gauss_seidel

gauss_seidel, an Octave 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 C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version and an R version.

Related Data and Programs:

gauss_seidel_test

gauss_seidel_stochastic, an Octave code which uses a stochastic version of the Gauss-Seidel iteration to solve a linear system with a symmetric positive definite (SPD) matrix.

jacobi, an Octave code which implements the Jacobi iteration for linear systems.

test_matrix, an Octave code which defines test matrices for which the condition number, determinant, eigenvalues, eigenvectors, inverse, null vectors, P*L*U factorization or linear system solution are known. Examples include the Fibonacci, Hilbert, Redheffer, Vandermonde, Wathen and Wilkinson 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.