MATRIX_EXPONENTIAL
Algorithms for the Matrix Exponential


MATRIX_EXPONENTIAL is a FORTRAN90 library which exhibits and compares some algorithms for approximating the matrix exponential function.

Formally, for a square matrix A and scalar t, the matrix exponential exp(A*t) can be defined as the sum:

exp(A*t) = sum ( 0 <= i < oo ) A^i t^i / i!

The simplest form of the matrix exponential problem asks for the value when t = 1. Even for this simple case, and for a matrix of small order, it can be quite difficult to compute the matrix exponential accurately.

MATRIX_EXPONENTIAL needs the R8LIB library. The test code for MATRIX_EXPONENTIAL requires the TEST_MATRIX_EXPONENTIAL library.

Licensing:

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

Languages:

MATRIX_EXPONENTIAL 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:

EXPOKIT, a FORTRAN77 library which solves various forms of the matrix exponential problem, by Roger Sidje.

R8LIB, a FORTRAN90 library which contains many utility routines using double precision real (R8) arithmetic.

TEST_MAT, a FORTRAN90 library which defines test matrices.

TEST_MATRIX_EXPONENTIAL, a FORTRAN90 library which defines a set of test cases for computing the matrix exponential.

Reference:

  1. Alan Laub,
    Review of "Linear System Theory" by Joao Hespanha,
    SIAM Review,
    Volume 52, Number 4, December 2010, page 779-781.
  2. Cleve Moler, Charles VanLoan,
    Nineteen Dubious Ways to Compute the Exponential of a Matrix, SIAM Review,
    Volume 20, Number 4, October 1978, pages 801-836.
  3. Cleve Moler, Charles VanLoan,
    Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later,
    SIAM Review,
    Volume 45, Number 1, March 2003, pages 3-49.
  4. Roger Sidje,
    EXPOKIT: Software Package for Computing Matrix Exponentials,
    ACM Transactions on Mathematical Software,
    Volume 24, Number 1, 1998, pages 130-156.
  5. Robert Ward,
    Numerical computation of the matrix exponential with accuracy estimate,
    SIAM Journal on Numerical Analysis,
    Volume 14, Number 4, September 1977, pages 600-610.

Source Code:

Examples and Tests:

List of Routines:

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


Last modified on 05 March 2013.