Write a \"python function\" to perform the Gauss-Seidel method for solving a sys

Question

Write a "python function" to perform the Gauss-Seidel method for solving a system of equations Ax=b for a dense matirx n x n size A. The parameters of the function should include the matrix A, the right hand side vector b, the initial xo, the tolerance epsilon, and the maximum number of iterations. The function should return the solution x and a success/failure flag.

Explanation / Answer

FOLLOW THIS You can solve a linear system in various ways, depending on whether there exists a unique solution or not. A simple way is by reducing it to reduced-echelon form (rref). Consider the system: x + 5y = 4 2x - y = 1 You can write the coefficient matrix A, and the RHS, B as follows: (' is the transpose operator) >> A = [1 5; 2 -1] A = 1 5 2 -1 >> B = [4 1]' B = 4 1 You can write it as an augmented matrix (A|B): >> horzcat(A,B) ans = 1 5 4 2 -1 1 And then find the REF(A|B) >> rref(ans) ans = 1.0000 0 0.8182 0 1.0000 0.6364 And hence x ~ .8182, y ~ .6364. share|improve this answer

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