Mathematical Software (TOMS)


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ACM Transactions on Mathematical Software (TOMS), Volume 20 Issue 2, June 1994

GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable
Bruno Salvy, Paul Zimmermann
Pages: 163-177
DOI: 10.1145/178365.178368
We describe the GFUN package which contains functions for manipulating sequences, linear recurrences, or differential equations and generating functions of various types. This article is intended both as an elementary introduction to the subject...

A parallel block implementation of Level-3 BLAS for MIMD vector processors
Michel J. Daydé, Iain S. Duff, Antoine Petitet
Pages: 178-193
DOI: 10.1145/178365.174413
We describe an implementation of Level-3 BLAS (Basic Linear Algebra Subprograms) based on the use of the matrix-matrix multiplication kernel (GEMM). Blocking techniques are used to express the BLAS in terms of operations involving triangular...

Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations
J. G. Blom, P. A. Zegeling
Pages: 194-214
DOI: 10.1145/178365.178391
In the last decade, several numerical techniques have been developed to solve time-dependent partial differential equations (PDEs) in one dimension having solutions with steep gradients in space and in time. One of these techniques, a...

Implementing complex elementary functions using exception handling
T. E. Hull, Thomas F. Fairgrieve, Ping-Tak Peter Tang
Pages: 215-244
DOI: 10.1145/178365.178404
Algorithms are developed for reliable and accurate evaluations of the complex elementary functions required in FORTRAN 77 and FORTRAN 9, namely, cabs, csqrt, cexp, clog, csin, and ccos. The algorithms are presented in a pseudocode that has a...