EXPOKIT - A SOFTWARE PACKAGE FOR COMPUTING MATRIX EXPONENTIALS

Expokit provides a set of routines aimed at computing matrix exponenti als. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand ve ctor, or the solution of a system of linear ODEs with constant inhomog eneity. The backbone of the sparse routines consists of matrix-free Kr ylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of l arge dimension. The software handles real and complex matrices and pro vides specific routines for symmetric and Hermitian matrices. The comp utation of matrix exponentials is a numerical issue of critical import ance in the area of Markov chains and furthermore, the computed soluti on is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the c omputation of transient states of Markov chains.