#LnormInf corresponds to the absolute value of the greatest element of the vector. ![]() The Python script that implements the GaussSeideliteration for the. X = x*(1-omega) + (omega/A)*(b - np.dot(A, x) - np.dot(A, x_old)) 6.3.3 GaussSeidel Iteration The Jacobiiteration calculates a new guess for the. Print ("The solution vector in iteration", iter1, "is:", x) The Poisson Equation in Any Space Dimensions def sor_method(A, b, omega, initial_guess, tolerance, max_iterations): But if we could speedup the Python loops somehow, we could benefit from the fewer. See section 3 on the paper The Optimal Relaxation Parameter for the SOR Method Applied to So you might think that the Gauss-Seidel method is completely useless. ![]() Obviously, with higher omega values the number of iterations should decrease.Īs for a working algorithm on SOR this is what I have computed, where best convergence is reached when the optimal omega is used. Phi = sor_solver(A, b, omega, initial_guess, residual_convergence)įor an extended answer on omega and its uses please refer to my other answer SOR method as what is quoted below is not accurate. #An example case that mirrors the one in the Wikipedia article ![]() Here I have some python script, which solves the system of linear equations using Gauss-Seidel method: import numpy as np
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