JACOBI
The Jacobi Iteration for Linear Systems

JACOBI is a MATLAB library which sets up the Jacobi 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:

JACOBI is available in a C++ version and a MATLAB version.

Related Data and Programs:

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

JACOBI_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 Jacobi iteration.

TEST_MAT, a MATLAB library which defines test matrices.

Reference:

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

Examples and Tests:

• jacobi_test.m, calls all the tests;
• jacobi_test_output.txt, the output file.
• jacobi_test01.m, tests JACOBI1 on the -1,2,-1 matrix;
• jacobi_residual.png a PNG image of the square of the norm of the residual (Ax-b).
• jacobi_evolution.png a PNG image of the evolution or trajectories of the solution values as the iteration proceeds.
• jacobi_motion.png a PNG image of the "motion" of the solution values, which is the averaged distance each entry moves during an iteration.

You can go up one level to the MATLAB source codes.