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