In numerical linear algebra, the Gauss-Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel, and can be applied to any matrix with non-zero diagonal elements, though convergence is only guaranteed when the matrix is strictly diagonally dominant, or symmetric and positive definite. The method was first mentioned only in a private letter from Gauss to his student Gerling in 1823, and was not published until 1874, by Seidel.
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