Efficient Computation of the Matrix Exponential by Generalized Polar Decompositions

Authors:
Arieh Iserles;Antonella Zanna
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2004

Citing 0
Cited 3

Geometrical methods for non-negative ICA: Manifolds, Lie groups and toral subalgebras

Neurocomputing
A method for approximation of the exponential map in semidirect product of matrix Lie groups and some applications

Journal of Computational and Applied Mathematics
A structure preserving approximation method for Hamiltonian exponential matrices

Applied Numerical Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we explore the computation of the matrix exponential in a manner that is consistent with Lie-group structure. Our point of departure is the method of generalized polar decompositions, which we modify and combine with similarity transformations that bring the underlying matrix to a form more amenable to efficient computation. We develop techniques valid for a range of Lie groups: the orthogonal group, the symplectic group, Lorentz, isotropy, and scaling groups. However, the GPD approach is equally promising in a more general context. Even when Lie-group structure is not at issue, our algorithm is more efficient in many settings than classical methods for the computation of the matrix exponential.