test_matrix_exponential

test_matrix_exponential, a Python code which contains some simple tests for software that computes 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, that is

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

Even for this simple case, and for a matrix of small order, it can be quite difficult to compute the matrix exponential accurately.

The information on this web page is distributed under the MIT license.

test_matrix_exponential is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

matrix_exponential, a Python code which demonstrates some simple approaches to the problem of computing the exponential of a matrix.

test_matrix, a Python code which defines test matrices.

Alan Laub,
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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.
Cleve Moler,
Cleve's Corner: A Balancing Act for the Matrix Exponential,
July 23rd, 2012.
Roger Sidje,
EXPOKIT: Software Package for Computing Matrix Exponentials,
ACM Transactions on Mathematical Software,
Volume 24, Number 1, 1998, pages 130-156.
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.

Last modified on 04 February 2017.