Re: R-alpha: matrix exponential

Gordon K Smyth (
Thu, 21 Nov 1996 11:28:35 +1100

Message-Id: <>
Date: Thu, 21 Nov 1996 11:28:35 +1100
From: Gordon K Smyth <>
Subject: Re: R-alpha: matrix exponential

The matrix exponential problem is one on which numerical analysts have done
a lot of work.  There are problems with most obvious approaches, as
described in the excellent paper by Moler and van Loan cited by Bill Venables.

For statistical applications we most often want expm(Q)v where Q is a large
sparse (often banded) matrix and v is a vector.  Since expm(Q) is dense even
though Q is sparse, it is important to compute the result without explicitly
forming the intermediate result expm(Q).  Roger Sidje, Department of
Mathematics, University of Queensland, has produced high quality algorithms
to solve this problem.  Code in either MATLAB or Fortran can be obtained
from "".  As I understand it, Roger's code
uses Krylov space methods to refine the usual Pade approximation, which is
the default algorithm used by MATLAB.

Dr Gordon K Smyth           Telephone:  7-3365-3116, Fax:  7-3365-1477
Department of Mathematics, University of Queensland, Q 4072, Australia
E-mail:,     Web:

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