Gauss-Seidel method

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An iterative method to solve LaTeX: Ax=b using the latest values of the components of LaTeX: x during the updates. Specifically, LaTeX: A is split into LaTeX: L-T, where LaTeX: L is lower triangular, and the update solvesLaTeX:  Lx' = Tx + b. (Surprisingly, history indicates Gauss did not know about this method, and Seidel did not recommend it.) Often people refer to the method to mean the use of latest values, rather than the specific splitting. It arises, for example, in parallel computation, where using the latest value of LaTeX: x during the computation of LaTeX: x' is not done since it would not be able to take advantage of the parallelism.


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