# 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 solves$LaTeX: Lx' = Tx + b$. (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.