**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...