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4/14/11
Gaussian Elimination
Algorithm to matrices:
A =
½ times 1st row subtract from second
3/2 times 1st row, subtract from third
And so forth
2
2
3
1
2
0
3
1
1
2
2
3
0
3
3/2
0
2
7/2
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4/14/11
Gaussian Elimination
Algorithm to matrices:
A =
subtracting hjk/hkk where hkk is diagonal element.
Factor hjk/hkk
must be subtracted
from the entire row.
2
2
3
1
2
0
3
1
1
2
2
3
0
3
3/2
0
2
7/2
Click to edit Master subtitle style
4/14/11
Gaussian Elimination
Algorithm to matrices:
Factor hjk/hkk
must be subtracted.
In matrix form –
=
1
0
0
1/2
1
0
3/2
0
1
2
2
3
1
2
0
3
1
1
2
2
3
0
3
3/2
0
2
7/2
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View Full Document 4/14/11
Gaussian Elimination
Algorithm to matrices:
Factor hjk/hkk
must be subtracted.
In matrix form –
Lk
=
1
… 1

hk+1k/hk
k …
1 …
hmk/hkk
1
4/14/11
Gaussian Elimination
Algorithm to matrices: Lm1 … L2L1A = U
Lk
=
1
… 1

hk+1k/hk
k …
1 …
hmk/hkk
1
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Gaussian Elimination
Algorithm to matrices: Lm1 … L2L1A = U
upper triangular
Lk
=
1
… 1

hk+1k/hk
k …
1 …
hmk/hkk
1
4/14/11
Gaussian Elimination
Algorithm to matrices: Lm1 … L2L1A = U
L1 lower triangular
Lk
=
1
… 1

hk+1k/hk
k …
1 …
hmk/hkk
1
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View Full Document 4/14/11
Gaussian Elimination
Algorithm to matrices: A = LU
lower upper triangular
Lk
=
1
… 1

hk+1k/hk
k …
1 …
hmk/hkk
1
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This note was uploaded on 04/13/2011 for the course CSCE 211 taught by Professor Staff during the Spring '08 term at Columbia SC.
 Spring '08
 Staff

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