gauss_seidel

gauss_seidel, a MATLAB code which uses the Gauss-Seidel iteration to solve a linear system with a symmetric positive definite (SPD) matrix.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

gauss_seidel is available in a MATLAB version and an R version.

Related Data and Programs:

cg_rc, a MATLAB code which implements the conjugate gradient method for solving a positive definite sparse linear system A*x=b, using reverse communication.

gauss_seidel_test

gauss_seidel_poisson_1d, a MATLAB code which demonstrates how the linear system for a discretized version of the steady 1D Poisson equation can be solved by the Gauss-Seidel iteration.

jacobi, a MATLAB code which implements the Jacobi iteration for linear systems.

sor, a MATLAB code which implements a simple version of the successive over-relaxation (SOR) method for the iteration solution of a linear system of equations.

test_mat, a MATLAB code which defines test matrices.

Reference:

• Tim Kelley,
  Iterative Methods for Linear and Nonlinear Equations,
  SIAM, 2004,
  ISBN: 0898713528,
  LC: QA297.8.K45.

Source Code:

• dif2.m, defines the -1, 2, -1 tridiagonal matrix.
• gauss_seidel1.m, carries out one step of the Gauss Seidel iteration.
• gauss_seidel2.m, carries out one step of the Gauss Seidel iteration, assuming sparse matrix storage.