![]() #LnormInf corresponds to the absolute value of the greatest element of the vector. Some information about the Python code: a) Recall that Xx is the vector generated by the Gauss-Seidel iterations. ![]() The Python code for the Gauss-Seidel iterations is provided to you at the end of this question. X = x*(1-omega) + (omega/A)*(b - np.dot(A, x) - np.dot(A, x_old)) Question: Q1) In this question, you will use the Gauss-Seidel method to solve systems of linear equations. Print ("The solution vector in iteration", iter1, "is:", x) import numpy as np from scipy.linalg import solve def gauss(A, b, x. The Poisson Equation in Any Space Dimensions def sor_method(A, b, omega, initial_guess, tolerance, max_iterations): I need to do Gauss seidel method in python code please. See section 3 on the paper The Optimal Relaxation Parameter for the SOR Method Applied to 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 In numerical linear algebra, the GaussSeidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method. 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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