GAUSS_SEIDEL
The Gauss Seidel Iteration for Linear Systems

GAUSS_SEIDEL, a MATLAB library which sets up the Gauss Seidel iteration for linear systems.

Licensing:

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

Languages:

GAUSS_SEIDEL is available in a MATLAB version.

Related Data and Programs:

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

gauss_seidel, a MATLAB library which implements the Gauss-Seidel iteration for linear systems.

gauss_seidel_test

GAUSS_SEIDEL_POISSON_1D, a MATLAB program 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 library which implements the Jacobi iteration for linear systems.

SOR, a MATLAB library 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 library 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.
• timestamp.m, prints the current YMDHMS date as a time stamp.

Examples and Tests:

• gauss_seidel_test.m, calls all the tests;
• gauss_seidel_test.sh, runs all the tests;
• gauss_seidel_test.txt, the output file.
• gauss_seidel_test01.m, tests gauss_seidel1;
• gauss_seidel_test02.m, tests gauss_seidel2;
• gauss_seidel_error.png a PNG image of the square of the norm of the residual (Ax-b).
• gauss_seidel_evolution.png a PNG image of the evolution or trajectories of the solution values as the iteration proceeds.
• gauss_seidel_motion.png a PNG image of the "motion" of the solution values, which is the averaged distance each entry moves during an iteration.