21 lines
324 B
Org Mode
21 lines
324 B
Org Mode
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Jacobi Iteration (cont.)
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x^{k+1} = D^{-1}(b - (L + U)x^k)
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{
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x^{k+1} = x^k + D^-1 r^k
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r^{k} = b - Ax^k
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}
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error: || x^{k+1} - x^k ||_2
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residual: || r^k ||_2
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Gauss-Seidel Iteration:
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A = (L + D + U)
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\Rightarrow Ax = b
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(D + U)x = b - Lx
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x = (D + U)^-1 (b - Lx)
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x^{k+1} = (D+U)^{-1}(b - Lx^k)
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(D + U)^{-1} x (bsubst)
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