Main Content

Matrix exponential

The algorithm `expm`

uses is described in [1] and [2].

**Note**

The files, `expmdemo1.m`

, `expmdemo2.m`

,
and `expmdemo3.m`

illustrate
the use of Padé approximation, Taylor series approximation, and
eigenvalues and eigenvectors, respectively, to compute the matrix
exponential. References [3] and [4] describe and compare many algorithms for
computing a matrix exponential.

[1] Higham, N. J., “The Scaling and Squaring
Method for the Matrix Exponential Revisited,” *SIAM
J. Matrix Anal. Appl.*, 26(4) (2005), pp. 1179–1193.

[2] Al-Mohy, A. H. and N. J. Higham, “A
new scaling and squaring algorithm for the matrix exponential,” *SIAM
J. Matrix Anal. Appl.*, 31(3) (2009), pp. 970–989.

[3] Golub, G. H. and C. F. Van Loan, *Matrix
Computation*, p. 384, Johns Hopkins University Press,
1983.

[4] Moler, C. B. and C. F. Van Loan, “Nineteen
Dubious Ways to Compute the Exponential of a Matrix,” * SIAM
Review 20*, 1978, pp. 801–836. Reprinted and updated
as “Nineteen Dubious Ways to Compute the Exponential of a Matrix,
Twenty-Five Years Later,” *SIAM Review 45*,
2003, pp. 3–49.