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Gauss-Seidel Iteration

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An iteration step of the Gauss-Seidel iteration to solve the LSE $ Ax=b$ is defined by

$\displaystyle x^{\text{new}}_i = (b_i - \sum_{j<i} a_{i,j} x^{\text{new}}_j - \sum_{j>i} a_{i,j} x^{\text{old}}_j ) / a_{i,i},\quad i=1,\ldots,n\, . $

This method is almost identical to the Jacobi iteration. The difference is that the Gauss-Seidel iteration uses the already updated values $ x^{\text{new}}_j$, $ j=1,\ldots,i-1$ to compute $ x^{\text{new}}_i$.

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  automatically generated 4/24/2007