jacobi_openmp, a FORTRAN90 code which uses the OpenMP application program interface to parallelize a Jacobi iteration solving A*x=b.

Each step of the Jacobi iteration produces a vector xnew. The i-th entry of xnew is found by ``solving'' the i-th linear equation for the i-th variable. This operation can be done in parallel. It is a little more complicated to compute the maximum difference between the old and new x values, and to compute the maximum residual, but these can be done.

The example uses a standard -1,2,-1 matrix which has very slow convergence. Here, the point is not so much to get the answer, but to show that the process can be speeded up by employing OpenMP.


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


jacobi_openmp is available in a C version and a C++ version and a FORTRAN90 version.

Related Data and Programs:

DIJKSTRA_OPENMP, a FORTRAN90 code which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.

FFT_OPENMP, a FORTRAN90 code which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.

HEATED_PLATE_OPENMP, a FORTRAN90 code which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.

HELLO_OPENMP, a FORTRAN90 code which prints out "Hello, world!" from each OpenMP thread.

JACOBI, a FORTRAN90 code which implements the Jacobi iteration for solving symmetric positive definite (SPD) systems of linear equations.


MANDELBROT_OPENMP, a FORTRAN90 code which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set, using OpenMP for parallel execution.

MD_OPENMP, a FORTRAN90 code which carries out a molecular dynamics simulation using OpenMP.

MULTITASK_OPENMP, a FORTRAN90 code which demonstrates how to "multitask", that is, to execute several unrelated and distinct tasks simultaneously, using OpenMP for parallel execution.

MXM_OPENMP, a FORTRAN90 code which computes a dense matrix product C=A*B, using OpenMP for parallel execution.

openmp_test, FORTRAN90 codes which use the OpenMP application code interface for carrying out parallel computations in a shared memory environment.

POISSON_OPENMP, a FORTRAN90 code which computes an approximate solution to the Poisson equation in a rectangle, using the Jacobi iteration to solve the linear system, and OpenMP to carry out the Jacobi iteration in parallel.

PRIME_OPENMP, a FORTRAN90 code which counts the number of primes between 1 and N, using OpenMP for parallel execution.

QUAD_OPENMP, a FORTRAN90 code which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.

QUAD2D_OPENMP, a FORTRAN90 code which applies a product quadrature rule to estimate an integral over a 2D rectangle, using OpenMP for parallel execution.

RANDOM_OPENMP, a FORTRAN90 code which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.

SATISFY_OPENMP, a FORTRAN90 code which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, using OpenMP for parallel execution.

SCHEDULE_OPENMP, a FORTRAN90 code which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.

SGEFA_OPENMP, a FORTRAN90 code which reimplements the SGEFA/SGESL linear algebra routines from LINPACK for use with OpenMP.

SUPERLU_OPENMP, FORTRAN90 codes which illustrate how to use the SUPERLU library with the OpenMP parallel programming interface, which applies a fast direct solution method to solve sparse linear systems, by James Demmel, John Gilbert, and Xiaoye Li.

ZIGGURAT_OPENMP, a FORTRAN90 code which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.


  1. Peter Arbenz, Wesley Petersen,
    Introduction to Parallel Computing - A practical guide with examples in C,
    Oxford University Press,
    ISBN: 0-19-851576-6,
    LC: QA76.58.P47.
  2. Rohit Chandra, Leonardo Dagum, Dave Kohr, Dror Maydan, Jeff McDonald, Ramesh Menon,
    Parallel Programming in OpenMP,
    Morgan Kaufmann, 2001,
    ISBN: 1-55860-671-8,
    LC: QA76.642.P32.
  3. Barbara Chapman, Gabriele Jost, Ruud vanderPas, David Kuck,
    Using OpenMP: Portable Shared Memory Parallel Processing,
    MIT Press, 2007,
    ISBN13: 978-0262533027,
    LC: QA76.642.C49.
  4. OpenMP Architecture Review Board,
    OpenMP Application Program Interface,
    Version 3.0,
    May 2008.

Source code:

Last revised on 21 July 2020.