Mathematical Software (TOMS)


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ACM Transactions on Mathematical Software (TOMS), Volume 24 Issue 1, March 1998

Algorithm 779: Fermi-Dirac functions of order -1/2, 1/2, 3/2, 5/2
Allan J. MacLeod
Pages: 1-12
DOI: 10.1145/285861.285862
The computation of Fermi-Dirac integrals *** is discussed for the values *** = -1, 1/2, 3/2, 5/2. We derive Chebyshev polynomial expansions which allow the computation of these functions to double precision IEEE accuracy....

Generation of high-order interpolants for explicit Runge-Kutta pairs
P. W. Sharp, J. H. Verner
Pages: 13-29
DOI: 10.1145/285861.285863
Explicit Runge-Kutta pairs can be enhanced by providing them with interpolants. Enhancements include the ability to estimate and control the defect, to produce dense output, and to calculate past values in delay differential equations. The...

PELLPACK: a problem-solving environment for PDE-based applications on multicomputer platforms
E. N. Houstis, J. R. Rice, S. Weerawarana, A. C. Catlin, P. Papachiou, K.-Y. Wang, M. Gaitatzes
Pages: 30-73
DOI: 10.1145/285861.285864
The article presents the software architecture and implementation of the problem-solving environment (PSE) PELLPACK for modeling physical objects described by partial differential equations (PDEs). The scope of this PSE is broad, as PELLPACK...

The design, implementation, and evaluation of a symmetric banded linear solver for distributed-memory parallel computers
Anshul Gupta, Fred G. Gustavson, Mahesh Joshi, Sivan Toledo
Pages: 74-101
DOI: 10.1145/285861.285865
This article describes the design, implementation, and evaluation of a parallel algorithm for the Cholesky factorization of symmetric banded matrices. The algorithm is part of IBM's parallel engineering and scientific subroutine library version...

Algorithm 780: exponential pseudorandom distribution
Kenneth G. Hamilton
Pages: 102-1060
DOI: 10.1145/285861.285866
An algorithm is presented for the calculation of exponentially distributed random numbers. It is based on mathematics that was published by Ahrend and Dieter, but some errors have been corrected....

The computation of spectral density functions for singular Sturm-Liouville problems involving simple continuous spectra
C. T. Fulton, S. Pruess
Pages: 107-129
DOI: 10.1145/285861.285867
The software package SLEDGE has as one of its options the estimation of spectral density functions p(t) for a wide class of singular Strurm-Liouville problems. In this article the underlaying theory and implementation issues...

Expokit: a software package for computing matrix exponentials
Roger B. Sidje
Pages: 130-156
DOI: 10.1145/285861.285868
Expokit provides a set of routines 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...