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Zbl 0917.65063
Sidje, Roger B.
Expokit: A software package for computing matrix exponentials. (English)
[J] ACM Trans. Math. Softw. 24, No.1, 130-156 (1998). ISSN 0098-3500

Summary: Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ordinary differential equations with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
34-04 Machine computation, programs (ordinary differential equations)
65Y15 Packaged methods
34A30 Linear ODE and systems
65F30 Other matrix algorithms

Keywords: algorithms; Krylov methods; Markov chains; matrix exponential; expokit; software package; large sparse matrix

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