jacobi

jacobi, a MATLAB code which uses the Jacobi iteration to solve a symmetric positive definite (SPD) linear system.

Licensing:

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

Languages:

jacobi is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version and an R version.

Related Data and Programs:

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

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

jacobi_test

jacobi_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 Jacobi iteration.

test_mat, a MATLAB code which defines test matrices.

Source Code:

• dif2.m, defines the -1, 2, -1 tridiagonal matrix.
• jacobi1.m, carries out one step of the Jacobi iteration.
• jacobi2.m, carries out one step of the Jacobi iteration, using MATLAB's vector notation.
• jacobi3.m, carries out one step of the Jacobi iteration, using an even better version of MATLAB's vector notation.