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

Authors:
Souji Koikari
Affiliations:
Kyoto University, Kyoto, Japan
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2009

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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.