# 28_2 - 1 Gaussian Elimination with Partial Pivoting In...

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Unformatted text preview: 1 Gaussian Elimination with Partial Pivoting In terms of matrix operations. Step1: Swap 1 st row with the 2 nd row. Define permutation matrix: ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = 1 1 1 1 P ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ 15 2 3 1 39 7 4 3 22 3 4 2 [ ] ) 1 ( ) 1 ( b A [ ] [ ] ) 1 ( 1 1 ) 1 ( 1 1 ) 2 ( ) 2 ( b P M A P M b A = Gaussian Elimination with Partial Pivoting Step2: Swap 2 nd row with the 3 rd row. Define permutation matrix: ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = 1 1 1 2 P ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − − 2 4 39 7 4 3 3 1 3 5 3 5 3 4 [ ] ) 2 ( ) 2 ( b A [ ] [ ] ) 2 ( 2 2 ) 2 ( 2 2 ) 3 ( ) 3 ( b P M A P M b A = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − − 5 28 5 7 3 1 3 5 2 39 7 4 3 x1=1, x2=2, x3=4 Gaussian Elimination with Partial Pivoting [ ] [ ] ' ' 5 7 3 1 3 5 2 ' 1 ) 3 ( 22 1 2 22 ) 2 ( 22 ) 2 ( 22 1 2 22 ) 2 ( 22 ) 2 ( 22 1 22 ) 2 ( 22 ) 2 ( 22 ) 2 ( 22 1 22 ) 2 ( 22 ) 2 ( 1 ) 2 ( 22 ) 1 ( 1 ) 2 ( 22 ) 1 ( 1 2 ) 2 ( 22 1 22 ) 2 ( 1 ) 1 ( 1 ) 1 ( 1 1 ) 1 ( 1...
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28_2 - 1 Gaussian Elimination with Partial Pivoting In...

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