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Algorithm 894: On a block Schur--Parlett algorithm for ϕ-functions based on the sep-inverse estimate

Published: 07 April 2009 Publication History

Abstract

FORTRAN 95 software is provided for computing the matrix values of φ-functions required in exponential integrators. The subroutines in the library accept as their argument a full, diagonal, or upper quasitriangular matrix with real or complex entries in one of four precisions. Two different algorithms are implemented, one is the scaling and squaring method, and the other is a modified block Schur--Parlett algorithm. In the latter algorithm, a recursive three-by-three blocking is applied to the argument based on an estimate of the sep-inverse function. The estimation of the sep-inverse function is carried out by Hager--Higham estimator implemented as the subroutine xLACON in LAPACK. Our modifications to the block Schur--Parlett algorithm are described together with the results of numerical experiments.

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cover image ACM Transactions on Mathematical Software
ACM Transactions on Mathematical Software  Volume 36, Issue 2
March 2009
149 pages
ISSN:0098-3500
EISSN:1557-7295
DOI:10.1145/1499096
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 07 April 2009
Accepted: 01 September 2008
Revised: 01 March 2008
Received: 01 July 2007
Published in TOMS Volume 36, Issue 2

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  1. φ-functions
  2. block Schur--Parlett algorithm
  3. exponential integrators
  4. matrix functions

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