R-beta: Expokit - Matrix Exponential Kit

Roger B. Sidje (rbs@maths.uq.edu.au)
Mon, 27 Oct 1997 13:02:35 +1000

Date: Mon, 27 Oct 1997 13:02:35 +1000
From: "Roger B. Sidje" <rbs@maths.uq.edu.au>
To: r-testers@stat.math.ethz.ch
Subject: R-beta: Expokit - Matrix Exponential Kit

Expokit is a set of user-friendly routines (in FORTRAN 77 and MATLAB)
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 ODEs with constant inhomogeneity. The computation
of small dense matrix exponentials is based on the rational Chebyshev
approximation or the irreducible Pade approximation combined with
the scaling-and-squaring technique. 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 very large dimension. The software
handles real and complex matrices and provides tailored routines for 
symmetric and Hermitian matrices. When dealing with Markov chains, 
the computation of the matrix exponential 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. Expokit is the first comprehensive package
specifically design for matrix exponentials from the outset. Current
users of the package find it very fast, easy-to-use, and useful. 
Expokit is self-contained and a number of sample drivers are 
included that illustrate its utilization.


The work resulting from Expokit has been accepted for publication
in ACM-TOMS (Transactions On Mathematical Software). We are considering
submitting the code itself to ACM-CALGO (Collected Algorithms). In order
to strengthen the robustness and reliability of the software, comments 
and bugs that users might have will be appreciated.

Roger B. Sidje
Advanced Computational Modelling Centre
Department of Mathematics
University of Queensland
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