JACOBI
The Jacobi Iteration for Linear Systems

JACOBI is a Python 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 C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

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

TEST_MAT, a Python library which defines test matrices.

WATHEN, a Python library which compares storage schemes (full, banded, sparse triplet, sparse) and solution strategies (A\x, Linpack, conjugate gradient (CG)) for linear systems involving the Wathen matrix, which can arise when solving a problem using the finite element method (FEM).

Source Code:

• jacobi.py, carries out one step of the Jacobi iteration.
• jacobi.txt, the output file.
• 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 Python source codes.