The Jacobi Iteration for Linear Systems

**JACOBI**
is a MATLAB library which
sets up the Jacobi iteration for linear systems.

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

**JACOBI** is available in
a C version and
a C++ version and
a FORTRAN77 version and
a FORTRAN90 version and
a MATLAB version.

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.

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.

- 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.

- 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.