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First notice that a linear system of size can be written as: This is different from the Jacobi method where all the components in an iteration are calculated based on the previous iteration. In the Gauss-Seidel method, the system is solved using forward substitution so that each component uses the most recent value obtained for the previous component. The Gauss-Seidel method offers a slight modification to the Jacobi method which can cause it to converge faster. Open Educational Resources Iterative Methods:

Linearization of Nonlinear Relationships.Convergence of Jacobi and Gauss-Seidel Methods.Cholesky Factorization for Positive Definite Symmetric Matrices.