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The Gauss-Seidel iterative method is one of the most common techniques for solving systems of linear equations iteratively. It’s particularly useful for symmetric and diagonally dominant matrices. The rate of convergence of the Gauss-Seidel method depends on the spectral radius of the iteration matrix.

Here’s how it works:

  1. Initialization: Start with an initial guess for the solution vector, denoted by


  2. Iterative Process: Update each component of the solution vector iteratively using the following formula:


    represents the