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|00000000| 5c 73 65 63 74 69 6f 6e | 7b 66 61 63 74 6f 72 20 |\section|{factor |
|00000010| 2d 2d 2d 20 4c 55 20 46 | 61 63 74 6f 72 69 73 61 |--- LU F|actorisa|
|00000020| 74 69 6f 6e 7d 0d 5c 6c | 61 62 65 6c 7b 66 6e 3a |tion}.\l|abel{fn:|
|00000030| 66 61 63 74 6f 72 7d 0d | 5c 69 6e 64 65 78 7b 66 |factor}.|\index{f|
|00000040| 61 63 74 6f 72 28 29 7d | 0d 5c 69 6e 64 65 78 7b |actor()}|.\index{|
|00000050| 4c 55 20 66 61 63 74 6f | 72 69 73 61 74 69 6f 6e |LU facto|risation|
|00000060| 7d 0d 5c 62 65 67 69 6e | 7b 72 61 69 6c 7d 0d 46 |}.\begin|{rail}.F|
|00000070| 61 63 74 6f 72 20 3a 20 | 27 66 61 63 74 6f 72 27 |actor : |'factor'|
|00000080| 20 27 28 27 20 4d 61 74 | 72 69 78 20 27 29 27 20 | '(' Mat|rix ')' |
|00000090| 3b 0d 5c 65 6e 64 7b 72 | 61 69 6c 7d 0d 0d 5c 76 |;.\end{r|ail}..\v|
|000000a0| 65 72 62 2b 66 61 63 74 | 6f 72 2b 20 63 6f 6d 70 |erb+fact|or+ comp|
|000000b0| 75 74 65 73 20 74 68 65 | 20 4c 55 20 66 61 63 74 |utes the| LU fact|
|000000c0| 6f 72 69 7a 61 74 69 6f | 6e 20 6f 66 20 74 68 65 |orizatio|n of the|
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|00000170| 20 20 20 20 5c 69 74 65 | 6d 7b 5c 76 65 72 62 2b | \ite|m{\verb+|
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|000001a0| 76 6f 74 20 69 6e 64 69 | 63 65 73 0d 20 20 20 20 |vot indi|ces. |
|000001b0| 20 20 20 20 5c 69 74 65 | 6d 7b 5c 76 65 72 62 2b | \ite|m{\verb+|
|000001c0| 72 63 6f 6e 64 2b 7d 20 | 74 68 65 20 72 65 63 69 |rcond+} |the reci|
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|000001e0| 6e 64 69 74 69 6f 6e 20 | 65 73 74 69 6d 61 74 65 |ndition |estimate|
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|00000200| 6e 7d 0d 0d 5c 76 65 72 | 62 2b 66 61 63 74 6f 72 |n}..\ver|b+factor|
|00000210| 2b 20 72 65 74 75 72 6e | 73 20 74 68 65 20 72 65 |+ return|s the re|
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|00000250| 6f 6e 76 65 6e 69 65 6e | 74 6c 79 20 75 73 65 64 |onvenien|tly used|
|00000260| 20 77 69 74 68 20 5c 76 | 65 72 62 2b 62 61 63 6b | with \v|erb+back|
|00000270| 73 75 62 2b 20 66 6f 72 | 20 72 65 70 65 74 69 74 |sub+ for| repetit|
|00000280| 69 76 65 0d 73 6f 6c 75 | 74 69 6f 6e 73 2e 20 54 |ive.solu|tions. T|
|00000290| 68 65 20 5c 76 65 72 62 | 2b 6c 75 2b 20 66 75 6e |he \verb|+lu+ fun|
|000002a0| 63 74 69 6f 6e 20 75 73 | 65 73 20 74 68 65 20 72 |ction us|es the r|
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|000002c0| 62 2b 66 61 63 74 6f 72 | 2b 20 74 6f 20 70 72 6f |b+factor|+ to pro|
|000002d0| 64 75 63 65 20 73 65 70 | 61 72 61 74 65 20 4c 20 |duce sep|arate L |
|000002e0| 61 6e 64 20 55 20 6d 61 | 74 72 69 63 65 73 2e 0d |and U ma|trices..|
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|00000310| 70 6c 65 20 6f 66 20 66 | 61 63 74 6f 72 28 29 7d |ple of f|actor()}|
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|00000550| 33 36 0d 5c 65 6e 64 7b | 76 65 72 62 61 74 69 6d |36.\end{|verbatim|
|00000560| 7d 0d 0d 0d 53 65 65 20 | 61 6c 73 6f 3a 20 50 61 |}...See |also: Pa|
|00000570| 67 65 7e 5c 70 61 67 65 | 72 65 66 7b 66 6e 3a 62 |ge~\page|ref{fn:b|
|00000580| 61 63 6b 73 75 62 7d 20 | 5c 76 65 72 62 2b 62 61 |acksub} |\verb+ba|
|00000590| 63 6b 73 75 62 28 29 2b | 2c 0d 50 61 67 65 7e 5c |cksub()+|,.Page~\|
|000005a0| 70 61 67 65 72 65 66 7b | 66 6e 3a 69 6e 76 7d 20 |pageref{|fn:inv} |
|000005b0| 5c 76 65 72 62 2b 69 6e | 76 28 29 2b 2c 0d 50 61 |\verb+in|v()+,.Pa|
|000005c0| 67 65 7e 5c 70 61 67 65 | 72 65 66 7b 66 6e 3a 73 |ge~\page|ref{fn:s|
|000005d0| 6f 6c 76 65 7d 20 5c 76 | 65 72 62 2b 73 6f 6c 76 |olve} \v|erb+solv|
|000005e0| 65 28 29 2b 2e 0d 0d 5c | 6e 65 77 70 61 67 65 0d |e()+...\|newpage.|
|000005f0| 0d 0d 0d 0d | |.... | |
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