What mistakes did I make? I think it is in TriSolve method since if I replaced it with regular LU solver such as (np.linalg.solve) it works. Below is the same implementation in MATLAB which works: function x = gSeidel(A,B,N) For some reason it is not converging even after 50000 iterations to the solution even when the matrix A is strict diagonal dominant.

#O(n) per iteration, so overall O(nN), good for large SPD/SDD matricesĪ = np.array(,])Īns = is my Gauss-Seidel method in Python. all functions, myMatrixTools.From scipy.linalg import solve_triangular as triSolve.all input should be valid (n/N = ints, the rest can be floats) -> no validations were made.In Gauss Seidel method, we first arrange given system of linear equations in diagonally dominant form. Numpy version 1.19.3 (previous to 1.19.4 -> had some issues initializing it) This program implements Gauss Seidel Iteration Method for solving systems of linear equation in python programming language.myMatrixTools.py - constains few basic matrix manipulation and analysis functions for usage.main2.py - constains larger user-input of size N, matrix a and vector b.main.py - contains basic usage demonstration of jacobi_calc() or gauss_seidel_calc(), using a 3x3 matrix, and basic arguments.

rel_diff, the relative difference between last 2.

If max_iter is None, the default value will set as 200.

max_iter, the maxim number of possible iterations to receive the most exact solution.

These methods are however used as smoothers in scipy, or even FEniCs supported PETSc. Within each solver, the individual block linear system with preconditioners are approximated by a few runs of AMG V-cycle or a Gauss Seidel sweep. If tolerance is None, the default value will set as 1e-16. I am working on block preconditioning and seemingly it is common to write customised Krylov solvers for them.

tolerance, the desired limitation of tolerance of solution's anomaly. 0:00 / 15:31 Cdigo Mtodo de Gauss-Seidel (Python) Para tudo tem um cdigo 644 subscribers Subscribe 5.4K views 3 years ago Mtodos Numricos: Sistemas Lineares Breve explicao do.

If x is None, the initial guess will bw determined as a vector of 0's. if b is None - the functions returns None. If a is None or NxM, where N != M - the functions returns None.

a, the NxN matrix that the method is being performed on.

The algorithms will terminate when the change in x is less than tolerance, or if max_iter iterations have been exceeded.įor each function: (jacobi_calc() or gauss_seidel_calc()) Jacobi & Gauss-Seidel Algorithms Using Python The following methods solve the line system of equations, Ax=b,using Jacobi OR Gauss-Seidel algorithms, starting from an initial guess, x0.

Gauss seidel code in python