MGMRES
Restarted GMRES solver for sparse linear systems


MGMRES is a FORTRAN90 library which applies the restarted Generalized Minimum Residual (GMRES) algorithm to solve a sparse linear system, using compressed row (CR) or sparse triplet (ST) format, by Lili Ju.

One matrix format used is the sparse triplet (ST) format, which simply stores NZ_NUM, the number of nonzeros, and stores the K-th nonzero matrix entry as

Another matrix format used is the compressed row (CR) format, which is similar to the sparse triplet format except that the vector of row indices is compressed to a vector of length N+1 which points to the beginning of the set of entries for each row.

Licensing:

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

Languages:

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

Related Data and Programs:

CC, a data directory which contains examples of the Compressed Column (CC) sparse matrix file format;

CG_RC, a FORTRAN90 library which implements the conjugate gradient method for solving a positive definite sparse linear system A*x=b, using reverse communication.

CR, a data directory which contains examples of the Compressed Row (CR) sparse matrix file format;

DLAP, a FORTRAN90 library which implements iterative methods for solving linear systems.

FEM2D_POISSON_SPARSE, a FORTRAN90 program which solves the steady Poisson equation on a 2D triangulated region. The program uses a copy of mgmres to solve the linear system.

HBSMC, a dataset directory which contains large sparse matrices stored in the Harwell-Boeing (HB) format.

JACOBI, a FORTRAN90 library which implements the Jacobi iteration for solving symmetric positive definite systems of linear equations.

LINPACK, a FORTRAN90 library which carries out direct methods for solving linear systems.

MM, a data directory which contains a description and examples of the Matrix Market (MM) format for storing matrices.

SPARSEKIT, a FORTRAN90 library which implements operations on sparse matrices, including conversion between various formats.

ST, a data directory which contains a description and examples of the sparse triplet (ST) format for storing sparse matrices, used by the C and C++ versions of mgmres.

SUPERLU, FORTRAN90 programs which illustrate how to use the SUPERLU library, which applies a fast direct solution method to solve sparse linear systems, by James Demmel, John Gilbert, and Xiaoye Li.

TEMPLATES, a FORTRAN90 library which carries out simple versions of various iterative solvers.

TEST_MAT, a FORTRAN90 library which defines test matrices.

Author:

Original C version by Lili Ju, Mathematics Department, University of South Carolina; FORTRAN90 version by John Burkardt.

Reference:

  1. Richard Barrett, Michael Berry, Tony Chan, James Demmel, June Donato, Jack Dongarra, Victor Eijkhout, Roidan Pozo, Charles Romine, Henk van der Vorst,
    Templates for the Solution of Linear Systems:
    Building Blocks for Iterative Methods,
    SIAM, 1994,
    ISBN: 0898714710,
    LC: QA297.8.T45.
  2. Tim Kelley,
    Iterative Methods for Linear and Nonlinear Equations,
    SIAM, 2004,
    ISBN: 0898713528,
    LC: QA297.8.K45.
  3. Yousef Saad,
    Iterative Methods for Sparse Linear Systems,
    Second Edition,
    SIAM, 20003,
    ISBN: 0898715342,
    LC: QA188.S17.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.


Last revised on 28 August 2012.