JACOBI
The Jacobi Iteration for Linear Systems

JACOBI is a C++ library which sets up the Jacobi iteration for linear systems.

The program uses the GNUPLOT_I interface program to create plots of the residual and the "motion" of the solution over the iteration.

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

GNUPLOT_I, a C library which allows an executing C, C++, FORTRAN77 or FORTRAN90 program to interact with the GNUPLOT graphics program, by Nicholas Devillard.

JACOBI_OPENMP, a C++ program which illustrates the use of the OpenMP application program interface to parallelize a Jacobi iteration solving A*x=b.

TEST_MAT, a C++ library which defines test matrices.

Reference:

• Tim Kelley,
  Iterative Methods for Linear and Nonlinear Equations,
  SIAM, 2004,
  ISBN: 0898713528,
  LC: QA297.8.K45.

Source Code:

• jacobi.cpp, the source code.
• jacobi.hpp, the include file.

Examples and Tests:

• jacobi_test.cpp, a sample calling program.
• jacobi_test.txt, the output file.
• motion.png, a plot of the motion, or change in the solution, as the iteration progresses.
• residual.png, a plot of the residual as the iteration progresses.

List of Routines:

• DIF2 returns the DIF2 matrix.
• R8MAT_MV multiplies a matrix times a vector.
• R8MAT_RESIDUAL_NORM returns the norm of A*x-b.
• R8VEC_COPY copies an R8VEC.
• R8VEC_DIFF_NORM_SQUARED: square of the L2 norm of the difference of R8VEC's.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.