jacobi

jacobi, a Python code which uses the Jacobi 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:

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

test_mat, a Python code which defines test matrices.

wathen, a Python code 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, the source code.
• jacobi.sh, runs all the tests.
• 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.