With , the Gauss-Seidel method solves . It uses each newly computed coordinate immediately in the remaining triangular solve. It is successive over-relaxation with parameter one, and converges from every start when is symmetric positive definite.
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The Gauss-Seidel method is an iterative technique used to solve a system of linear equations of the form \(Ax = b\), where \(A\) is a matrix, \(x\) is the vector of unknowns, and \(b\) is the output vector. This method is particularly useful for large systems where direct methods like Gaussian elimination might be computationally expensive.