Algorithm 894: On a Block Schur-Parlett Algorithm for phi-functions Based on the Sep-Inverse Estimate

作者：Koikari Souji^*

来源：ACM Transactions on Mathematical Software, 2009, 36(2): 12.

DOI：10.1145/1499096.1499101

• Algorithms
• phi-functions
• exponential integrators
• matrix functions
• block Schur-Parlett algorithm

FORTRAN 95 software is provided for computing the matrix values of phi-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.

• 出版日期2009-3