![]() ![]() #LnormInf corresponds to the absolute value of the greatest element of the vector. ![]() ![]() Print ("The solution vector in iteration", iter1, "is:", x) Define a function, called gs1iteration, which accepts as input values for x and y (which we think of as being x n-1 and y n-1 respectively), and returns a list newx,newy, where newx is the updated value xn and newy is the updated value yn using the Gauss-Seidel method and equations. The Poisson Equation in Any Space Dimensions def sor_method(A, b, omega, initial_guess, tolerance, max_iterations): Gauss-Seidel Method, differences from key in Python. See section 3 on the paper The Optimal Relaxation Parameter for the SOR Method Applied to This program implements Gauss Seidel Iteration Method for solving systems of linear equation in python programming language. 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 Python code of the Gauss-Seidel method 19 Add to basket Description Reviews (0) Description A np.array ( -5, 1, -2, 1, 6, 3, 2, -1, -4) b np.array ( 13, 1, -1) x0 np.zeros ( (3, 1), 'float') Eps 1e-8 Iterations 16 x -2. 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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