For the problem of computing the matrix-exponential the following article may be of interest (and may be added to our - to be constructed - virtual library?). I've not read it yet, though.
MATRIX EXPONENTIALS AND INVERSION OF CONFLUENT VANDERMONDE MATRICES
UWE LUTHER† AND KARLA ROST‡
Abstract. For a given matrix A we compute the matrix exponential e^A
under the assumption that the eigenvalues of A are known, but without
determining the eigenvectors. The presented approach exploits the
connection between matrix exponentials and confluent Vandermonde
matrices V . This approach and the resulting methods are very simple
and can be regarded as an alternative to the Jordan canonical form
methods. The discussed inversion algorithms for V as well as the
matrix representation of V^-1 are of independent interest also in many
other applications.
Key words. matrix exponential, Vandermonde matrix, fast algorithm, inverse.
AMS subject classifications. 34A30, 65F05, 15A09, 15A23.
Electronic Transactions on Numerical Analysis.
Volume 18, pp. 91-100, 2004.
Copyright Ó 2004, Kent State University.
ISSN 1068-9613.
ETNA
Kent State University
etna@mcs.kent.edu
Preprint (2003) online: Luther/Rost
UWE LUTHER† AND KARLA ROST‡
Abstract. For a given matrix A we compute the matrix exponential e^A
under the assumption that the eigenvalues of A are known, but without
determining the eigenvectors. The presented approach exploits the
connection between matrix exponentials and confluent Vandermonde
matrices V . This approach and the resulting methods are very simple
and can be regarded as an alternative to the Jordan canonical form
methods. The discussed inversion algorithms for V as well as the
matrix representation of V^-1 are of independent interest also in many
other applications.
Key words. matrix exponential, Vandermonde matrix, fast algorithm, inverse.
AMS subject classifications. 34A30, 65F05, 15A09, 15A23.
Electronic Transactions on Numerical Analysis.
Volume 18, pp. 91-100, 2004.
Copyright Ó 2004, Kent State University.
ISSN 1068-9613.
ETNA
Kent State University
etna@mcs.kent.edu
Gottfried Helms, Kassel