C0000801C0080801C 0080801C0080C01C0180401C0100401C0100701C07007FFFFF00> 25 26 -1 0 28] 84 @pc restore 26 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 16 r save [ 18 26 -1 0 21] 104 @pc restore 21 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 9 26 0 0 10] 108 @pc restore 10 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [<07E0381C6006C003C003C003C003600F1FFE3FFC3FF07000600020002FC0186030307038703870 387038303018730FCE> 16 24 -1 8 19] 103 @pc restore 19 r save [<780000E40000E20000E1000001000001000000800000800001C00001C00001C00003A00003A000 0790000710000710000E08000E08001E0C001C04001C04003C0600FF1F80> 17 23 -1 7 20] 121 @pc restore 32 r save [<003F0001C0C00300300E00081C00081C0004380004780002700002700002F00000F00000F00000 F00000F00000F000007000027000027800023800061C00061C000E0E001E03002E01C0C6003F02> 23 26 -2 0 28] 67 @pc restore 28 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 12 16 -1 0 15] 114 @pc restore 25 r save [<003F0001C0C00300300E00081C00081C0004380004780002700002700002F00000F00000F00000 F00000F00000F000007000027000027800023800061C00061C000E0E001E03002E01C0C6003F02> 23 26 -2 0 28] 67 @pc restore 28 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 20 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 18 23 -1 7 21] 112 @pc restore 22 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [ 10 2 0 -7 13] 45 @pc restore 74 2676 p save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<00800001C00001C00001C00003A00003A0000790000710000710000E08000E08001E0C001C0400 1C04003C0600FF1F80> 17 16 -1 0 20] 118 @pc restore 20 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 30 r save [ 26 26 -1 0 29] 65 @pc restore 29 r save [<07E0381C6006C003C003C003C003600F1FFE3FFC3FF07000600020002FC0186030307038703870 387038303018730FCE> 16 24 -1 8 19] 103 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 29 16 -1 0 32] 109 @pc restore 32 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 26 r save [ 24 26 -2 0 29] 78 @pc restore 29 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [<60F0F060> 4 4 -3 0 11] 46 @pc restore 28 r save [<003F0001C0C00300300E00081C00081C0004380004780002700002700002F00000F00000F00000 F00000F00000F000007000027000027800023800061C00061C000E0E001E03002E01C0C6003F02> 23 26 -2 0 28] 67 @pc restore 28 r save [<003F0001C0C00300300E00081C00081C0004380004780002700002700002F00000F00000F00000 F00000F00000F000007000027000027800023800061C00061C000E0E001E03002E01C0C6003F02> 23 26 -2 0 28] 67 @pc restore 28 r save [ 25 26 -2 0 28] 82 @pc restore 28 r save [ 10 2 0 -7 13] 45 @pc restore 13 r save [<0FC0186020106008C00CC00CC00CC00C401C603830F819F007C00F803E603C3070106018601860 182018303018600780> 14 24 -2 0 19] 56 @pc restore 19 r save [<0FC0186020106008C00CC00CC00CC00C401C603830F819F007C00F803E603C3070106018601860 182018303018600780> 14 24 -2 0 19] 56 @pc restore 19 r save [<078018603030703860186018E01CE01CE01CE01CE01CE01CE01CE01CE01CE01CE01CE01C601860 183030303018600780> 14 24 -2 0 19] 48 @pc restore 19 r save [<1F002180604070607030003800180018001C0F9C185C303C603C601CE01CE01CE01CE018E01860 187030303018600780> 14 24 -2 0 19] 57 @pc restore 19 r save [<07C01860303030187018601C601CE01CE01CE01CE018F018F030E860E7C0E00060007000300030 3818380C18061001E0> 14 24 -2 0 19] 54 @pc restore 19 r save [ 12 24 -3 0 19] 49 @pc restore 19 r save [<0F8030E0403040388018E01CE01C401C001C001C001800382030386027C0200020002000200020 003FC03FE03FF03018> 14 24 -2 0 19] 53 @pc restore 19 r save [<8040202010101070F0F060> 4 11 -3 7 11] 44 @pc restore 24 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore 34 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [ 18 16 -1 0 21] 110 @pc restore 35 r save [ 18 23 -1 7 21] 112 @pc restore 21 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 28 r save [<10F0001B0C001E07001C03001C03801C01C01C01C01C01C01C01C01C01C01C01C01C01801C0380 1E07001F0E001CF8001C00001C00001C00001C00001C00001C00001C00001C00001C0000FC0000> 18 26 -1 0 21] 98 @pc restore 21 r save [<780000E40000E20000E1000001000001000000800000800001C00001C00001C00003A00003A000 0790000710000710000E08000E08001E0C001C04001C04003C0600FF1F80> 17 23 -1 7 20] 121 @pc restore 32 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 18 26 -1 0 21] 104 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 29 r save [ 26 26 -1 0 29] 65 @pc restore 29 r save [ 18 23 -1 7 21] 112 @pc restore 21 r save [ 18 23 -1 7 21] 112 @pc restore 21 r save [ 9 26 0 0 10] 108 @pc restore 10 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore 36 r save [ 30 26 -2 0 35] 77 @pc restore 35 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 18 26 -1 0 21] 104 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 29 16 -1 0 32] 109 @pc restore 32 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 9 26 0 0 10] 108 @pc restore 25 r save [<87E0D818E004C006C00280038003800300030007000E003E07FC1FF83FE07E007000E000C002C0 02C002C0066006200E18360FC2> 16 26 -2 0 21] 83 @pc restore 21 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 29 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [<07CFC00C2E001C1E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E00 1C0E001C0E00FC7E00> 18 16 -1 0 21] 117 @pc restore 21 r save [<10F0001B0C001E07001C03001C03801C01C01C01C01C01C01C01C01C01C01C01C01C01801C0380 1E07001F0E001CF8001C00001C00001C00001C00001C00001C00001C00001C00001C0000FC0000> 18 26 -1 0 21] 98 @pc restore 21 r save [ 18 23 -1 7 21] 112 @pc restore 21 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [<07E0381C6006C003C003C003C003600F1FFE3FFC3FF07000600020002FC0186030307038703870 387038303018730FCE> 16 24 -1 8 19] 103 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 29 16 -1 0 32] 109 @pc restore 46 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFC00E000E000E000E 000E000E000E100738031801F0> 13 26 0 0 12] 102 @pc restore 24 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 18 26 -1 0 21] 104 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 30 r save [<007F000001C1C000070070000E0038001C001C003C001E0038000E0078000F0078000F00F00007 80F0000780F0000780F0000780F0000780F0000780F0000780F00007807000070078000F003800 0E003C001E001C001C000E0038000700700001C1C000007F0000> 25 26 -2 0 30] 79 @pc restore 30 r save [<7F8FE3FC0E0380E00E0380E00E0380E00E0380E00E0380E00E0380E00E0380E00E0380E00E0380 E00E0380E00E0380E00E0380E00E0380E00E0380E0FFFFFFE00E0380000E0380000E0380000E03 80000E0380000E038040060380E00703C06001C17040007E1F80> 30 26 0 0 32] 14 @pc restore 32 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 74 2722 p save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFC00E000E000E000E 000E000E000E100738031801F0> 13 26 0 0 12] 102 @pc restore 25 r save [ 22 26 -2 0 26] 69 @pc restore 26 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<07E0381C6006C003C003C003C003600F1FFE3FFC3FF07000600020002FC0186030307038703870 387038303018730FCE> 16 24 -1 8 19] 103 @pc restore 19 r save [<780000E40000E20000E1000001000001000000800000800001C00001C00001C00003A00003A000 0790000710000710000E08000E08001E0C001C04001C04003C0600FF1F80> 17 23 -1 7 20] 121 @pc restore 34 r save [ 25 26 -2 0 28] 82 @pc restore 28 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [ 18 26 -1 0 21] 104 @pc restore 21 r save [<8040202010101070F0F060> 4 11 -3 7 11] 44 @pc restore 23 r save [<003E0000C1800180400300400700200600200E00100E00100E00100E00100E00100E00100E0010 0E00100E00100E00100E00100E00100E00100E00100E00100E00100E00100E00100E0038FFE1FF> 24 26 -2 0 29] 85 @pc restore 29 r save [<60F0F060> 4 4 -3 0 11] 46 @pc restore 11 r save [<87E0D818E004C006C00280038003800300030007000E003E07FC1FF83FE07E007000E000C002C0 02C002C0066006200E18360FC2> 16 26 -2 0 21] 83 @pc restore 34 r save [ 24 26 -2 0 29] 68 @pc restore 29 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 18 23 -1 7 21] 112 @pc restore 21 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 29 16 -1 0 32] 109 @pc restore 32 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 28 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFC00E000E000E000E 000E000E000E100738031801F0> 13 26 0 0 12] 102 @pc restore 25 r save [ 22 26 -2 0 26] 69 @pc restore 26 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<07E0381C6006C003C003C003C003600F1FFE3FFC3FF07000600020002FC0186030307038703870 387038303018730FCE> 16 24 -1 8 19] 103 @pc restore 19 r save [<780000E40000E20000E1000001000001000000800000800001C00001C00001C00003A00003A000 0790000710000710000E08000E08001E0C001C04001C04003C0600FF1F80> 17 23 -1 7 20] 121 @pc restore 18 r save [<8040202010101070F0F060> 4 11 -3 7 11] 44 @pc restore 23 r save [<07CFC00C2E001C1E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E00 1C0E001C0E00FC7E00> 18 16 -1 0 21] 117 @pc restore 21 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 12 16 -1 0 15] 114 @pc restore 29 r save [<003F0001C0C00300300E00081C00081C0004380004780002700002700002F00000F00000F00000 F00000F00000F000007000027000027800023800061C00061C000E0E001E03002E01C0C6003F02> 23 26 -2 0 28] 67 @pc restore 28 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 27 r save [ 24 26 -2 0 29] 68 @pc restore 29 r save [ 22 26 -2 0 26] 69 @pc restore 26 r save [ 10 2 0 -7 13] 45 @pc restore 13 r save [ 26 26 -1 0 29] 65 @pc restore 29 r save [<003F0001C0C00300300E00081C00081C0004380004780002700002700002F00000F00000F00000 F00000F00000F000007000027000027800023800061C00061C000E0E001E03002E01C0C6003F02> 23 26 -2 0 28] 67 @pc restore 28 r save [<078018603030703860186018E01CE01CE01CE01CE01CE01CE01CE01CE01CE01CE01CE01C601860 183030303018600780> 14 24 -2 0 19] 48 @pc restore 19 r save [<0F8030E0403040388018E01CE01C401C001C001C001800382030386027C0200020002000200020 003FC03FE03FF03018> 14 24 -2 0 19] 53 @pc restore 19 r save [ 10 2 0 -7 13] 45 @pc restore 13 r save [<0FC0186020106008C00CC00CC00CC00C401C603830F819F007C00F803E603C3070106018601860 182018303018600780> 14 24 -2 0 19] 56 @pc restore 19 r save [<07FF007000700070007000700070FFFFC070407020703070107008700C70047002700370017000 F000F0007000300030> 16 24 -1 0 19] 52 @pc restore 19 r save [<007F000001C1C000070070000E0038001C001C003C001E0038000E0078000F0078000F00F00007 80F0000780F0000780F0000780F0000780F0000780F0000780F00007807000070078000F003800 0E003C001E001C001C000E0038000700700001C1C000007F0000> 25 26 -2 0 30] 79 @pc restore 30 r save [ 25 26 -2 0 28] 82 @pc restore 28 r save [ 14 24 -2 0 19] 50 @pc restore 19 r save [ 12 24 -3 0 19] 49 @pc restore 19 r save [<07FF007000700070007000700070FFFFC070407020703070107008700C70047002700370017000 F000F0007000300030> 16 24 -1 0 19] 52 @pc restore 19 r save [<078018603030703860186018E01CE01CE01CE01CE01CE01CE01CE01CE01CE01CE01CE01C601860 183030303018600780> 14 24 -2 0 19] 48 @pc restore 19 r save [<078018603030703860186018E01CE01CE01CE01CE01CE01CE01CE01CE01CE01CE01CE01C601860 183030303018600780> 14 24 -2 0 19] 48 @pc restore 19 r save [<60F0F060> 4 4 -3 0 11] 46 @pc restore @eop 1 @bop0 1 @bop1 cmr10.329 @sf 837 67 p save [ 44 1 0 -12 45] 124 @pc restore 45 r save [ 44 1 0 -12 45] 124 @pc restore 45 r save [ 44 1 0 -12 45] 124 @pc restore 45 r save [ 44 1 0 -12 45] 124 @pc restore 45 r save [ 44 1 0 -12 45] 124 @pc restore 46 r save [ 44 1 0 -12 45] 124 @pc restore 45 r save [ 44 1 0 -12 45] 124 @pc restore 45 r save [ 44 1 0 -12 45] 124 @pc restore 888 124 p m (CS) 15 (-) 15 (91) 15 (-) 15 (137) ks 837 180 p save [ 44 1 0 -12 45] 124 @pc restore 45 r save [ 44 1 0 -12 45] 124 @pc restore 45 r save [ 44 1 0 -12 45] 124 @pc restore 45 r save [ 44 1 0 -12 45] 124 @pc restore 45 r save [ 44 1 0 -12 45] 124 @pc restore 46 r save [ 44 1 0 -12 45] 124 @pc restore 45 r save [ 44 1 0 -12 45] 124 @pc restore 45 r save [ 44 1 0 -12 45] 124 @pc restore 203 466 p save [ 55 49 -3 0 62] 65 @pc restore 90 r save [ 48 49 -2 0 56] 80 @pc restore 55 r save [<00FF800FF807FFF03FF80FFFF87FF83FF03CFF007FC00EFE007F8003FE00FF0003FE00FF0001FE 00FF0001FE00FF0001FE00FF0001FE007F8001FE003F8001FE001FC001FE000FF001FE0007FE01 FE0001FFF1FE00003FFFFE000001FFFE00000001FE00000001FE00010001FE0007C001FE000FE0 01FE001FF001FE001FF003FC001FF003F8001FF007F0000FE01FE00007FFFFC00003FFFF000000 7FF80000> 37 32 -2 0 40] 97 @pc restore 40 r save [ 29 32 -2 0 34] 114 @pc restore 34 r save [<00FF800FF807FFF03FF80FFFF87FF83FF03CFF007FC00EFE007F8003FE00FF0003FE00FF0001FE 00FF0001FE00FF0001FE00FF0001FE007F8001FE003F8001FE001FC001FE000FF001FE0007FE01 FE0001FFF1FE00003FFFFE000001FFFE00000001FE00000001FE00010001FE0007C001FE000FE0 01FE001FF001FE001FF003FC001FF003F8001FF007F0000FE01FE00007FFFFC00003FFFF000000 7FF80000> 37 32 -2 0 40] 97 @pc restore 40 r save [ 18 50 -3 0 23] 108 @pc restore 23 r save [ 18 50 -3 0 23] 108 @pc restore 23 r save [<0003FF0000003FFFE00000FFFFF80003FE00FC0007F8001E000FF0000F001FE00007801FC00003 803FC00003803FC00000007F800000007F80000000FF80000000FF80000000FF80000000FFFFFF FF80FFFFFFFF80FFFFFFFF80FF80003F80FF80003F807F80003F807F80003F007FC0003F003FC0 003F003FC0007E001FE0007E000FE000FC0007F801F80003FC07F00000FFFFE000003FFF800000 07FC0000> 33 32 -2 0 38] 101 @pc restore 38 r save [ 18 50 -3 0 23] 108 @pc restore 50 r save [ 55 49 -3 0 62] 65 @pc restore 62 r save [ 18 50 -3 0 23] 108 @pc restore 23 r save [<001FFF800000FFFFF00007FFFFFE000FF801FF001FC0003F803F00000FC07E000007E0FC000003 F0FC000003F0FC000003F0FC000003F0FC000007F07E00000FF03F00007FE01FFFFFFFE007FFFF FFC003FFFFFF8007FFFFFF000FFFFFFE000FFFFFF8001FFFFFC0001F800000001F000000001E00 0000001E000000000E000000000E1FF0000006FFFE000007FFFF000007F83FC0000FE00FE0000F E00FE0001FC007F0001FC007F0003FC007F8003FC007F8003FC007F8003FC007F8003FC007F800 1FC007F0001FC007F0600FE00FE0F00FE00FE1F807F83FF1F801FFFF7FF800FFFE3FF0001FF007 E0> 37 47 -2 15 41] 103 @pc restore 41 r save [<0007FE0000003FFFC00001FFFFF80003FE07FC0007F801FE000FE0007F001FE0007F803FC0003F C03FC0003FC07F80001FE07F80001FE07F80001FE0FF80001FF0FF80001FF0FF80001FF0FF8000 1FF0FF80001FF0FF80001FF0FF80001FF0FF80001FF07F80001FE07F80001FE07F80001FE03FC0 003FC03FC0003FC01FC0003F800FE0007F0007F000FE0003FC03FC0000FFFFF000003FFFC00000 07FE0000> 36 32 -2 0 41] 111 @pc restore 41 r save [ 29 32 -2 0 34] 114 @pc restore 34 r save [ 17 51 -3 0 23] 105 @pc restore 23 r save [<000FE0007FF000FFF801FE1C03FC0E03F80E07F80707F80707F80707F80707F80707F80707F807 07F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F800 07F80007F80007F800FFFFFEFFFFFEFFFFFE1FF80007F80003F80001F80000F80000F800007800 007800007800003800003800003800003800003800> 24 46 -2 0 32] 116 @pc restore 32 r save [ 41 50 -3 0 46] 104 @pc restore 46 r save [ 64 32 -3 0 71] 109 @pc restore 96 r save [<7FFFF0007FFFF0007FFFF00003FC000003FC000003FC000003FC000003FC000003FC000003FC00 0003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC 000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC0000FF FFF800FFFFF800FFFFF80003FC000003FC000003FC000003FC000003FC000003FC000003FC0000 03FC01C003FC03E003FC07F001FC0FF801FE0FF800FE0FF8007F0FF8003FC7F0001FFFE00007FF C00000FF00> 29 50 -2 0 25] 102 @pc restore 25 r save [<0007FE0000003FFFC00001FFFFF80003FE07FC0007F801FE000FE0007F001FE0007F803FC0003F C03FC0003FC07F80001FE07F80001FE07F80001FE0FF80001FF0FF80001FF0FF80001FF0FF8000 1FF0FF80001FF0FF80001FF0FF80001FF0FF80001FF07F80001FE07F80001FE07F80001FE03FC0 003FC03FC0003FC01FC0003F800FE0007F0007F000FE0003FC03FC0000FFFFF000003FFFC00000 07FE0000> 36 32 -2 0 41] 111 @pc restore 41 r save [ 29 32 -2 0 34] 114 @pc restore 62 r save [<000FE0007FF000FFF801FE1C03FC0E03F80E07F80707F80707F80707F80707F80707F80707F807 07F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F800 07F80007F80007F800FFFFFEFFFFFEFFFFFE1FF80007F80003F80001F80000F80000F800007800 007800007800003800003800003800003800003800> 24 46 -2 0 32] 116 @pc restore 32 r save [ 41 50 -3 0 46] 104 @pc restore 46 r save [<0003FF0000003FFFE00000FFFFF80003FE00FC0007F8001E000FF0000F001FE00007801FC00003 803FC00003803FC00000007F800000007F80000000FF80000000FF80000000FF80000000FFFFFF FF80FFFFFFFF80FFFFFFFF80FF80003F80FF80003F807F80003F807F80003F007FC0003F003FC0 003F003FC0007E001FE0007E000FE000FC0007F801F80003FC07F00000FFFFE000003FFF800000 07FC0000> 33 32 -2 0 38] 101 @pc restore 65 r save [ 60 49 -2 0 65] 78 @pc restore 65 r save [<0007FE0000003FFFC00001FFFFF80003FE07FC0007F801FE000FE0007F001FE0007F803FC0003F C03FC0003FC07F80001FE07F80001FE07F80001FE0FF80001FF0FF80001FF0FF80001FF0FF8000 1FF0FF80001FF0FF80001FF0FF80001FF0FF80001FF07F80001FE07F80001FE07F80001FE03FC0 003FC03FC0003FC01FC0003F800FE0007F0007F000FE0003FC03FC0000FFFFF000003FFFC00000 07FE0000> 36 32 -2 0 41] 111 @pc restore 41 r save [ 41 32 -3 0 46] 110 @pc restore 46 r save [ 20 7 -1 -12 27] 45 @pc restore 27 r save [ 35 49 -5 0 46] 83 @pc restore 46 r save [<0FC00000003FF80000007FFC0000007A3E000000FF0F000000FF07800000FF03800000FF01C000 007E01E000003C00E000000000F00000000070000000007000000000380000000038000000007C 000000007C00000000FE00000000FE00000001FF00000001FF00000003FF80000003FF80000007 FFC0000007F9C000000FF9E000000FF0E000000FF0E000001FE07000001FE07000003FE0380000 3FC03800007FC03C00007F801C0000FF801E0000FF000E0001FF000F0001FE00070003FE000780 03FC00038007FC0003C007F80001C007F80003E0FFFF801FFEFFFF801FFEFFFF801FFE> 39 46 -2 14 44] 121 @pc restore 44 r save [ 64 32 -3 0 71] 109 @pc restore 71 r save [ 64 32 -3 0 71] 109 @pc restore 68 r save [<0003FF0000003FFFE00000FFFFF80003FE00FC0007F8001E000FF0000F001FE00007801FC00003 803FC00003803FC00000007F800000007F80000000FF80000000FF80000000FF80000000FFFFFF FF80FFFFFFFF80FFFFFFFF80FF80003F80FF80003F807F80003F807F80003F007FC0003F003FC0 003F003FC0007E001FE0007E000FE000FC0007F801F80003FC07F00000FFFFE000003FFF800000 07FC0000> 33 32 -2 0 38] 101 @pc restore 38 r save [<000FE0007FF000FFF801FE1C03FC0E03F80E07F80707F80707F80707F80707F80707F80707F807 07F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F800 07F80007F80007F800FFFFFEFFFFFEFFFFFE1FF80007F80003F80001F80000F80000F800007800 007800007800003800003800003800003800003800> 24 46 -2 0 32] 116 @pc restore 32 r save [ 29 32 -2 0 34] 114 @pc restore 34 r save [ 17 51 -3 0 23] 105 @pc restore 23 r save [<0007FC00007FFF8000FFFFE003FF01F007F800780FF0001C1FE0001C3FE0000E3FC0000E7FC000 007FC000007F800000FF800000FF800000FF800000FF800000FF800000FF800000FF800000FF80 00007F8000007F8000407FC001F03FC003F83FC007FC1FE007FC0FE007FC07F007FC03FC03F800 FFFFF0007FFFE00007FF00> 31 32 -3 0 37] 99 @pc restore 646 558 p save [ 49 49 -2 0 54] 69 @pc restore 54 r save [ 17 51 -3 0 23] 105 @pc restore 23 r save [<001FFF800000FFFFF00007FFFFFE000FF801FF001FC0003F803F00000FC07E000007E0FC000003 F0FC000003F0FC000003F0FC000003F0FC000007F07E00000FF03F00007FE01FFFFFFFE007FFFF FFC003FFFFFF8007FFFFFF000FFFFFFE000FFFFFF8001FFFFFC0001F800000001F000000001E00 0000001E000000000E000000000E1FF0000006FFFE000007FFFF000007F83FC0000FE00FE0000F E00FE0001FC007F0001FC007F0003FC007F8003FC007F8003FC007F8003FC007F8003FC007F800 1FC007F0001FC007F0600FE00FE0F00FE00FE1F807F83FF1F801FFFF7FF800FFFE3FF0001FF007 E0> 37 47 -2 15 41] 103 @pc restore 41 r save [<0003FF0000003FFFE00000FFFFF80003FE00FC0007F8001E000FF0000F001FE00007801FC00003 803FC00003803FC00000007F800000007F80000000FF80000000FF80000000FF80000000FFFFFF FF80FFFFFFFF80FFFFFFFF80FF80003F80FF80003F807F80003F807F80003F007FC0003F003FC0 003F003FC0007E001FE0007E000FE000FC0007F801F80003FC07F00000FFFFE000003FFF800000 07FC0000> 33 32 -2 0 38] 101 @pc restore 38 r save [ 41 32 -3 0 46] 110 @pc restore 45 r save [<000038000000007C000000007C00000000FE00000000FE00000001FF00000001FF00000003FF80 000003FF80000007FFC0000007F9C000000FF9E000000FF0E000000FF0E000001FE07000001FE0 7000003FE03800003FC03800007FC03C00007F801C0000FF801E0000FF000E0001FF000F0001FE 00070003FE00078003FC00038007FC0003C007F80001C007F80003E0FFFF801FFEFFFF801FFEFF FF801FFE> 39 32 -2 0 44] 118 @pc restore 39 r save [<00FF800FF807FFF03FF80FFFF87FF83FF03CFF007FC00EFE007F8003FE00FF0003FE00FF0001FE 00FF0001FE00FF0001FE00FF0001FE007F8001FE003F8001FE001FC001FE000FF001FE0007FE01 FE0001FFF1FE00003FFFFE000001FFFE00000001FE00000001FE00010001FE0007C001FE000FE0 01FE001FF001FE001FF003FC001FF003F8001FF007F0000FE01FE00007FFFFC00003FFFF000000 7FF80000> 37 32 -2 0 40] 97 @pc restore 40 r save [ 18 50 -3 0 23] 108 @pc restore 23 r save [<000FFC0FFF80007FFF0FFF8000FFFF8FFF8001FE03CFF80003F8006FF00003F8003FF00007F800 1FF00007F8001FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF000 07F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F800 0FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF000 07F8000FF0000FF8001FF000FFF801FFF000FFF801FFF000FFF801FFF00001F80003F000> 41 32 -3 0 46] 117 @pc restore 46 r save [<0003FF0000003FFFE00000FFFFF80003FE00FC0007F8001E000FF0000F001FE00007801FC00003 803FC00003803FC00000007F800000007F80000000FF80000000FF80000000FF80000000FFFFFF FF80FFFFFFFF80FFFFFFFF80FF80003F80FF80003F807F80003F807F80003F007FC0003F003FC0 003F003FC0007E001FE0007E000FE000FC0007F801F80003FC07F00000FFFFE000003FFF800000 07FC0000> 33 32 -2 0 38] 101 @pc restore 63 r save [ 48 49 -2 0 56] 80 @pc restore 56 r save [ 29 32 -2 0 34] 114 @pc restore 34 r save [<0007FE0000003FFFC00001FFFFF80003FE07FC0007F801FE000FE0007F001FE0007F803FC0003F C03FC0003FC07F80001FE07F80001FE07F80001FE0FF80001FF0FF80001FF0FF80001FF0FF8000 1FF0FF80001FF0FF80001FF0FF80001FF0FF80001FF07F80001FE07F80001FE07F80001FE03FC0 003FC03FC0003FC01FC0003F800FE0007F0007F000FE0003FC03FC0000FFFFF000003FFFC00000 07FE0000> 36 32 -2 0 41] 111 @pc restore 41 r save [<07001FE00007807FFE0007C1FFFF0007E3E07FC007F7001FE007FE0007F007FC0007F807F80003 FC07F80003FC07F80001FE07F80001FE07F80001FE07F80001FF07F80001FF07F80001FF07F800 01FF07F80001FF07F80001FF07F80001FF07F80001FF07F80001FE07F80001FE07F80001FE07F8 0003FC07F80003FC07F80003F807FE0007F007FF000FE007FFE03FC007F9FFFF8007F87FFE0007 F80FF00007F800000007F800000007F800000007F800000007F800000007F800000007F8000000 07F800000007F800000007F800000007F800000007F800000007F80000000FF8000000FFF80000 00FFF8000000FFF800000001F8000000> 40 50 -2 0 46] 98 @pc restore 46 r save [ 18 50 -3 0 23] 108 @pc restore 23 r save [<0003FF0000003FFFE00000FFFFF80003FE00FC0007F8001E000FF0000F001FE00007801FC00003 803FC00003803FC00000007F800000007F80000000FF80000000FF80000000FF80000000FFFFFF FF80FFFFFFFF80FFFFFFFF80FF80003F80FF80003F807F80003F807F80003F007FC0003F003FC0 003F003FC0007E001FE0007E000FE000FC0007F801F80003FC07F00000FFFFE000003FFF800000 07FC0000> 33 32 -2 0 38] 101 @pc restore 38 r save [ 64 32 -3 0 71] 109 @pc restore 728 811 p save [<07F00000001FFC000000383F000000700FC00000E007E00000C003F00000F803F00000FE01F800 00FE01FC0000FE00FC0000FE00FC00007E00FE000018007E000000007E000000007F000000007F 000000003F000000003F000000003F800000003F800000001F800000001F800000001FC0000000 1FC00000000FC00000000FC00000000FE00000000FE000000007E000000007E000000007E00000 0007F000000003F000000003F000000003F000000003F800000001F800000001F800000001F800 000001FC00000000FC00000000FC00000000FC00000000FE000000007E000000007E000000007F 000000007F0000007FFFF800007FFFF8> 37 50 -7 1 38] 74 @pc restore 38 r save [<03E007800FF81FC01E1E3C603C077C303C03FC187C01FC187800FC1878007C0CFC007C0CFC007C 0CFC003E04FC003E00FC003E00FC003E007E001F007E001F007E001F007E001F003F000F803F00 0F801F000F801F800F800F8007C0078007C007C007C003E00FC001E00FE000F01FE0003C3BE000 1FF1C00007E000> 30 31 -7 0 37] 97 @pc restore 37 r save [<00FE000003FF80000F81E0001E0078003E001C003C0006007C0003007C0001807C000100FC0000 00FC000000FC000000FC000000FC0000007E0000007E0000007E0000007E0000003F0000003F00 00001F0000001F800E000F801F0007C01F8003C01F8001E00F8000F00780007C0380003F070000 0FFE000001F800> 25 31 -7 0 33] 99 @pc restore 33 r save [ 28 50 -6 0 33] 107 @pc restore 58 r save [<07F00000001FFC000000383F000000700FC00000E007E00000C003F00000F803F00000FE01F800 00FE01FC0000FE00FC0000FE00FC00007E00FE000018007E000000007E000000007F000000007F 000000003F000000003F000000003F800000003F800000001F800000001F800000001FC0000000 1FC00000000FC00000000FC00000000FE00000000FE000000007E000000007E000000007E00000 0007F000000003F000000003F000000003F000000003F800000001F800000001F800000001F800 000001FC00000000FC00000000FC00000000FC00000000FE000000007E000000007E000000007F 000000007F0000007FFFF800007FFFF8> 37 50 -7 1 38] 74 @pc restore 38 r save [<78FCFEFFFF7F3F1E> 8 8 -8 0 22] 46 @pc restore 47 r save [ 50 49 -4 0 54] 68 @pc restore 54 r save [<00FE000003FF80000F83E0001E00F8003E007C003C003E007C001F007C000F807C000FC0FC0007 C0FC0007E0FC0003E0FC0003F0FC0003F07E0001F87E0001F87E0001F87E0001F83F0000F83F00 00F81F0000F81F8000F80F8000F807C000F803C000F001E001F000F001E0007C03C0001F078000 0FFF000001FC00> 29 31 -7 0 37] 111 @pc restore 37 r save [<0E0001F0000F0007F8000F80070C000F800F06000F800F03000F800F018007C00F818007C00F80 C007C00F80C007C007C0C003E007C04003E007C00003E003E00003E003E00001F003E00001F001 F00001F001F00001F001F00000F800F80000F800F800C0F800F800C0F800F800607C007800607C 007C00607E007C00307F007800307F8078001879C0F8001C78F0F0000FF03FE00003C00FC000> 34 31 -6 0 40] 110 @pc restore 40 r save [<1FF800007FFF00007C0FC000FC03E0007E01F0007C00F8003C007C0000007C0000003E0000003E 0000003E0000003E0000001F0000001F00003E1F0000FF9F0001E1EF8003C07F8003C03F8007C0 1F8007800FC0078007C00FC007C00FC007C00FC003E00FC003E00FC003E00FC003E007E001F007 E001F007E001F007E001F003F000F803F000F801F000F801F800F800F8007C0078007C007C007C 003E00FC001E00FE000F01FE0003C3BE0001FF1C00007E00> 31 45 -3 14 33] 103 @pc restore 33 r save [<03E007800FF81FC01E1E3C603C077C303C03FC187C01FC187800FC1878007C0CFC007C0CFC007C 0CFC003E04FC003E00FC003E00FC003E007E001F007E001F007E001F007E001F003F000F803F00 0F801F000F801F800F800F8007C0078007C007C007C003E00FC001E00FE000F01FE0003C3BE000 1FF1C00007E000> 30 31 -7 0 37] 97 @pc restore 37 r save [<0E0000000F0000000F8000000F8000000F8000000F80000007C0000007C0000007C0000007C000 0003E0000003E0000003E0000003E0000001F0000001F0000001F0000001F0000000F8000000F8 0000C0F80000C0F80000607C0380607C07C0607C07E0307E07E0307F03E0187B81E01C79C1C00F F0FF8003C03F00> 27 31 -6 0 30] 114 @pc restore 30 r save [<0E0000000F0000000F8000000F8000000F8000000F80000007C0000007C0000007C0000007C000 0003E0000003E0000003E0000003E0000001F0000001F0000001F0000001F0000000F8000000F8 0000C0F80000C0F80000607C0380607C07C0607C07E0307E07E0307F03E0187B81E01C79C1C00F F0FF8003C03F00> 27 31 -6 0 30] 114 @pc restore 27 r save [<03E007800FF81FC01E1E3C603C077C303C03FC187C01FC187800FC1878007C0CFC007C0CFC007C 0CFC003E04FC003E00FC003E00FC003E007E001F007E001F007E001F007E001F003F000F803F00 0F801F000F801F800F800F8007C0078007C007C007C003E00FC001E00FE000F01FE0003C3BE000 1FF1C00007E000> 30 31 -7 0 37] 97 @pc restore 37 r save [<00E0000000F0000000F0000000700000007800000038000000380000E0380E00F0181F00FC183F 007E183F001F8C7C0003CCF00000FDC000003F8000000E0000001F8000007EE00001F27C0007E3 1F000FC30FC01F8307E01F0381F00E0380E0000380000001C0000001C0000001C0000001E00000 01E0000000E000> 28 31 -14 -23 37] 42 @pc restore 966 943 p save [<03FC03E00F0307F03E008F087C005E0478003E04F8003E04F8003E04F8001E04F8001E04F8001E 047C001E003C001E003E001E001F001E000F801E0003E01E0000FC1E00000FFE0000001E000000 1E0000001E0008001E003E001E003E001E003E001C003C003C0010003800100070000C00E00003 03C00000FE0000> 30 31 -3 0 33] 97 @pc restore 33 r save [ 33 31 -2 0 37] 110 @pc restore 37 r save [<003F81FF00E061FF038011F0070009E00E0005E01E0003E01C0001E03C0001E03C0001E0780001 E0780001E0F80001E0F80001E0F80001E0F80001E0F80001E0F80001E0F80001E0F80001E0F800 01E0780001E07C0001E03C0001E03C0001E01E0001E00E0003E00F0003E0078005E001C019E000 F061E0001F81E0000001E0000001E0000001E0000001E0000001E0000001E0000001E0000001E0 000001E0000001E0000001E0000001E0000001E0000001E0000001E0000003E000003FE000003F E0000001E0> 32 50 -3 0 37] 100 @pc restore 813 1076 p save [ 67 49 -4 0 64] 77 @pc restore 64 r save [<03E007800FF81FC01E1E3C603C077C303C03FC187C01FC187800FC1878007C0CFC007C0CFC007C 0CFC003E04FC003E00FC003E00FC003E007E001F007E001F007E001F007E001F003F000F803F00 0F801F000F801F800F800F8007C0078007C007C007C003E00FC001E00FE000F01FE0003C3BE000 1FF1C00007E000> 30 31 -7 0 37] 97 @pc restore 37 r save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pc restore 22 r save [<01FC0007FF000F03C01E00F03C00387C000C780006F80003F80002F80000F80000F80000F80000 F80000FC0000FC0000FFF000FFFF807E0FF07E00783E001C3F000E1F00071F80070F800707C007 03E00700F00F007C1E001FFC0003F0> 24 31 -8 0 33] 101 @pc restore 30 r save [<03E007800FF81FC01E1E3C603C077C303C03FC187C01FC187800FC1878007C0CFC007C0CFC007E 0CFC007E04FC003E00FC003E00FC003F007E003F007E001F007E001F007E001F803F001F803F00 0F801F000F801F800FC00F800FC0078007C007C007C003E00FE001E00FE000F01FE0003C3BE000 1FF3F00007E3F0000001F0000001F0000001F8000001F8000000F8000000F8000000FC000000FC 0000007C0000007C0000007E0000007E0000003E0000003E0000003F0000003F000007FF000007 FF0000001F> 32 50 -7 0 37] 100 @pc restore 61 r save [<801FC00000C0FFF80000E1E03C000073800E00007E000780007E0003C0007C0001C0003C0000E0 00380000F0003800007000380000780018000038001800003C001800003C001800003C000C0000 3E000000003E000000003E000000003E000000003E000000007E00000000FE00000003FC000000 3FFC000001FFFC000007FFF800000FFFF000001FFFE000003FFF8000007FFC0000007FC0000000 7F000000007E000000007C000000007C0000000078000060007800006000780000600078000060 003C000070003C000070001C000070001E000070000E0000F800070000F800078001F80003C001 F80000E0033C0000781E1C00003FFC0C000007F004> 38 51 -6 1 40] 83 @pc restore 40 r save [<03C0000FF0000E38001E0C001E0C001E06001F06001F03001F03000F83000F81000F800007C000 07C00003E00003E00003E00001F00001F00001F000C0F800C0F80060F800607C00607C00307C00 303C00183C000C780007F00003E000000000000000000000000000000000000000000000000000 000000000000000000000E00001F00001F80001F80000F80000700> 17 48 -6 0 22] 105 @pc restore 22 r save [<03E007800FF81FC01E1E3C603C077C303C03FC187C01FC187800FC1878007C0CFC007C0CFC007E 0CFC007E04FC003E00FC003E00FC003F007E003F007E001F007E001F007E001F803F001F803F00 0F801F000F801F800FC00F800FC0078007C007C007C003E00FE001E00FE000F01FE0003C3BE000 1FF3F00007E3F0000001F0000001F0000001F8000001F8000000F8000000F8000000FC000000FC 0000007C0000007C0000007E0000007E0000003E0000003E0000003F0000003F000007FF000007 FF0000001F> 32 50 -7 0 37] 100 @pc restore 37 r save [<03E007800FF81FC01E1E3C603C077C303C03FC187C01FC187800FC1878007C0CFC007C0CFC007C 0CFC003E04FC003E00FC003E00FC003E007E001F007E001F007E001F007E001F003F000F803F00 0F801F000F801F800F800F8007C0078007C007C007C003E00FC001E00FE000F01FE0003C3BE000 1FF1C00007E000> 30 31 -7 0 37] 97 @pc restore 37 r save [<0E0001F0000F0007F8000F80070C000F800F06000F800F03000F800F018007C00F818007C00F80 C007C00F80C007C007C0C003E007C04003E007C00003E003E00003E003E00001F003E00001F001 F00001F001F00001F001F00000F800F80000F800F800C0F800F800C0F800F800607C007800607C 007C00607E007C00307F007800307F8078001879C0F8001C78F0F0000FF03FE00003C00FC000> 34 31 -6 0 40] 110 @pc restore 40 r save [<03C0000FF0000E38001E0C001E0C001E06001F06001F03001F03000F83000F81000F800007C000 07C00003E00003E00003E00001F00001F00001F000C0F800C0F80060F800607C00607C00307C00 303C00183C000C780007F00003E000000000000000000000000000000000000000000000000000 000000000000000000000E00001F00001F80001F80000F80000700> 17 48 -6 0 22] 105 @pc restore cmr10.329 @sf 713 1294 p m (Computer) 15 (Science) 17 (Departmen) 0 (t) ks 786 1351 p m (Univ) 0 (ersit) 0 (y) 14 (of) 14 (T) -3 (ennessee) ks 760 1407 p m (Kno) 0 (xville,) 16 (TN) 15 (37996-1301) ks 983 1524 p m (and) s 714 1640 p m (Mathematical) 15 (Sciences) 17 (Section) ks 701 1696 p m (Oak) 16 (Ridge) 16 (National) 16 (Lab) 1 (oratory) ks 802 1753 p m (Oak) 15 (Ridge,) 16 (TN) 15 (37831) ks 888 1959 p m (CS) 15 (-) 15 (91) 15 (-) 15 (137) ks 825 2166 p m (Septem) 0 (b) 1 (er) 15 (13,) 14 (1991) ks 74 2458 p save [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -14 23] 42 @pc restore 38 r m (Electronic) 16 (mail) 16 (address:) 20 (dongarra) ks save [<001FF00000E01F00010001C0060000700800000008000000100F07802030CC4020605C2040C03C 2041C01C1041C01C1081801C1083801C1083801C1083801C1083801C1083801C1083801C108180 1C1041C01C2041C01C2040C02020206040402030C040100F008008000100080001000600060001 00080000E07000001F8000> 28 32 -3 0 35] 64 @pc restore 35 r m (cs.utk.edu) 15 (and) 15 (sidani) ks save [<001FF00000E01F00010001C0060000700800000008000000100F07802030CC4020605C2040C03C 2041C01C1041C01C1081801C1083801C1083801C1083801C1083801C1083801C1083801C108180 1C1041C01C2041C01C2040C02020206040402030C040100F008008000100080001000600060001 00080000E07000001F8000> 28 32 -3 0 35] 64 @pc restore 35 r m (cs.utk.edu.) s 74 2556 p m (This) 18 (w) 0 (ork) 15 (w) 0 (as) 15 (supp) 1 (orted) 18 (in) 18 (part) 16 (b) 0 (y) 16 (the) 17 (National) 18 (Science) 19 (F) -3 (oundation) 16 (Science) 19 (and) 18 (T) -3 (ec) 0 (hnology) ks 74 2613 p m (Cen) 0 (ter) 20 (Co) 1 (op) 1 (erativ) 0 (e) 20 (Agreemen) 0 (t) 20 (No.) 38 (CCR-8809615,) 21 (and) 22 (in) 22 (part) 20 (b) 0 (y) 21 (the) 21 (Applied) 24 (Mathemati-) ks 74 2669 p m (cal) 20 (Sciences) 20 (subprogram) 18 (of) 19 (the) 19 (O\016ce) 19 (of) 19 (Energy) 19 (Researc) 0 (h,) 19 (U.S) 18 (Departmen) 0 (t) 17 (of) 19 (Energy) -3 (,) 18 (under) ks 74 2726 p m (Con) 0 (tract) 13 (DE-A) 0 (C05-84) -1 (OR21400.) ks @eop @end .