![]() Co-efficeint matrix, contant vector, initial guesses and tolerence are be prompted for user input. #LnormInf corresponds to the absolute value of the greatest element of the vector. Heres an implementation of Gaussian elimination in Python: import numpy as np Define the system of linear equations as a matrix equation AX B A. Script for Gauss Seidel method This matlab script can solve a system of linear equations by Gauss Seidel method, an iterative method. 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): ![]() If the function returns None, the minimization is aborted. Return the function value and set approxgradTrue. Return the function value but supply gradient function separately as fprime. See section 3 on the paper The Optimal Relaxation Parameter for the SOR Method Applied to Must do one of: Return f and g, where f is the value of the function and g its gradient (a list of floats). 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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