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11 dict begin
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cleartomark
%%EndFont 
%%BeginFont: CMSY5
%!PS-AdobeFont-1.1: CMSY5 1.0
%%CreationDate: 1991 Aug 15 07:21:16
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 48 /prime put
dup 105 /angbracketright put
readonly def
/FontBBox{21 -944 1448 791}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 1 /periodcentered put
dup 2 /multiply put
dup 6 /plusminus put
dup 15 /bullet put
dup 17 /equivalence put
dup 18 /reflexsubset put
dup 20 /lessequal put
dup 21 /greaterequal put
dup 25 /approxequal put
dup 26 /propersubset put
dup 28 /lessmuch put
dup 29 /greatermuch put
dup 32 /arrowleft put
dup 33 /arrowright put
dup 34 /arrowup put
dup 35 /arrowdown put
dup 41 /arrowdblright put
dup 49 /infinity put
dup 50 /element put
dup 54 /negationslash put
dup 55 /mapsto put
dup 76 /L put
dup 82 /R put
dup 91 /union put
dup 102 /braceleft put
dup 103 /braceright put
dup 106 /bar put
dup 107 /bardbl put
dup 112 /radical put
dup 114 /nabla put
dup 120 /section put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY6
%!PS-AdobeFont-1.1: CMSY6 1.0
%%CreationDate: 1991 Aug 15 07:21:34
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
readonly def
/FontBBox{-4 -948 1329 786}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI6
%!PS-AdobeFont-1.1: CMMI6 1.100
%%CreationDate: 1996 Jul 23 07:53:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 65 /A put
dup 110 /n put
readonly def
/FontBBox{11 -250 1241 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY8
%!PS-AdobeFont-1.1: CMSY8 1.0
%%CreationDate: 1991 Aug 15 07:22:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 6 /plusminus put
dup 25 /approxequal put
dup 49 /infinity put
dup 120 /section put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI8
%!PS-AdobeFont-1.1: CMMI8 1.100
%%CreationDate: 1996 Jul 23 07:53:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 33 /omega put
dup 34 /epsilon put
dup 68 /D put
dup 73 /I put
dup 76 /L put
dup 77 /M put
dup 80 /P put
dup 85 /U put
dup 105 /i put
dup 107 /k put
dup 119 /w put
dup 120 /x put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 61 /equal put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI5
%!PS-AdobeFont-1.1: CMMI5 1.100
%%CreationDate: 1996 Aug 02 08:21:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 61 /slash put
dup 84 /T put
dup 105 /i put
dup 107 /k put
readonly def
/FontBBox{37 -250 1349 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR5
%!PS-AdobeFont-1.1: CMR5 1.00B
%%CreationDate: 1992 Feb 19 19:55:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 49 /one put
dup 50 /two put
dup 111 /o put
dup 112 /p put
dup 116 /t put
readonly def
/FontBBox{-341 -250 1304 965}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 20 /bracketleftbigg put
dup 21 /bracketrightbigg put
dup 26 /braceleftbigg put
dup 32 /parenleftBigg put
dup 33 /parenrightBigg put
dup 48 /parenlefttp put
dup 49 /parenrighttp put
dup 50 /bracketlefttp put
dup 51 /bracketrighttp put
dup 52 /bracketleftbt put
dup 53 /bracketrightbt put
dup 54 /bracketleftex put
dup 55 /bracketrightex put
dup 56 /bracelefttp put
dup 58 /braceleftbt put
dup 60 /braceleftmid put
dup 62 /braceex put
dup 64 /parenleftbt put
dup 65 /parenrightbt put
dup 66 /parenleftex put
dup 67 /parenrightex put
dup 80 /summationtext put
dup 83 /uniontext put
dup 88 /summationdisplay put
dup 112 /radicalbig put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 1 /Delta put
dup 3 /Lambda put
dup 10 /Omega put
dup 12 /fi put
dup 22 /macron put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 94 /circumflex put
dup 97 /a put
dup 100 /d put
dup 103 /g put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 115 /s put
dup 120 /x put
dup 126 /tilde put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 61 /equal put
dup 97 /a put
dup 105 /i put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 116 /t put
dup 120 /x put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY7
%!PS-AdobeFont-1.1: CMSY7 1.0
%%CreationDate: 1991 Aug 15 07:21:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 2 /multiply put
dup 3 /asteriskmath put
dup 21 /greaterequal put
dup 48 /prime put
dup 49 /infinity put
dup 54 /negationslash put
dup 109 /arrowdblbothv put
dup 110 /backslash put
readonly def
/FontBBox{-15 -951 1252 782}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /alpha put
dup 27 /sigma put
dup 33 /omega put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 64 /partialdiff put
dup 65 /A put
dup 66 /B put
dup 69 /E put
dup 70 /F put
dup 72 /H put
dup 73 /I put
dup 77 /M put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 88 /X put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 109 /m put
dup 110 /n put
dup 112 /p put
dup 115 /s put
dup 116 /t put
dup 120 /x put
dup 121 /y put
readonly def
/FontBBox{0 -250 1171 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /alpha put
dup 12 /beta put
dup 13 /gamma put
dup 14 /delta put
dup 15 /epsilon1 put
dup 17 /eta put
dup 18 /theta put
dup 20 /kappa put
dup 21 /lambda put
dup 24 /xi put
dup 25 /pi put
dup 26 /rho put
dup 27 /sigma put
dup 28 /tau put
dup 33 /omega put
dup 34 /epsilon put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 64 /partialdiff put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 96 /lscript put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
currentdict end
currentfile eexec
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b(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)87
b(57)1054 2491 y(4.3.2)98 b(Matrix)20 b(v)o(ector)f(products)47
b(.)42 b(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)
f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)87 b(60)1054
2591 y(4.3.3)98 b(Sparse)20 b(Incomplete)e(F)o(actorizations)76
b(.)41 b(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)
h(.)f(.)g(.)g(.)h(.)87 b(63)863 2690 y(4.4)f(P)o(arallelism)80
b(.)41 b(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)
g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f
(.)g(.)g(.)h(.)87 b(67)1054 2790 y(4.4.1)98 b(Inner)19
b(products)76 b(.)42 b(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f
(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)
h(.)87 b(67)1054 2890 y(4.4.2)98 b(V)-9 b(ector)19 b(updates)68
b(.)42 b(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)
f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)87
b(69)1054 2989 y(4.4.3)98 b(Matrix-v)o(ector)18 b(products)40
b(.)i(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f
(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)87 b(69)1054
3089 y(4.4.4)98 b(Preconditioning)26 b(.)42 b(.)f(.)g(.)g(.)h(.)f(.)g
(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)
g(.)g(.)h(.)f(.)g(.)g(.)h(.)87 b(69)1054 3189 y(4.4.5)98
b(W)-7 b(a)n(v)o(efronts)20 b(in)g(the)g(Gauss-Seidel)g(and)g
(Conjugate)e(Gradient)h(methods)81 b(.)41 b(.)g(.)g(.)h(.)87
b(70)1054 3288 y(4.4.6)98 b(Block)o(ed)20 b(operations)e(in)j(the)f
(GMRES)h(method)65 b(.)42 b(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h
(.)f(.)g(.)g(.)h(.)87 b(71)739 3471 y Fv(5)82 b(Remaining)21
b(topics)2439 b(73)863 3571 y FG(5.1)86 b(The)20 b(Lanczos)g
(Connection)56 b(.)41 b(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g
(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)
87 b(73)863 3670 y(5.2)f(Block)20 b(and)g FC(s)p FG(-step)g(Iterati)n
(v)o(e)f(Methods)33 b(.)41 b(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)
g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)87
b(74)863 3770 y(5.3)f(Reduced)20 b(System)g(Preconditioning)27
b(.)41 b(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)
g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)87 b(74)863 3869
y(5.4)f(Domain)20 b(Decomposition)e(Methods)29 b(.)41
b(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h
(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)87 b(75)1054 3969
y(5.4.1)98 b(Ov)o(erlapping)18 b(Subdomain)g(Methods)57
b(.)41 b(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)
h(.)f(.)g(.)g(.)h(.)87 b(76)1054 4069 y(5.4.2)98 b(Non-o)o(v)o
(erlapping)16 b(Subdomain)i(Methods)31 b(.)41 b(.)g(.)g(.)h(.)f(.)g(.)g
(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)87
b(77)1054 4168 y(5.4.3)98 b(Further)19 b(Remarks)62 b(.)41
b(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g
(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)87
b(79)863 4268 y(5.5)f(Multigrid)19 b(Methods)71 b(.)41
b(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h
(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)87
b(80)863 4368 y(5.6)f(Ro)n(w)21 b(Projection)e(Methods)59
b(.)41 b(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)
g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)87
b(81)739 4550 y Fv(A)64 b(Obtaining)20 b(the)h(Softwar)o(e)2224
b(83)739 4733 y(B)69 b(Ov)o(er)o(view)20 b(of)g(the)g(BLAS)2258
b(85)739 4915 y(C)64 b(Glossary)2741 b(87)863 5015 y
FG(C.1)73 b(Notation)36 b(.)42 b(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)
g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h
(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)87 b(91)739
5198 y Fv(D)64 b(Flo)o(wchart)20 b(of)g(iterati)o(v)o(e)f(methods)1925
b(107)p eop end
%%Page: 9 9
TeXDict begin 9 8 bop 291 1179 a FF(List)52 b(of)f(Figur)l(es)415
1694 y FG(2.1)86 b(The)20 b(Jacobi)g(Method)59 b(.)41
b(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g
(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)129
b(8)415 1794 y(2.2)86 b(The)20 b(Gauss-Seidel)g(Method)f(.)42
b(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g
(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)129
b(9)415 1893 y(2.3)86 b(The)20 b(SOR)h(Method)47 b(.)42
b(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g
(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)87
b(10)415 1993 y(2.4)f(The)20 b(SSOR)h(Method)64 b(.)41
b(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g
(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)87
b(12)415 2093 y(2.5)f(The)20 b(Preconditioned)d(Conjugate)i(Gradient)g
(Method)30 b(.)41 b(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g
(.)h(.)f(.)g(.)g(.)87 b(13)415 2192 y(2.6)f(The)20 b(Preconditioned)d
(GMRES)p Fy(\()p FC(m)p Fy(\))22 b FG(Method)71 b(.)41
b(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h
(.)f(.)g(.)g(.)87 b(18)415 2292 y(2.7)f(The)20 b(Preconditioned)d
(BiConjugate)i(Gradient)h(Method)75 b(.)41 b(.)h(.)f(.)g(.)g(.)h(.)f(.)
g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)87 b(20)415 2392
y(2.8)f(The)20 b(Preconditioned)d(Quasi)k(Minimal)f(Residual)g(Method)f
(without)g(Look-ahead)48 b(.)42 b(.)f(.)g(.)g(.)87 b(22)415
2491 y(2.9)f(The)20 b(Preconditioned)d(Conjugate)i(Gradient)g(Squared)g
(Method)48 b(.)41 b(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)
87 b(23)415 2591 y(2.10)44 b(The)20 b(Preconditioned)d(BiConjugate)i
(Gradient)h(Stabilized)g(Method)33 b(.)42 b(.)f(.)g(.)g(.)h(.)f(.)g(.)h
(.)f(.)g(.)g(.)87 b(24)415 2690 y(2.11)44 b(The)20 b(Preconditioned)d
(Chebyshe)n(v)i(Method)66 b(.)41 b(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g
(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)87
b(26)415 2873 y(3.1)f(Preconditioner)18 b(solv)o(e)h(of)h(a)h(system)f
FC(M)9 b(x)23 b Fy(=)g FC(y)s FG(,)d(with)h FC(M)31 b
Fy(=)23 b FC(LU)90 b FG(.)41 b(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g
(.)g(.)87 b(39)415 2973 y(3.2)f(Preconditioner)22 b(solv)o(e)i(of)h(a)g
(system)g FC(M)9 b(x)31 b Fy(=)g FC(y)s FG(,)25 b(with)g
FC(M)40 b Fy(=)31 b(\()p FC(D)24 b Fy(+)d FC(L)p Fy(\))p
FC(D)2847 2943 y FA(\000)p Fz(1)2936 2973 y Fy(\()p FC(D)j
Fy(+)e FC(U)9 b Fy(\))31 b(=)606 3072 y(\()p FC(D)21
b Fy(+)d FC(L)p Fy(\)\()p FC(I)25 b Fy(+)18 b FC(D)1147
3042 y FA(\000)p Fz(1)1237 3072 y FC(U)9 b Fy(\))p FG(.)76
b(.)41 b(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)
h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)87
b(39)415 3172 y(3.3)f(Construction)23 b(of)h(a)g FC(D)r
FG(-)p FC(I)7 b(LU)33 b FG(incomplete)22 b(f)o(actorization)h
(preconditioner)m(,)e(storing)i(the)h(in-)606 3272 y(v)o(erses)c(of)g
(the)g(pi)n(v)n(ots)63 b(.)41 b(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h
(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)
g(.)h(.)f(.)g(.)g(.)87 b(40)415 3371 y(3.4)f(W)-7 b(a)n(v)o(efront)15
b(solution)g(of)h Fy(\()p FC(D)5 b Fy(+)s FC(L)p Fy(\))p
FC(x)22 b Fy(=)h FC(u)16 b FG(from)f(a)h(central)g(dif)n(ference)d
(problem)i(on)g(a)i(domain)606 3471 y(of)j FC(n)e Fx(\002)g
FC(n)j FG(points.)40 b(.)h(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g
(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)
f(.)g(.)h(.)f(.)g(.)g(.)87 b(42)415 3571 y(3.5)f(Preconditioning)29
b(step)k(algorithm)e(for)g(a)i(Neumann)d(e)o(xpansion)h
FC(M)2705 3540 y Fz(\()p FB(p)p Fz(\))2840 3571 y Fx(\031)45
b FC(M)3040 3540 y FA(\000)p Fz(1)3161 3571 y FG(of)32
b(an)606 3670 y(incomplete)19 b(f)o(actorization)f FC(M)32
b Fy(=)23 b(\()p FC(I)i Fy(+)18 b FC(L)p Fy(\))p FC(D)r
Fy(\()p FC(I)26 b Fy(+)18 b FC(U)9 b Fy(\))p FG(.)36
b(.)41 b(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)
g(.)87 b(43)415 3770 y(3.6)f(Block)20 b(v)o(ersion)f(of)h(a)h
FC(D)r FG(-)p FC(I)7 b(LU)28 b FG(f)o(actorization)51
b(.)41 b(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)
f(.)g(.)h(.)f(.)g(.)g(.)87 b(44)415 3869 y(3.7)f(Algorithm)19
b(for)g(approximating)e(the)k(in)m(v)o(erse)e(of)g(a)i(banded)e(matrix)
77 b(.)42 b(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)87
b(45)415 3969 y(3.8)f(Incomplete)18 b(block)i(f)o(actorization)e(of)i
(a)h(block)e(tridiagonal)f(matrix)81 b(.)42 b(.)f(.)g(.)g(.)h(.)f(.)g
(.)h(.)f(.)g(.)g(.)87 b(45)415 4152 y(4.1)f(Pro\002le)20
b(of)g(a)h(nonsymmetric)d(sk)o(yline)h(or)h(v)n(ariable-band)d(matrix.)
60 b(.)41 b(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)87
b(61)415 4251 y(4.2)f(A)21 b(rearrangement)c(of)j(Conjugate)f(Gradient)
g(for)g(parallelism)54 b(.)41 b(.)g(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h
(.)f(.)g(.)g(.)87 b(68)1890 5806 y(ix)p eop end
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TeXDict begin 1 10 bop 291 1139 a FD(Chapter)44 b(1)291
1556 y FF(Intr)l(oduction)291 1989 y FG(Which)20 b(of)g(the)g(follo)n
(wing)e(statements)j(is)g(true?)415 2159 y Fx(\017)41
b FG(Users)31 b(w)o(ant)f(\223black)f(box\224)g(softw)o(are)h(that)g
(the)o(y)f(can)h(use)g(with)g(complete)f(con\002dence)g(for)g(general)
498 2258 y(problem)19 b(classes)i(without)e(ha)n(ving)g(to)i
(understand)d(the)i(\002ne)g(algorithmic)f(details.)415
2430 y Fx(\017)41 b FG(Users)20 b(w)o(ant)g(to)g(be)g(able)f(to)h(tune)
f(data)h(structures)f(for)g(a)h(particular)e(application,)g(e)n(v)o(en)
h(if)h(the)f(softw)o(are)498 2529 y(is)i(not)f(as)h(reliable)f(as)h
(that)f(pro)o(vided)e(for)h(general)g(methods.)291 2699
y(It)h(turns)g(out)g(both)f(are)h(true,)g(for)f(dif)n(ferent)g(groups)g
(of)h(users.)415 2800 y(T)m(raditionally)-5 b(,)23 b(users)i(ha)n(v)o
(e)f(ask)o(ed)h(for)f(and)g(been)f(pro)o(vided)g(with)h(black)g(box)g
(softw)o(are)g(in)h(the)g(form)e(of)291 2900 y(mathematical)30
b(libraries)g(such)h(as)h FE(LAPACK)p FG(,)f FE(LINPACK)p
FG(,)f FE(NAG)p FG(,)h(and)f FE(IMSL)p FG(.)h(More)g(recently)-5
b(,)32 b(the)f(high-)291 2999 y(performance)23 b(community)i(has)i
(disco)o(v)o(ered)d(that)j(the)o(y)f(must)h(write)g(custom)f(softw)o
(are)g(for)g(their)h(problem.)291 3099 y(Their)g(reasons)g(include)f
(inadequate)g(functionality)f(of)j(e)o(xisting)f(softw)o(are)g
(libraries,)h(data)g(structures)f(that)291 3199 y(are)d(not)g(natural)g
(or)h(con)m(v)o(enient)d(for)i(a)h(particular)e(problem,)h(and)g(o)o(v)
o(erly)f(general)g(softw)o(are)i(that)f(sacri\002ces)291
3298 y(too)19 b(much)h(performance)d(when)j(applied)f(to)h(a)h(special)
f(case)h(of)e(interest.)415 3399 y(Can)h(we)g(meet)g(the)g(needs)f(of)h
(both)f(groups)f(of)i(users?)25 b(W)-7 b(e)21 b(belie)n(v)o(e)e(we)h
(can.)k(Accordingly)-5 b(,)17 b(in)j(this)h(book,)291
3499 y(we)c(introduce)f(the)i(use)f(of)h Ft(templates)p
FG(.)23 b(A)18 b(template)f(is)i(a)f(description)e(of)h(a)h(general)e
(algorithm)g(rather)h(than)g(the)291 3598 y(e)o(x)o(ecutable)d(object)i
(code)g(or)g(the)h(source)f(code)g(more)f(commonly)g(found)f(in)j(a)g
(con)m(v)o(entional)d(softw)o(are)i(library)-5 b(.)291
3698 y(Ne)n(v)o(ertheless,)26 b(although)e(templates)i(are)g(general)f
(descriptions)g(of)h(k)o(e)o(y)f(algorithms,)h(the)o(y)g(of)n(fer)e
(whate)n(v)o(er)291 3798 y(de)o(gree)c(of)i(customization)f(the)h(user)
g(may)f(desire.)31 b(F)o(or)21 b(e)o(xample,)g(the)o(y)h(can)f(be)h
(con\002gured)e(for)i(the)g(speci\002c)291 3897 y(data)e(structure)f
(of)h(a)g(problem)f(or)h(for)f(the)i(speci\002c)f(computing)e(system)i
(on)g(which)g(the)g(problem)e(is)j(to)g(run.)415 3998
y(W)-7 b(e)21 b(focus)f(on)g(the)g(use)g(of)g(iterati)n(v)o(e)g
(methods)f(for)h(solving)f(lar)o(ge)g(sparse)h(systems)h(of)f(linear)g
(equations.)415 4099 y(Man)o(y)i(methods)f(e)o(xist)i(for)f(solving)g
(such)g(problems.)31 b(The)22 b(trick)h(is)g(to)g(\002nd)g(the)f(most)h
(ef)n(fecti)n(v)o(e)e(method)291 4199 y(for)j(the)h(problem)e(at)i
(hand.)39 b(Unfortunately)-5 b(,)22 b(a)k(method)d(that)i(w)o(orks)g
(well)g(for)g(one)f(problem)f(type)i(may)f(not)291 4298
y(w)o(ork)19 b(as)i(well)g(for)e(another)-5 b(.)24 b(Indeed,)19
b(it)i(may)e(not)h(w)o(ork)g(at)g(all.)415 4399 y(Thus,)37
b(besides)e(pro)o(viding)c(templates,)38 b(we)c(suggest)g(ho)n(w)g(to)h
(choose)e(and)h(implement)f(an)h(ef)n(fecti)n(v)o(e)291
4499 y(method,)29 b(and)f(ho)n(w)h(to)g(specialize)f(a)i(method)d(to)i
(speci\002c)g(matrix)f(types.)51 b(W)-7 b(e)30 b(restrict)f(ourselv)o
(es)f(to)h Ft(iter)n(-)291 4599 y(ative)e(methods)p FG(,)h(which)f(w)o
(ork)g(by)g(repeatedly)f(impro)o(ving)f(an)i(approximate)e(solution)i
(until)g(it)h(is)h(accurate)291 4698 y(enough.)36 b(These)24
b(methods)g(access)h(the)g(coef)n(\002cient)e(matrix)h
FC(A)i FG(of)e(the)h(linear)f(system)h(only)f(via)g(the)h(matrix-)291
4798 y(v)o(ector)c(product)f FC(y)30 b Fy(=)d FC(A)20
b Fx(\001)g FC(x)k FG(\(and)d(perhaps)g FC(z)31 b Fy(=)c
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(variable)f(co-)960 3240 y(ef)o(\002cient)c(case)p FG(,)h(SIAM)h(J.)f
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b(pr)l(ocedur)m(e)g(for)i(systems)g(of)f(partial)g(dif)o(fer)m(ential)f
(equations)p FG(,)46 b(BIT)-6 b(,)42 b(29)g(\(1989\),)960
3610 y(pp.)20 b(938\226954.)780 3780 y([27])42 b(R)t(.)25
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FG(,)c Ft(Mar)m(c)o(hing)d(algorithms)i(for)h(elliptic)f(boundary)e
(value)h(pr)l(oblems.)h(I:)g(The)960 3879 y(constant)f(coef)o
(\002cient)g(case)p FG(,)h(SIAM)g(J.)h(Numer)-5 b(.)19
b(Anal.,)h(14)g(\(1977\),)e(pp.)h(792\226829.)780 4049
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4149 y(symmetric)i(linear)f(systems)p FG(,)i(T)-6 b(ech.)24
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(step)i(Biconjugate)d(gr)o(adient)960 4518 y(method)p
FG(,)19 b(Numerische)g(Mathematik,)g(66)h(\(1993\),)d(pp.)j
(295\226319.)780 4688 y([30])42 b(G)t(.)22 b(B)q FJ(AU)t(D)t(E)t(T)r
FG(,)c Ft(Async)o(hr)l(onous)d(iter)o(ative)i(methods)f(for)i(multipr)l
(ocessor)o(s)p FG(,)g(J.)f(Assoc.)g(Comput.)f(Mach.,)960
4788 y(25)k(\(1978\),)e(pp.)h(226\226244.)780 4957 y([31])42
b(R)t(.)33 b(B)t FJ(E)t(AU)t(W)t(E)t(N)t(S)r FG(,)c Ft(On)f(Axelsson')m
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g(pp.)g(221\226)960 5057 y(242.)780 5227 y([32])p 960
5214 V 231 w(,)20 b Ft(Appr)l(oximate)e(factorizations)h(with)h(S/P)f
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(criteria)i(for)f(partial)f(matrix)h(factorizations)f(in)960
5596 y(iter)o(ative)20 b(methods)p FG(,)g(SIAM)g(J.)h(Numer)-5
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FG(G)t(.)g(M)t FJ(E)t(U)t(R)t(A)t(N)t(T)r FG(,)20 b Ft(Bloc)n(k)g(pr)m
(econditioning)e(for)i(the)h(conjugate)d(gr)o(a-)960
2253 y(dient)i(method)p FG(,)f(SIAM)h(J.)h(Sci.)g(Statist.)g(Comput.,)e
(6)h(\(1985\),)e(pp.)h(220\226252.)780 2421 y([57])42
b(P)-5 b(.)27 b(C)t FJ(O)t(N)t(C)t(U)t(S)t FG(,)h(G)t(.)f(G)t
FJ(O)t(L)t(U)t(B)t FG(,)h FJ(A)t(N)t(D)f FG(D)t(.)g(O)t(')t(L)t
FJ(E)t(A)t(RY)r FG(,)c Ft(A)f(g)o(ener)o(alized)f(conjugate)g(gr)o
(adient)g(method)g(for)960 2520 y(the)i(numerical)g(solution)f(of)i
(elliptic)f(partial)g(dif)o(fer)m(ential)f(equations)p
FG(,)g(in)i(Sparse)f(Matrix)g(Computa-)960 2620 y(tions,)d(J.)h(Bunch)f
(and)f(D.)i(Rose,)f(eds.,)g(Academic)f(Press,)i(Ne)n(w)g(Y)-9
b(ork,)19 b(1976,)f(pp.)i(309\226332.)780 2788 y([58])42
b(P)-5 b(.)25 b(C)t FJ(O)t(N)t(C)t(U)t(S)h(A)t(N)t(D)f
FG(G)t(.)f(H)t(.)h(G)t FJ(O)t(L)t(U)t(B)r FG(,)c Ft(Use)g(of)f(fast)h
(dir)m(ect)f(methods)f(for)i(the)f(ef)o(\002cient)f(numerical)h(solu-)
960 2888 y(tion)g(of)h(nonsepar)o(able)c(elliptic)j(equations)p
FG(,)f(SIAM)h(J.)h(Numer)-5 b(.)19 b(Anal.,)h(10)g(\(1973\),)e(pp.)h
(1103\2261120.)780 3056 y([59])42 b(E)t(.)34 b(C)t FJ(U)t(T)t(H)t(I)t
(L)t(L)f(A)t(N)t(D)h FG(J)t(.)g(M)t FJ(C)t FG(K)t FJ(E)t(E)r
FG(,)e Ft(Reducing)27 b(the)i(bandwidth)f(of)h(spar)o(se)h(symmetric)f
(matrices)p FG(,)j(in)960 3155 y(A)m(CM)21 b(Proceedings)d(of)i(the)g
(24th)g(National)g(Conference,)e(1969.)780 3324 y([60])42
b(E)t(.)32 b(D)t(')t(A)t FJ(Z)t(E)t(V)t(E)t(D)t(O)t FG(,)i(V)-7
b(.)32 b(E)t FJ(I)t(J)t(K)t(H)t(O)t(U)t(T)o FG(,)i FJ(A)t(N)t(D)f
FG(C)t(.)f(R)q FJ(O)t(M)t(I)t(N)t(E)r FG(,)f Ft(LAP)-7
b(A)n(CK)28 b(working)f(note)g(56:)40 b(Reducing)960
3423 y(communication)22 b(costs)i(in)g(the)g(conjugate)e(gr)o(adient)g
(algorithm)h(on)g(distrib)n(uted)h(memory)g(multipr)l(o-)960
3523 y(cessor)p FG(,)35 b(tech.)c(report,)h(Computer)e(Science)h
(Department,)h(Uni)n(v)o(ersity)e(of)h(T)-6 b(ennessee,)34
b(Knoxville,)960 3622 y(TN,)20 b(1993.)780 3791 y([61])42
b(E)t(.)21 b(D)t(')t(A)t FJ(Z)t(E)t(V)t(E)t(D)t(O)g(A)t(N)t(D)g
FG(C)t(.)h(R)q FJ(O)t(M)t(I)t(N)t(E)r FG(,)c Ft(Reducing)d
(communication)f(costs)j(in)g(the)g(conjugate)e(gr)o(adient)960
3890 y(algorithm)h(on)g(distrib)n(uted)h(memory)g(multipr)l(ocessor)o
(s)p FG(,)g(T)-6 b(ech.)16 b(Rep.)h(ORNL/TM-12192,)e(Oak)h(Ridge)960
3990 y(National)k(Lab,)g(Oak)g(Ridge,)f(TN,)i(1992.)780
4158 y([62])42 b(E)t(.)32 b(D)t FJ(E)g FG(S)t FJ(T)t(U)t(R)t(L)t(E)t(R)
r FG(,)f Ft(A)d(par)o(allel)f(r)m(estructur)m(ed)g(ver)o(sion)h(of)g
(GMRES\(m\))p FG(,)g(T)-6 b(ech.)28 b(Rep.)f(91-85,)h(Delft)960
4258 y(Uni)n(v)o(ersity)19 b(of)h(T)-6 b(echnology)h(,)17
b(Delft,)j(The)g(Netherlands,)f(1991.)780 4426 y([63])42
b(E)t(.)23 b(D)t FJ(E)g FG(S)t FJ(T)t(U)t(R)t(L)t(E)t(R)g(A)t(N)t(D)h
FG(D)t(.)f(R)t(.)g(F)t FJ(O)t(K)t(K)t(E)t(M)t(A)r FG(,)d
Ft(Nested)f(Krylo)o(v)g(methods)f(and)g(pr)m(eserving)g(the)g(ortho)o
(g-)960 4525 y(onality)p FG(,)h(T)-6 b(ech.)20 b(Rep.)g(Preprint)g
(796,)f(Utrecht)g(Uni)n(v)o(ersity)-5 b(,)19 b(Utrecht,)g(The)h
(Netherlands,)f(1993.)780 4693 y([64])42 b(S)t(.)28 b(D)t
FJ(E)t(M)t(K)r(O)t FG(,)g(W)l(.)h(M)t FJ(O)t(S)t(S)t
FG(,)f FJ(A)t(N)t(D)f FG(P)-5 b(.)28 b(S)t FJ(M)t(I)t(T)t(H)r
FG(,)c Ft(Decay)f(r)o(ates)g(for)h(in)m(ver)o(ses)f(of)g(band)f
(matrices)p FG(,)i(Mathe-)960 4793 y(matics)d(of)f(Computation,)e(43)i
(\(1984\),)d(pp.)j(491\226499.)780 4961 y([65])42 b(J)t(.)30
b(D)t FJ(E)t(M)t(M)t(E)t(L)r FG(,)d Ft(The)e(condition)e(number)i(of)g
(equivalence)e(tr)o(ansformations)h(that)h(bloc)n(k)g(dia)o(gonalize)
960 5061 y(matrix)c(pencils)p FG(,)e(SIAM)i(J.)g(Numer)-5
b(.)19 b(Anal.,)h(20)g(\(1983\),)d(pp.)j(599\226610.)780
5229 y([66])42 b(J)t(.)30 b(D)t FJ(E)t(M)t(M)t(E)t(L)t
FG(,)f(M)t(.)h(H)t FJ(E)t(A)m(T)t(H)t FG(,)f FJ(A)t(N)t(D)g
FG(H)t(.)g FJ(V)-5 b(A)t(N)30 b(D)t(E)t(R)f FG(V)q FJ(O)t(R)t(S)t(T)r
FG(,)e Ft(P)-7 b(ar)o(allel)24 b(linear)h(alg)o(ebr)o(a)p
FG(,)f(in)h(Acta)g(Nu-)960 5328 y(merica,)20 b(V)-11
b(ol.)20 b(2,)g(Cambridge)f(Press,)h(Ne)n(w)h(Y)-9 b(ork,)19
b(1993.)780 5497 y([67])42 b(S)t(.)35 b(D)t FJ(O)t(I)r
FG(,)e Ft(On)d(par)o(allelism)g(and)f(con)m(ver)m(g)o(ence)f(of)i
(incomplete)f(LU)i(factorizations)p FG(,)g(Appl.)f(Numer)-5
b(.)960 5596 y(Math.,)20 b(7)g(\(1991\),)e(pp.)h(417\226436.)p
eop end
%%Page: 97 107
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FG(,)i(I)t(.)e(D)t FJ(U)t(FF)t FG(,)g FJ(A)t(N)t(D)h
FG(S)t(.)f(H)t FJ(A)t(M)t(M)t(A)t(R)t(L)t(I)t(N)t(G)r
FG(,)d Ft(A)f(set)h(of)e(le)o(vel)h(3)f(Basic)h(Linear)512
615 y(Alg)o(ebr)o(a)h(Subpr)l(o)o(gr)o(ams)p FG(,)f(A)m(CM)j(T)m(rans.)
e(Math.)h(Soft.,)g(16)g(\(1990\),)d(pp.)j(1\22617.)332
785 y([69])42 b(J)t(.)36 b(D)t FJ(O)t(N)t(G)t(A)t(R)t(R)t(A)t
FG(,)k(J)t(.)c(D)t FJ(U)t FG(C)t FJ(R)q(O)t(Z)t FG(,)k(S)t(.)c(H)t
FJ(A)t(M)t(M)t(A)t(R)t(L)t(I)t(N)t(G)t FG(,)k FJ(A)t(N)t(D)c
FG(R)t(.)g(H)t FJ(A)t(N)t(S)t(O)t(N)r FG(,)f Ft(An)c(e)n(xtended)g(set)
h(of)512 885 y(FORTRAN)21 b(Basic)g(Linear)h(Alg)o(ebr)o(a)e(Subpr)l(o)
o(gr)o(ams)p FG(,)f(A)m(CM)j(T)m(rans.)f(Math.)g(Soft.,)g(14)g
(\(1988\),)e(pp.)h(1\226)512 984 y(32.)332 1154 y([70])42
b(J)t(.)21 b(D)t FJ(O)t(N)t(G)t(A)t(R)t(R)t(A)t FG(,)i(I)t(.)d(D)t
FJ(U)t(FF)t FG(,)h(D)t(.)g(S)t FJ(O)t(R)t(E)t(N)t(S)t(E)t(N)t
FG(,)h FJ(A)t(N)t(D)f FG(H)t(.)f FJ(V)-5 b(A)t(N)21 b(D)t(E)t(R)g
FG(V)q FJ(O)t(R)t(S)t(T)r FG(,)d Ft(Solving)c(Linear)i(Systems)512
1254 y(on)k(V)-9 b(ector)20 b(and)f(Shar)m(ed)g(Memory)h(Computer)o(s)p
FG(,)g(SIAM,)g(Philadelphia,)f(P)-8 b(A,)21 b(1991.)332
1424 y([71])42 b(J)t(.)23 b(D)t FJ(O)t(N)t(G)t(A)t(R)t(R)t(A)i(A)t(N)t
(D)e FG(E)t(.)g(G)t FJ(R)q(O)t(S)t(S)t(E)r FG(,)d Ft(Distrib)n(ution)f
(of)f(mathematical)g(softwar)m(e)h(via)f(electr)l(onic)h(mail)p
FG(,)512 1523 y(Comm.)g(A)m(CM,)i(30)f(\(1987\),)d(pp.)j(403\226407.)
332 1693 y([72])42 b(J)t(.)20 b(D)t FJ(O)t(N)t(G)t(A)t(R)t(R)t(A)t
FG(,)i(C)t(.)f(M)t FJ(O)t(L)t(E)t(R)t FG(,)g(J)t(.)f(B)s
FJ(U)t(N)t(C)t(H)t FG(,)i FJ(A)t(N)t(D)f FG(G)t(.)f(S)t
FJ(T)t(E)t(W)l(A)t(RT)r FG(,)c Ft(LINP)-7 b(A)n(CK)16
b(User)o(s')g(Guide)p FG(,)g(SIAM,)512 1793 y(Philadelphia,)j(1979.)332
1963 y([73])42 b(J)t(.)30 b(D)t FJ(O)t(N)t(G)t(A)t(R)t(R)t(A)h(A)t(N)t
(D)f FG(H)t(.)g(V)-6 b FJ(A)t(N)30 b(D)t(E)t(R)g FG(V)q
FJ(O)t(R)t(S)t(T)r FG(,)d Ft(P)-7 b(erformance)24 b(of)i(various)f
(computer)o(s)g(using)f(stan-)512 2062 y(dar)m(d)18 b(spar)o(se)i
(linear)f(equations)f(solving)g(tec)o(hniques)p FG(,)g(in)h(Computer)f
(Benchmarks,)g(J.)i(Dongarra)c(and)512 2162 y(W)-8 b(.)21
b(Gentzsch,)f(eds.,)g(Else)n(vier)f(Science)h(Publishers)g(B.V)-11
b(.,)21 b(Ne)n(w)f(Y)-9 b(ork,)19 b(1993,)g(pp.)g(177\226188.)332
2332 y([74])42 b(F)m(.)29 b(D)t FJ(O)t(R)t(R)r FG(,)d
Ft(The)e(dir)m(ect)h(solution)e(of)h(the)g(discr)m(ete)g(Poisson)g
(equation)e(on)i(a)g(r)m(ectangle)p FG(,)f(SIAM)i(Re)n(v)-5
b(.,)512 2432 y(12)20 b(\(1970\),)e(pp.)h(248\226263.)332
2602 y([75])42 b(M)t(.)23 b(D)t FJ(RY)t(JA)h(A)t(N)t(D)g
FG(O)t(.)g(B)t(.)g(W)t FJ(I)t(D)t(L)t(U)t(N)t(D)r FG(,)c
Ft(T)-8 b(owar)m(ds)20 b(a)f(uni\002ed)e(theory)i(of)g(domain)f
(decomposition)f(algo-)512 2701 y(rithms)26 b(for)f(elliptic)g(pr)l
(oblems)p FG(,)h(T)-6 b(ech.)24 b(Rep.)h(486,)g(also)g(Ultracomputer)e
(Note)i(167,)g(Department)e(of)512 2801 y(Computer)c(Science,)g
(Courant)h(Institute,)f(1989.)332 2971 y([76])42 b(D)t(.)26
b(D)t FJ(U)t(B)t(O)t(I)t(S)t FG(,)g(A)t(.)g(G)t FJ(R)t(E)t(E)t(N)t(B)r
(AU)t(M)t FG(,)h FJ(A)t(N)t(D)f FG(G)t(.)f(R)q FJ(O)t(D)t(R)t(I)t(G)t
(U)t(E)r FG(,)e Ft(Appr)l(oximating)c(the)j(in)m(ver)o(se)f(of)g(a)h
(matrix)512 3070 y(for)f(use)f(in)g(iter)o(ative)h(algorithms)e(on)h
(vector)g(pr)l(ocessor)o(s)p FG(,)h(Computing,)d(22)i(\(1979\),)e(pp.)h
(257\226268.)332 3240 y([77])42 b(I)t(.)21 b(D)t FJ(U)t(FF)t
FG(,)h(R)t(.)g(G)t FJ(R)t(I)t(M)t(E)t(S)t FG(,)g FJ(A)t(N)t(D)g
FG(J)t(.)f(L)t FJ(E)t(W)t(I)t(S)r FG(,)d Ft(Spar)o(se)e(matrix)h(test)h
(pr)l(oblems)p FG(,)f(A)m(CM)g(T)m(rans.)f(Math.)g(Soft.,)512
3340 y(15)k(\(1989\),)e(pp.)h(1\22614.)332 3510 y([78])42
b(I)t(.)25 b(D)t FJ(U)t(FF)g(A)t(N)t(D)g FG(G)t(.)h(M)t
FJ(E)t(U)t(R)t(A)t(N)t(T)r FG(,)21 b Ft(The)f(ef)o(fect)h(of)g(or)m
(dering)e(on)i(pr)m(econditioned)d(conjugate)g(gr)o(adients)p
FG(,)512 3610 y(BIT)-6 b(,)20 b(29)g(\(1989\),)e(pp.)h(635\226657.)332
3780 y([79])42 b(I)t(.)25 b(S)t(.)h(D)t FJ(U)t(FF)t FG(,)g(A)t(.)f(M)t
(.)h(E)t FJ(R)t(I)t(S)t(M)t(A)t(N)t FG(,)g FJ(A)t(N)t(D)g
FG(J)t(.)t(K)t(.)t(R)t FJ(E)t(I)t(D)r FG(,)c Ft(Dir)m(ect)g(methods)e
(for)i(spar)o(se)f(matrices)p FG(,)h(Oxford)512 3879
y(Uni)n(v)o(ersity)d(Press,)i(London,)c(1986.)332 4049
y([80])42 b(T)n(.)d(D)t FJ(U)t(P)t(O)t(N)t(T)o FG(,)k(R)t(.)d(K)t
FJ(E)t(N)t(D)q(A)t(L)t(L)t FG(,)j FJ(A)t(N)t(D)c FG(H)t(.)h(R)t
FJ(A)q(C)t(H)t(F)t(O)t(R)t(D)r FG(,)h Ft(An)35 b(appr)l(oximate)e
(factorization)h(pr)l(oce-)512 4149 y(dur)m(e)22 b(for)i(solving)e
(self-adjoint)f(elliptic)i(dif)o(fer)m(ence)f(equations)p
FG(,)g(SIAM)h(J.)g(Numer)-5 b(.)22 b(Anal.,)h(5)g(\(1968\),)512
4248 y(pp.)c(559\226573.)332 4418 y([81])42 b(E)t(.)31
b(D)t(')t(Y)-5 b FJ(A)t(K)r(O)t(N)t(O)q(V)r FG(,)28 b
Ft(The)f(method)f(of)g(variable)g(dir)m(ections)g(in)h(solving)f
(systems)i(of)f(\002nite)f(dif)o(fer)m(ence)512 4518
y(equations)p FG(,)18 b(So)o(viet)i(Math.)g(Dokl.,)f(2)h(\(1961\),)e
(pp.)i(577\226580.)26 b(T)o(OM)20 b(138,)f(271\226274.)332
4688 y([82])42 b(L)t(.)24 b(E)t FJ(H)t(R)t(L)t(I)t(C)t(H)r
FG(,)e Ft(An)e(Ad-Hoc)f(SOR)h(method)p FG(,)e(J.)j(Comput.)e(Phys.,)h
(43)f(\(1981\),)f(pp.)i(31\22645.)332 4858 y([83])42
b(M)t(.)21 b(E)t FJ(I)t(E)t(R)t(M)t(A)t(N)t(N)h(A)t(N)t(D)g
FG(R)t(.)g(V)-6 b FJ(A)t(R)t(G)t(A)r FG(,)18 b Ft(Is)g(the)e(optimal)h
FC(!)j Ft(best)d(for)g(the)g(SOR)g(iter)o(ation)f(method?)p
FG(,)g(Linear)512 4957 y(Algebra)j(Appl.,)g(182)h(\(1993\),)e(pp.)h
(257\226277.)332 5127 y([84])42 b(V)-7 b(.)31 b(E)t FJ(I)t(J)t(K)t(H)t
(O)t(U)t(T)r FG(,)c Ft(Analysis)f(of)g(par)o(allel)f(incomplete)g
(point)g(factorizations)p FG(,)h(Linear)f(Algebra)g(Appl.,)512
5227 y(154\226156)17 b(\(1991\),)h(pp.)i(723\226740.)332
5397 y([85])p 512 5384 191 4 v 231 w(,)28 b Ft(Be)o(war)m(e)d(of)h
(unperturbed)e(modi\002ed)h(incomplete)f(point)i(factorizations)p
FG(,)g(in)g(Proceedings)e(of)512 5497 y(the)17 b(IMA)m(CS)h
(International)d(Symposium)h(on)g(Iterati)n(v)o(e)h(Methods)f(in)i
(Linear)e(Algebra,)h(Brussels,)h(Bel-)512 5596 y(gium,)h(R.)i(Beauwens)
f(and)g(P)-9 b(.)20 b(de)g(Groen,)f(eds.,)h(1992.)p eop
end
%%Page: 98 108
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b(A)n(CK)32 b(working)h(note)f(50:)49 b(Distrib)n(uted)32
b(spar)o(se)h(data)f(structur)m(es)h(for)g(linear)f(alg)o(ebr)o(a)960
615 y(oper)o(ations)p FG(,)17 b(T)-6 b(ech.)19 b(Rep.)f(CS)i(92-169,)d
(Computer)g(Science)i(Department,)e(Uni)n(v)o(ersity)g(of)i(T)-6
b(ennessee,)960 715 y(Knoxville,)19 b(TN,)h(1992.)780
879 y([87])p 960 866 V 231 w(,)d Ft(LAP)-7 b(A)n(CK)15
b(working)h(note)f(51:)22 b(Qualitative)14 b(pr)l(operties)i(of)g(the)f
(conjugate)f(gr)o(adient)g(and)h(Lanc-)960 978 y(zos)22
b(methods)f(in)g(a)g(matrix)h(fr)o(ame)o(work)p FG(,)f(T)-6
b(ech.)21 b(Rep.)g(CS)h(92-170,)d(Computer)h(Science)h(Department,)960
1078 y(Uni)n(v)o(ersity)e(of)h(T)-6 b(ennessee,)20 b(Knoxville,)e(TN,)i
(1992.)780 1242 y([88])42 b(V)-7 b(.)32 b(E)t FJ(I)t(J)t(K)t(H)t(O)t(U)
t(T)g(A)t(N)t(D)h FG(B)t(.)f(P)t FJ(O)t(L)t(M)t(A)t(N)r
FG(,)e Ft(Decay)d(r)o(ates)g(of)h(in)m(ver)o(ses)g(of)f(banded)f
FC(M)9 b Ft(-matrices)27 b(that)g(ar)m(e)960 1342 y(near)20
b(to)h(Toeplitz)f(matrices)p FG(,)g(Linear)g(Algebra)f(Appl.,)g(109)g
(\(1988\),)f(pp.)i(247\226277.)780 1506 y([89])42 b(V)-7
b(.)32 b(E)t FJ(I)t(J)t(K)t(H)t(O)t(U)t(T)g(A)t(N)t(D)f
FG(P)-5 b(.)32 b(V)-6 b FJ(A)t(S)t(S)t(I)t(L)t(E)t(V)t(S)t(K)t(I)r
FG(,)29 b Ft(P)-7 b(ositive)27 b(de\002nitess)g(aspects)g(of)g
(vectorizable)f(pr)m(econdi-)960 1605 y(tioner)o(s)p
FG(,)21 b(P)o(arallel)f(Computing,)e(10)i(\(1989\),)d(pp.)j(93\226100.)
780 1769 y([90])42 b(S)t(.)36 b(E)t FJ(I)t(S)t(E)t(N)t(S)t(T)n(A)m(T)r
FG(,)e Ft(Ef)o(\002cient)c(implementation)f(of)j(a)f(class)h(of)g(pr)m
(econditioned)c(conjugate)i(gr)o(adient)960 1869 y(methods)p
FG(,)19 b(SIAM)i(J.)g(Sci.)f(Statist.)h(Comput.,)e(2)h(\(1981\),)e(pp.)
i(1\2264.)780 2033 y([91])42 b(R)t(.)e(E)t FJ(L)t(K)t(I)t(N)r
FG(,)g Ft(Con)m(ver)m(g)o(ence)33 b(theor)m(ems)i(for)h(Gauss-Seidel)d
(and)i(other)g(minimization)f(algorithms)p FG(,)960 2133
y(T)-6 b(ech.)27 b(Rep.)h(68-59,)g(Computer)e(Science)i(Center)m(,)h
(Uni)n(v)o(ersity)e(of)g(Maryland,)h(Colle)o(ge)f(P)o(ark,)i(MD,)960
2232 y(Jan.)20 b(1968.)780 2396 y([92])42 b(H)t(.)24
b(E)t FJ(L)t(M)t(A)t(N)r FG(,)19 b Ft(Appr)l(oximate)e(Sc)o(hur)h
(complement)g(pr)m(econditioner)o(s)f(on)h(serial)i(and)e(par)o(allel)g
(comput-)960 2496 y(er)o(s)p FG(,)j(SIAM)g(J.)f(Sci.)h(Statist.)g
(Comput.,)e(10)h(\(1989\),)e(pp.)h(581\226605.)780 2660
y([93])42 b(H)t(.)27 b(E)t FJ(L)t(M)t(A)t(N)g(A)t(N)t(D)f
FG(M)t(.)h(S)t FJ(C)t(H)t(U)t(L)n(T)t(Z)r FG(,)c Ft(Pr)m(econditioning)
c(by)j(fast)h(dir)m(ect)f(methods)g(for)g(non)f(self-adjoint)960
2760 y(nonsepar)o(able)d(elliptic)i(equations)p FG(,)e(SIAM)j(J.)g
(Numer)-5 b(.)19 b(Anal.,)h(23)g(\(1986\),)d(pp.)j(44\22657.)780
2924 y([94])42 b(L)t(.)22 b(E)t FJ(L)t(S)t(N)t(E)t(R)r
FG(,)17 b Ft(A)h(note)e(on)h(optimal)f(bloc)n(k-scaling)g(of)h
(matrices)p FG(,)h(Numer)-5 b(.)16 b(Math.,)h(44)g(\(1984\),)e(pp.)i
(127\226)960 3024 y(128.)780 3188 y([95])42 b(V)-7 b(.)25
b(F)o FJ(A)t(B)t(E)t(R)g(A)t(N)t(D)g FG(T)n(.)f(M)t FJ(A)t(N)t(T)t(E)t
(U)t(FF)t(E)t(L)r FG(,)19 b Ft(Necessary)h(and)f(suf)o(\002cient)g
(conditions)g(for)h(the)g(e)n(xistence)g(of)g(a)960 3287
y(conjugate)e(gr)o(adient)h(method)p FG(,)g(SIAM)i(J.)f(Numer)-5
b(.)20 b(Anal.,)f(21)h(\(1984\),)e(pp.)i(315\226339.)780
3451 y([96])42 b(G)t(.)c(F)o FJ(A)t(I)t(RW)t(E)t(A)m(T)t(H)t(E)t(R)t
FG(,)i(A)t(.)d(G)t FJ(O)t(U)t(R)t(L)t(A)m(Y)-6 b FG(,)42
b FJ(A)t(N)t(D)37 b FG(A)t(.)h(M)t FJ(I)t(T)t(C)t(H)t(E)t(L)t(L)r
FG(,)d Ft(Some)e(high)f(accur)o(acy)f(dif)o(fer)m(ence)960
3551 y(sc)o(hemes)18 b(with)g(a)g(splitting)f(oper)o(ator)f(for)i
(equations)e(of)i(par)o(abolic)e(and)h(elliptic)g(type)p
FG(,)h(Numer)-5 b(.)17 b(Math.,)960 3651 y(10)j(\(1967\),)e(pp.)h
(56\22666.)780 3815 y([97])42 b(R)t(.)31 b(F)t FJ(L)t(E)t(T)t(C)t(H)t
(E)t(R)r FG(,)d Ft(Conjugate)d(gr)o(adient)g(methods)g(for)h
(inde\002nite)f(systems)p FG(,)k(in)d(Numerical)f(Analysis)960
3914 y(Dundee)19 b(1975,)g(G.)h(W)-7 b(atson,)21 b(ed.,)e(Berlin,)h(Ne)
n(w)h(Y)-9 b(ork,)19 b(1976,)f(Springer)h(V)-9 b(erlag,)19
b(pp.)h(73\22689.)780 4078 y([98])42 b(G)t(.)25 b(F)t
FJ(O)t(R)t(S)t(Y)t(T)t(H)t(E)g(A)t(N)t(D)g FG(E)t(.)f(S)t
FJ(T)t(R)t(AU)t(S)t(S)r FG(,)d Ft(On)g(best)f(conditioned)e(matrices)p
FG(,)i(Proc.)g(Amer)-5 b(.)20 b(Math.)f(Soc.,)h(6)960
4178 y(\(1955\),)e(pp.)i(340\226345.)780 4342 y([99])42
b(R)t(.)31 b(F)t FJ(R)t(E)t(U)t(N)t(D)r FG(,)c Ft(Conjugate)d(gr)o
(adient-type)f(methods)h(for)i(linear)f(systems)i(with)f(comple)n(x)e
(symmetric)960 4442 y(coef)o(\002cient)19 b(matrices)p
FG(,)h(SIAM)g(J.)h(Sci.)g(Statist.)g(Comput.,)e(13)h(\(1992\),)d(pp.)j
(425\226448.)739 4606 y([100])41 b(R)t(.)24 b(F)t FJ(R)t(E)t(U)t(N)t(D)
t FG(,)f(M)t(.)g(G)t FJ(U)t(T)t(K)t(N)t(E)t(C)t(H)t(T)o
FG(,)g FJ(A)t(N)t(D)g FG(N)t(.)g(N)q FJ(A)q(C)t(H)t(T)t(I)t(G)t(A)t(L)r
FG(,)d Ft(An)e(implementation)f(of)i(the)f(look-ahead)960
4705 y(Lanczos)i(algorithm)g(for)h(non-Hermitian)e(matrices)p
FG(,)h(SIAM)h(J.)g(Sci.)g(Comput.,)e(14)h(\(1993\),)f(pp.)h(137\226)960
4805 y(158.)739 4969 y([101])41 b(R)t(.)46 b(F)t FJ(R)t(E)t(U)t(N)t(D)g
(A)t(N)t(D)f FG(N)t(.)h(N)q FJ(A)q(C)t(H)t(T)t(I)t(G)t(A)t(L)r
FG(,)h Ft(QMR:)41 b(A)g(quasi-minimal)e(r)m(esidual)h(method)g(for)h
(non-)960 5069 y(Hermitian)20 b(linear)g(systems)p FG(,)i(Numer)-5
b(.)19 b(Math.,)h(60)f(\(1991\),)f(pp.)i(315\226339.)739
5233 y([102])p 960 5220 V 230 w(,)d Ft(An)f(implementation)e(of)i(the)g
(QMR)g(method)f(based)g(on)h(coupled)e(two-term)i(r)m(ecurr)m(ences)p
FG(,)h(T)-6 b(ech.)960 5333 y(Rep.)20 b(92.15,)f(RIA)m(CS,)h(N)m(ASA)h
(Ames,)g(Ames,)f(CA,)h(1992.)739 5497 y([103])41 b(R)t(.)22
b(F)t FJ(R)t(E)t(U)t(N)t(D)g(A)t(N)t(D)f FG(T)n(.)g(S)t
FJ(Z)t(E)t(T)s(O)r FG(,)c Ft(A)g(quasi-minimal)d(r)m(esidual)j(squar)m
(ed)e(algorithm)h(for)h(non-Hermitian)960 5596 y(linear)j(systems)p
FG(,)h(tech.)f(rep.,)g(RIA)m(CS,)g(N)m(ASA)h(Ames,)f(Ames,)g(CA,)h
(1991.)p eop end
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(algorithm)e(for)i(non-Hermitian)e(lin-)512 615 y(ear)j(systems)p
FG(,)h(SIAM)g(J.)g(Sci.)f(Comput.,)f(14)h(\(1993\),)e(pp.)h
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1058 y([106])41 b(R)t(.)22 b(G)t FJ(L)t(O)r(W)t(I)t(N)t(S)t(K)t(I)t
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Ft(Domain)g(Decom-)512 1157 y(position)f(Methods)h(for)g(P)-7
b(artial)17 b(Dif)o(fer)m(ential)g(Equations)p FG(,)f(SIAM,)h
(Philadelphia,)f(1988.)21 b(Proceedings)512 1257 y(of)d(the)h(First)g
(International)d(Symposium)h(on)h(Domain)g(Decomposition)e(Methods)i
(for)g(P)o(artial)h(Dif)n(fer)n(-)512 1357 y(ential)h(Equations,)f(P)o
(aris,)h(France,)f(January)g(1987.)291 1528 y([107])41
b(G)t(.)28 b(G)t FJ(O)t(L)t(U)t(B)g(A)t(N)t(D)g FG(D)t(.)g(O)t(')t(L)t
FJ(E)t(A)t(RY)r FG(,)c Ft(Some)f(history)g(of)h(the)f(conjugate)f(gr)o
(adient)g(and)g(Lanczos)h(meth-)512 1628 y(ods)p FG(,)d(SIAM)g(Re)n(v)
-5 b(.,)20 b(31)f(\(1989\),)f(pp.)i(50\226102.)291 1799
y([108])41 b(G)t(.)26 b(G)t FJ(O)t(L)t(U)t(B)h(A)t(N)t(D)f
FG(C)t(.)h(V)-6 b FJ(A)t(N)26 b FG(L)t FJ(O)r(A)t(N)r
FG(,)d Ft(Matrix)f(Computations,)e FG(second)h(edition,)g(The)h(Johns)f
(Hopkins)512 1899 y(Uni)n(v)o(ersity)e(Press,)i(Baltimore,)e(1989.)291
2071 y([109])41 b(A)t(.)22 b(G)t FJ(R)t(E)t(E)t(N)t(B)r(AU)t(M)h(A)t(N)
t(D)f FG(Z)t(.)f(S)t FJ(T)t(R)t(A)t(K)r(O)t(S)r FG(,)e
Ft(Pr)m(edicting)e(the)g(behavior)f(of)i(\002nite)f(pr)m(ecision)g
(Lanczos)g(and)512 2170 y(conjugate)h(gr)o(adient)h(computations)p
FG(,)f(SIAM)i(J.)h(Mat.)f(Anal.)g(Appl.,)f(13)h(\(1992\),)e(pp.)i
(121\226137.)291 2342 y([110])41 b(W)l(.)21 b(D)t(.)f(G)t
FJ(R)q(O)t(P)t(P)h(A)t(N)t(D)f FG(D)t(.)g(E)t(.)f(K)t
FJ(E)t(Y)t(E)t(S)r FG(,)d Ft(Domain)f(decomposition)e(with)j(local)f
(mesh)h(r)m(e\002nement)p FG(,)f(SIAM)512 2441 y(J.)21
b(Sci.)f(Statist.)h(Comput.,)e(13)h(\(1992\),)e(pp.)h(967\226993.)291
2613 y([111])41 b(I)t(.)24 b(G)t FJ(U)t(S)t(T)n(A)t(F)t(S)t(S)t(O)t(N)r
FG(,)d Ft(A)f(class)h(of)f(\002r)o(st-or)m(der)h(factorization)e
(methods)p FG(,)g(BIT)-6 b(,)20 b(18)g(\(1978\),)e(pp.)h(142\226156.)
291 2785 y([112])41 b(M)t(.)29 b(H)t(.)g(G)t FJ(U)t(T)t(K)t(N)t(E)t(C)t
(H)t(T)r FG(,)c Ft(A)g(completed)e(theory)h(of)h(the)f(unsymmetric)h
(Lanczos)f(pr)l(ocess)h(and)e(r)m(elated)512 2884 y(algorithms,)17
b(part)g(II)p FG(,)g(T)-6 b(ech.)17 b(Rep.)h(90-16,)d(IPS)j(Research)g
(Report,)f(ETH)g(Z)7 b(\250)-35 b(urich,)17 b(Switzerland,)g(1990.)291
3056 y([113])p 512 3043 191 4 v 230 w(,)g Ft(The)g(unsymmetric)f
(Lanczos)g(algorithms)f(and)h(their)g(r)m(elations)g(to)h(P)2753
3057 y(\264)2746 3056 y(ade)e(appr)l(oximation,)g(con-)512
3155 y(tinued)20 b(fr)o(actions)g(and)g(the)g(QD)h(algorithm)p
FG(,)f(in)h(Proceedings)e(of)h(the)h(Copper)f(Mountain)f(Conference)512
3255 y(on)h(Iterati)n(v)o(e)f(Methods,)g(1990.)291 3427
y([114])p 512 3414 V 230 w(,)24 b Ft(V)-9 b(ariants)23
b(of)h(Bi-CGST)l(AB)f(for)h(matrices)g(with)g(comple)n(x)f(spectrum)p
FG(,)h(T)-6 b(ech.)23 b(Rep.)g(91-14,)f(IPS)512 3526
y(ETH,)e(Z)7 b(\250)-35 b(urich,)19 b(Switzerland,)g(1991.)291
3698 y([115])p 512 3685 V 230 w(,)h Ft(A)f(completed)f(theory)h(of)g
(the)h(unsymmetric)f(Lanczos)g(pr)l(ocess)g(and)g(r)m(elated)f
(algorithms,)h(part)512 3797 y(I)p FG(,)h(SIAM)g(J.)h(Matrix)f(Anal.)g
(Appl.,)f(13)h(\(1992\),)e(pp.)h(594\226639.)291 3969
y([116])41 b(W)l(.)h(H)t FJ(A)q(C)t(K)t(B)s(U)t(S)t(C)t(H)r
FG(,)i Ft(Multi-Grid)37 b(Methods)g(and)f(Applications)p
FG(,)j(Springer)n(-V)-9 b(erlag,)39 b(Berlin,)i(Ne)n(w)512
4069 y(Y)-9 b(ork,)19 b(1985.)291 4240 y([117])p 512
4227 V 230 w(,)38 b Ft(Iter)o(ative)c(L)1130 4241 y(\250)1123
4240 y(osung)f(gr)l(o\337er)h(sc)o(hwac)o(hbesetzter)f(Gleic)o
(hungssysteme)p FG(,)j(T)-6 b(eubner)m(,)36 b(Stuttgart,)512
4340 y(1991.)291 4511 y([118])41 b(A)t(.)25 b(H)t FJ(A)t(D)t(J)t(I)t(D)
t(I)t(M)t(O)t(S)r FG(,)e Ft(On)e(some)g(high)f(accur)o(acy)f(dif)o(fer)
m(ence)h(sc)o(hemes)h(for)g(solving)g(elliptic)g(equations)p
FG(,)512 4611 y(Numer)-5 b(.)19 b(Math.,)h(13)g(\(1969\),)e(pp.)h
(396\226403.)291 4783 y([119])41 b(L)t(.)33 b(H)t FJ(A)q(G)t(E)t(M)t(A)
t(N)i(A)t(N)t(D)f FG(D)t(.)f(Y)r FJ(O)t(U)t(N)t(G)r FG(,)f
Ft(Applied)c(Iter)o(ative)h(Methods)p FG(,)h(Academic)f(Press,)j(Ne)n
(w)d(Y)-9 b(ork,)512 4882 y(1981.)291 5054 y([120])41
b(W)l(.)25 b(H)t FJ(A)q(G)t(E)t(R)r FG(,)d Ft(Condition)d(estimator)o
(s)p FG(,)h(SIAM)g(J.)h(Sci.)g(Statist.)g(Comput.,)e(5)h(\(1984\),)e
(pp.)h(311\226316.)291 5225 y([121])41 b(M)t(.)21 b(H)t
FJ(E)t(S)t(T)t(E)t(N)t(E)t(S)f(A)t(N)t(D)i FG(E)t(.)f(S)t
FJ(T)t(I)t(E)t(F)t(E)t(L)r FG(,)c Ft(Methods)f(of)h(conjugate)e(gr)o
(adients)h(for)h(solving)f(linear)h(systems)p FG(,)512
5325 y(J.)k(Res.)g(Nat.)f(Bur)-5 b(.)21 b(Stand.,)e(49)h(\(1952\),)e
(pp.)h(409\226436.)291 5497 y([122])41 b(M)t(.)47 b(R)t(.)h(H)t
FJ(E)t(S)t(T)t(E)t(N)t(E)t(S)r FG(,)g Ft(Conjugacy)41
b(and)h(gr)o(adients)p FG(,)47 b(in)c(A)g(History)f(of)h(Scienti\002c)g
(Computing,)512 5596 y(Addison-W)-7 b(esle)o(y)i(,)18
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FG(,)i(SIAM)f(J.)g(Sci.)g(Statist.)g(Comput.,)g(11)960
615 y(\(1990\),)18 b(pp.)i(804\226809.)739 788 y([124])41
b(K)t(.)29 b(J)t FJ(E)t(A)g(A)t(N)t(D)g FG(D)t(.)g(Y)r
FJ(O)t(U)t(N)t(G)r FG(,)c Ft(Gener)o(alized)f(conjugate-gr)o(adient)c
(acceler)o(ation)i(of)i(nonsym-)f(metriz-)960 887 y(able)d(iter)o
(ative)g(methods)p FG(,)f(Linear)h(Algebra)f(Appl.,)g(34)h(\(1980\),)e
(pp.)h(159\226194.)739 1060 y([125])41 b(O)t(.)32 b(J)t
FJ(O)t(H)t(N)t(S)t(O)t(N)t FG(,)j(C)t(.)d(M)t FJ(I)t(C)t(C)t(H)t(E)t(L)
t(L)t(I)t FG(,)i FJ(A)t(N)t(D)e FG(G)t(.)g(P)m FJ(AU)t(L)r
FG(,)e Ft(P)-7 b(olynomial)26 b(pr)m(econditioning)e(for)k(conjugate)
960 1160 y(gr)o(adient)19 b(calculation)p FG(,)f(SIAM)j(J.)f(Numer)-5
b(.)20 b(Anal.,)f(20)h(\(1983\),)e(pp.)i(362\226376.)739
1332 y([126])41 b(M)t(.)31 b(J)t FJ(O)t(N)t(E)t(S)f(A)t(N)t(D)h
FG(P)-5 b(.)30 b(P)t FJ(L)t(A)t(S)t(S)t(M)t(A)t(N)t(N)r
FG(,)f Ft(P)-7 b(ar)o(allel)25 b(solution)g(of)h(unstructed,)h(spar)o
(se)f(systems)h(of)f(linear)960 1432 y(equations)p FG(,)e(in)h
(Proceedings)f(of)g(the)h(Sixth)g(SIAM)g(conference)d(on)i(P)o(arallel)
h(Processing)f(for)h(Scien-)960 1531 y(ti\002c)i(Computing,)e(R.)i
(Sinco)o(v)o(ec,)f(D.)g(K)n(e)o(yes,)h(M.)f(Leuze,)g(L.)g(Petzold,)h
(and)f(D.)g(Reed,)h(eds.,)g(SIAM,)960 1631 y(Philadelphia,)19
b(pp.)g(471\226475.)739 1804 y([127])p 960 1791 191 4
v 230 w(,)43 b Ft(A)38 b(par)o(allel)g(gr)o(aph)f(coloring)g(heuristic)
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1903 y(pp.)20 b(654\226669.)739 2076 y([128])41 b(W)l(.)21
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(solution)e(of)i(nonsymmetric)e(systems)j(of)f(linear)f(equations)p
FG(,)960 2176 y(SIAM)21 b(J.)f(Matrix)g(Anal.)g(Appl.,)f(13)h
(\(1992\),)e(pp.)h(926\226943.)739 2348 y([129])41 b(W)l(.)25
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FG(,)f(PhD)i(thesis,)960 2448 y(Uni)n(v)o(ersity)f(of)h(T)-7
b(oronto,)18 b(1958.)739 2621 y([130])41 b(S)t(.)31 b(K)t
FJ(A)t(N)t(I)t(E)t(L)r FG(,)d Ft(Estimates)e(for)h(some)f
(computational)d(tec)o(hniques)i(in)h(linear)g(alg)o(ebr)o(a)p
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3165 y([132])41 b(R)t(.)28 b(K)t FJ(E)t(T)t(T)t(L)t(E)t(R)r
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(hemes)h(in)g(r)l(ob)n(ust)h(multigrid)e(and)g(pr)m(e-)960
3265 y(conditioned)15 b(conjugate)f(gr)o(adient)i(methods)p
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3365 y(ics)24 b(960,)e(W)-8 b(.)24 b(Hackb)n(usch)d(and)h(U.)h(T)m
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b(Berlin,)i(Ne)n(w)g(Y)-9 b(ork,)22 b(1982,)960 3464
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w(,)25 b Ft(Linear)f(multigrid)f(methods)g(in)g(numerical)g(r)m
(eservoir)i(simulation)p FG(,)e(PhD)h(thesis,)h(Delft)e(Uni-)960
3737 y(v)o(ersity)d(of)g(T)-6 b(echnology)h(,)17 b(Delft,)j(The)g
(Netherlands,)e(1987.)739 3909 y([134])41 b(D)t(.)36
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FG(,)h(SIAM,)g(Philadelphia,)960 4108 y(1992.)k(Proceedings)20
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(Decomposition)f(Meth-)960 4208 y(ods,)g(Norfolk,)e(V)-11
b(A,)21 b(1991.)739 4381 y([135])41 b(D)t(.)29 b(E)t(.)g(K)t
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FJ(R)q(O)t(P)t(P)r FG(,)e Ft(A)d(comparison)f(of)i(domain)e
(decomposition)f(tec)o(hniques)h(for)960 4480 y(elliptic)18
b(partial)f(dif)o(fer)m(ential)g(equations)f(and)h(their)h(par)o(allel)
f(implementation)p FG(,)f(SIAM)i(J.)g(Sci.)g(Statist.)960
4580 y(Comput.,)h(8)h(\(1987\),)e(pp.)i(s166)f(\226)i(s202.)739
4753 y([136])p 960 4740 V 230 w(,)f Ft(Domain)e(decomposition)g(for)h
(nonsymmetric)g(systems)i(of)e(equations:)k(Examples)c(fr)l(om)h(com-)
960 4852 y(putational)32 b(\003uid)g(dynamics)p FG(,)k(in)e(Domain)f
(Decomposition)e(Methods,)36 b(proceedings)31 b(of)j(the)f(Sec-)960
4952 y(ond)e(Internation)e(Symposium,)j(Los)g(Angeles,)h(California,)g
(January)e(14\22616,)h(1988,)g(T)-6 b(.)31 b(F)-7 b(.)33
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(373\226384.)739 5224 y([137])p 960 5211 V 230 w(,)h
Ft(Domain)f(decomposition)f(tec)o(hniques)g(for)i(the)f(par)o(allel)g
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(\(1989/1990\),)c(pp.)j(281\226301.)739 5497 y([138])41
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5596 y(on)c(par)o(allel)f(computer)o(s)p FG(,)h(P)o(arallel)g(Comput.,)
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b FJ(A)t(N)26 b(D)t(E)t(R)g FG(V)q FJ(O)t(R)t(S)t(T)r
FG(,)c Ft(Appr)l(oximate)f(solutions)g(and)f(eig)o(en)m(value)960
3492 y(bounds)f(fr)l(om)i(Krylo)o(v)g(subspaces)p FG(,)e(Numer)-5
b(.)19 b(Lin.)h(Alg.)g(Appls.,)g(to)g(appear)-5 b(.)739
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b(of)i(spar)o(se)h(inde\002nite)d(systems)j(of)f(linear)g(equations)p
FG(,)960 3768 y(SIAM)21 b(J.)f(Numer)-5 b(.)20 b(Anal.,)g(12)f
(\(1975\),)f(pp.)i(617\226629.)739 3944 y([168])41 b(C)t(.)26
b(C)t(.)f(P)m FJ(A)t(I)t(G)t(E)g(A)t(N)t(D)g FG(M)t(.)g(A)t(.)g(S)t
FJ(AU)t(N)t(D)t(E)t(R)t(S)r FG(,)c Ft(LSQR:)f(An)g(algorithm)g(for)g
(spar)o(se)h(linear)f(equations)f(and)960 4043 y(spar)o(se)i(least)g
(squar)m(es)p FG(,)e(A)m(CM)i(T)m(rans.)e(Math.)h(Soft.,)g(8)g
(\(1982\),)e(pp.)i(43\22671.)739 4219 y([169])41 b(G)t(.)27
b(P)m FJ(AO)t(L)t(I)t(N)t(I)h(A)t(N)t(D)f FG(G)t(.)g(R)t
FJ(A)t(D)t(I)t(C)t(A)m(T)t(I)h(D)t(I)f FG(B)t FJ(R)q(O)t(Z)t(O)t(L)t(O)
r FG(,)d Ft(Data)e(structur)m(es)h(to)g(vectorize)g(CG)g(algorithms)960
4319 y(for)e(g)o(ener)o(al)e(spar)o(sity)i(patterns)p
FG(,)f(BIT)-6 b(,)20 b(29)g(\(1989\),)d(pp.)j(703\226718.)739
4494 y([170])41 b(B)t(.)25 b(P)m FJ(A)t(R)t(L)t(E)t(T)t(T)r
FG(,)c Ft(The)f(symmetric)h(eig)o(en)m(value)d(pr)l(oblem)p
FG(,)i(Prentice-Hall,)f(London,)f(1980.)739 4670 y([171])41
b(B)t(.)35 b(N)t(.)g(P)m FJ(A)t(R)t(L)t(E)t(T)t(T)o FG(,)h(D)t(.)f(R)t
(.)g(T)m FJ(A)m(Y)t(L)t(O)t(R)t FG(,)j FJ(A)t(N)t(D)d
FG(Z)t(.)f(A)t(.)h(L)t FJ(I)t(U)r FG(,)e Ft(A)d(look-ahead)e(Lanczos)i
(algorithm)f(for)960 4770 y(unsymmetric)20 b(matrices)p
FG(,)h(Mathematics)e(of)h(Computation,)e(44)i(\(1985\),)e(pp.)h
(105\226124.)739 4946 y([172])41 b(D)t(.)26 b(P)t FJ(E)t(A)q(C)t(E)t(M)
t(A)t(N)h(A)t(N)t(D)f(J)t FG(.)g(H)t(.)t(H)t(.)g(R)t
FJ(A)q(C)t(H)t(F)t(O)t(R)t(D)r FG(,)e Ft(The)e(numerical)f(solution)f
(of)i(par)o(abolic)d(and)i(elliptic)960 5045 y(dif)o(fer)m(ential)e
(equations)p FG(,)g(J.)i(Soc.)f(Indust.)f(Appl.)g(Math.,)h(3)g
(\(1955\),)e(pp.)h(28\22641.)739 5221 y([173])41 b(C)t(.)31
b(P)t FJ(O)t(M)t(M)t(E)t(R)t(E)t(L)t(L)r FG(,)c Ft(Solution)d(of)i(Lar)
m(g)o(e)g(Unsymmetric)g(Systems)g(of)g(Linear)g(Equations)p
FG(,)f(v)n(ol.)g(17)h(of)960 5321 y(Series)21 b(in)f
(Micro-electronics,)e(v)n(olume)h(17,)h(Hartung-Gorre)d(V)-9
b(erlag,)19 b(K)m(onstanz,)g(1992.)739 5497 y([174])p
960 5484 V 230 w(,)h Ft(Solution)d(of)h(lar)m(g)o(e)h(unsymmetric)g
(systems)h(of)e(linear)h(equations)p FG(,)e(PhD)i(thesis,)h(Swiss)g
(Federal)960 5596 y(Institute)g(of)g(T)-6 b(echnology)h(,)17
b(Z)7 b(\250)-35 b(urich,)19 b(Switzerland,)g(1992.)p
eop end
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1623 y(linear)g(equations)p FG(,)f(in)h(Lar)o(ge)e(Sparse)i(Sets)h(of)e
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Ft(Pr)m(econditioning)d(by)i(incomplete)f(bloc)n(k)h(cyclic)g(r)m
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(\(1984\),)f(pp.)i(549\226565.)291 2162 y([180])41 b(Y)-7
b(.)23 b(S)t FJ(A)t(A)t(D)r FG(,)d Ft(The)e(Lanczos)g(biortho)o
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3340 y(\(1989\),)18 b(pp.)h(1200\2261232.)291 3510 y([185])p
512 3497 V 230 w(,)31 b Ft(SP)-7 b(ARSKIT:)27 b(A)h(basic)h(tool)f(kit)
h(for)g(spar)o(se)g(matrix)g(computation)p FG(,)g(T)-6
b(ech.)28 b(Rep.)g(CSRD)i(TR)512 3610 y(1029,)18 b(CSRD,)k(Uni)n(v)o
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3780 y([186])p 512 3767 V 230 w(,)k Ft(A)g(\003e)n(xible)f(inner)n
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4049 y([187])41 b(Y)-7 b(.)25 b(S)t FJ(A)t(A)t(D)h(A)t(N)t(D)f
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4418 y(systems)p FG(,)g(SIAM)f(J.)h(Sci.)g(Statist.)g(Comput.,)e(7)h
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Ft(Bi-CGST)l(AB\()p FC(`)p Ft(\))d(for)j(linear)e(equations)g(in)m
(volving)512 4688 y(unsymmetric)h(matrices)g(with)h(comple)n(x)e
(spectrum)p FG(,)j(T)-6 b(ech.)25 b(Rep.)h(772,)h(Uni)n(v)o(ersity)d
(of)i(Utrecht,)h(De-)512 4788 y(partment)19 b(of)h(Mathematics,)f
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b(B)t(.)27 b(F)m(.)g(S)t FJ(M)t(I)t(T)t(H)r FG(,)c Ft(Domain)d
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b(ech.)20 b(Rep.)g(517,)f(Department)g(of)h(Computer)f(Science,)g
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Ft(CGS,)g(a)g(fast)h(Lanczos-type)d(solver)j(for)f(nonsymmetric)f
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(oximations)e(of)i(multidimensional)e(partial)h(dif)o(fer)n(-)960
615 y(ential)e(equations)p FG(,)e(SIAM)j(J.)g(Numer)-5
b(.)19 b(Anal.,)h(5)g(\(1968\),)e(pp.)h(530\226558.)739
785 y([194])41 b(P)-5 b(.)24 b(S)t FJ(W)l(A)t(R)t(Z)t(T)t(R)t(AU)t(B)t
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(Fourier)i(analysis)f(and)g(the)h(F)-10 b(A)n(CR)19 b(algo-)960
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FG(,)g(SIAM)h(Re)n(v)-5 b(.,)21 b(19)h(\(1977\),)960
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m(econditioned)d(Lanczos)i(methods)g(for)h(nonsymmetric)f(linear)960
1254 y(systems)p FG(,)j(T)-6 b(ech.)20 b(Rep.)g(SAND91-8240,)d(Sandia)j
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1424 y([196])41 b(A)t(.)32 b FJ(V)-5 b(A)t(N)31 b(D)t(E)t(R)h
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b(Math.,)i(14)960 1523 y(\(1969\),)18 b(pp.)i(14\22623.)739
1693 y([197])41 b(A)t(.)25 b FJ(V)-5 b(A)t(N)25 b(D)t(E)t(R)f
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b(A)t(N)25 b(D)t(E)t(R)g FG(V)q FJ(O)t(R)t(S)t(T)r FG(,)20
b Ft(The)g(r)o(ate)g(of)g(con)m(ver)m(g)o(ence)e(of)i(conjugate)e(gr)o
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h(3)960 2332 y(\(1982\),)18 b(pp.)i(350\226356.)739 2502
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b(Uni)n(v)o(ersity)-5 b(,)19 b(K)n(yoto,)g(Japan,)g(May)h(30,)g(1987.)
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o(elsson)f(and)g(L.)h(Y)-11 b(.)16 b(K)m(olotilina,)960
3979 y(eds.,)k(v)n(ol.)g(1457)f(of)h(Lecture)f(Notes)i(in)f
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4248 y(nonsymmetric)20 b(linear)g(systems)p FG(,)h(SIAM)f(J.)h(Sci.)g
(Statist.)g(Comput.,)e(13)g(\(1992\),)f(pp.)i(631\226644.)739
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4518 y Ft(wher)m(e)e FC(A)g Ft(is)g(symmetric)g(comple)n(x)p
FG(,)e(IEEE)h(T)m(rans.)g(Magnetics,)f(26)h(\(1990\),)e(pp.)h
(706\226708.)739 4688 y([207])41 b(H)t(.)27 b FJ(V)-5
b(A)t(N)27 b(D)t(E)t(R)g FG(V)q FJ(O)t(R)t(S)t(T)g(A)t(N)t(D)g
FG(C)t(.)h(V)t FJ(U)t(I)t(K)r FG(,)23 b Ft(GMRESR:)e(A)i(family)g(of)f
(nested)g(GMRES)g(methods)p FG(,)g(T)-6 b(ech.)960 4788
y(Rep.)18 b(91-80,)e(Delft)i(Uni)n(v)o(ersity)f(of)g(T)-6
b(echnology)h(,)15 b(F)o(aculty)j(of)f(T)-6 b(ech.)17
b(Math.,)h(Delft,)g(The)g(Netherlands,)960 4887 y(1991.)739
5057 y([208])41 b(J)t(.)33 b(V)-6 b FJ(A)t(N)33 b FG(R)q
FJ(O)t(S)t(E)t(N)t(D)q(A)t(L)t(E)r FG(,)e Ft(Minimizing)d(inner)g(pr)l
(oduct)f(data)g(dependencies)f(in)i(conjugate)f(gr)o(adient)960
5157 y(iter)o(ation)p FG(,)20 b(T)-6 b(ech.)19 b(Rep.)h(172178,)e
(ICASE,)i(N)m(ASA)h(Langle)o(y)e(Research)h(Center)m(,)f(1983.)739
5327 y([209])41 b(R)t(.)25 b(V)-6 b FJ(A)t(R)t(G)t(A)r
FG(,)22 b Ft(Matrix)e(Iter)o(ative)g(Analysis)p FG(,)g(Prentice-Hall)f
(Inc.,)h(Engle)n(w)o(ood)e(Clif)n(fs,)i(NJ,)h(1962.)739
5497 y([210])41 b(P)-5 b(.)33 b(V)-6 b FJ(A)t(S)t(S)t(I)t(L)t(E)t(V)t
(S)t(K)t(I)r FG(,)30 b Ft(Pr)m(econditioning)25 b(nonsymmetric)i(and)g
(inde\002nite)f(\002nite)i(element)g(matrices)p FG(,)i(J.)960
5596 y(Numer)-5 b(.)20 b(Alg.)g(Appl.,)f(1)h(\(1992\),)e(pp.)i
(59\22676.)p eop end
%%Page: 105 115
TeXDict begin 105 114 bop 291 282 a Fu(BIBLIOGRAPHY)2520
b FG(105)291 515 y([211])41 b(V)-7 b(.)35 b(V)q FJ(O)t(E)t(V)q(O)t(D)t
(I)t(N)r FG(,)e Ft(The)e(pr)l(oblem)e(of)h(non-self-adjoint)e(g)o(ener)
o(alization)g(of)i(the)g(conjugate)e(gr)o(adient)512
615 y(method)19 b(is)i(closed)p FG(,)f(U.S.S.R.)g(Comput.)f(Maths.)h
(and)g(Math.)g(Phys.,)f(23)h(\(1983\),)e(pp.)h(143\226144.)291
781 y([212])41 b(H)t(.)22 b(F)m(.)h(W)-5 b FJ(A)t(L)t(K)t(E)t(R)r
FG(,)20 b Ft(Implementation)15 b(of)j(the)g(GMRES)g(method)f(using)g
(Householder)f(tr)o(ansformations)p FG(,)512 881 y(SIAM)k(J.)h(Sci.)g
(Statist.)g(Comput.,)e(9)h(\(1988\),)e(pp.)h(152\226163.)291
1047 y([213])41 b(P)-5 b(.)25 b(W)t FJ(E)t(S)t(S)t(E)t(L)t(I)t(N)t(G)r
FG(,)20 b Ft(An)g(Intr)l(oduction)e(to)j(Multigrid)f(Methods)p
FG(,)f(W)m(ile)o(y)-5 b(,)19 b(Chichester)m(,)h(1991.)291
1213 y([214])41 b(O)t(.)25 b(W)t FJ(I)t(D)t(L)t(U)t(N)t(D)r
FG(,)e Ft(A)e(Lanczos)g(method)e(for)j(a)f(class)h(of)f(non-symmetric)f
(systems)i(of)f(linear)g(equations)p FG(,)512 1312 y(SIAM)f(J.)h(Numer)
-5 b(.)20 b(Anal.,)f(15)h(\(1978\),)e(pp.)h(801\226812.)291
1478 y([215])41 b(D)t(.)25 b(Y)r FJ(O)t(U)t(N)t(G)r FG(,)20
b Ft(Iter)o(ative)g(solution)f(of)i(lar)m(g)o(e)f(linear)g(systems)p
FG(,)h(Academic)e(Press,)i(Ne)n(w)g(Y)-9 b(ork,)19 b(1971.)291
1644 y([216])41 b(H)t(.)34 b(Y)t FJ(S)t(E)t(R)t(E)t(N)t(T)n(A)t(N)t(T)r
FG(,)e Ft(On)e(the)f(multile)o(vel)h(splitting)f(of)h(\002nite)g
(element)f(spaces)p FG(,)j(Numer)-5 b(.)29 b(Math.,)i(49)512
1744 y(\(1986\),)18 b(pp.)h(379\226412.)p eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF

.