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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
Matrices and Linear Systems of Equations 1-39
1.15.5 Method 5: LU Decomposition
(Triangular Decomposition)
Method
Theorem 1.11 Every n-square matrix A can be
expressed as a product of two triangular matrices,
one lower and another upper thus
A = LU
where
11 12 13
21 22 23 21
31 32 33 31 32
11 12 13
22 23
33
100
;10
1
0
00
aaa
Aa a a Ll
aaa ll
uuu
Uuu
u
⎡⎤⎡⎤
⎢⎥⎢⎥
==
⎢⎥⎢⎥
⎢⎥⎢⎥
⎣⎦⎣⎦
⎡⎤
⎢⎥
=
⎢⎥
⎢⎥
⎣⎦
Proof A = LU
11 12 13
21 22 23
31 32 33
11 12 13
21 11 21 12 22 21 12 23
31 11 31 12 32 22 31 13 32 23 33
aaa
aaa
aaa
uu u
lu lu u lu u
lu lu lu lu lu u
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎣⎦
⎡⎤
⎢⎥
=+ +
⎢⎥
⎢⎥
+++
⎣⎦
We have nine equations in nine unknowns which can
be solved for. Indeed we ha
ve
13
21
31
3
31
3
2 1 1100
[ ]
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Publisher Resources

ISBN: 9781299446557Publisher Website