Mathematical Software (TOMS)


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ACM Transactions on Mathematical Software (TOMS), Volume 20 Issue 4, Dec. 1994

Computing hyperelliptic integrals for surface measure of ellipsoids
Charles F. Dunkl, Donald E. Ramirez
Pages: 413-426
DOI: 10.1145/198429.198430
An algorithm for computing a class of hyperelliptic integrals and for determining the surface measure of ellipsoids is described. The algorithm is used to construct an omnibus optimal-design criterion.

Algorithm 736: Hyperelliptic integrals and the surface measure of ellipsoids
Charles F. Dunkl, Donald E. Ramirez
Pages: 427-435
DOI: 10.1145/198429.198431
The algorithm for computing a class of hyperelliptic integrals and for determining the surface measure of ellipsoids is described in detail by Dunkl and Ramirez [1994]. An efficient implementation of their algorithm is presented here.

A new algorithm for the evaluation of the incomplete gamma function on vector computers
H. Früchtl, P. Otto
Pages: 436-446
DOI: 10.1145/198429.198432
Several methods of evaluating the Incomplete Gamma Function are compared according to accuracy and computation time. An improved algorithm is presented which allows significantly faster computation of two-electron integrals on most vector...

Algorithm 737: INTLIB—a portable Fortran 77 interval standard-function library
R. B. Kearfott, M. Dawande, K. Du, C. Hu
Pages: 447-459
DOI: 10.1145/198429.198433
INTLIB is meant to be a readily available, portable, exhaustively documented interval arithmetic library, written in standard Fortran 77. Its underlying philosophy is to provide a standard for interval operations to aid in efficiently...

Evaluation and approximate evaluation of the multivariate Bernstein-Bézier form on a regularly partitioned simplex
Jörg Peters
Pages: 460-480
DOI: 10.1145/198429.198434
Polynomials of the total degree d in m variables have a geometrically intuitive representation in the Bernstein-Be´zier form defined over an m-dimensional simplex. The two algorithms given...

Reservoir-sampling algorithms of time complexity O(n(1 + log(N/n)))
Kim-Hung Li
Pages: 481-493
DOI: 10.1145/198429.198435
One-pass algorithms for sampling n records without replacement from a population of unknown size n are known as reservoir-sampling algorithms. In this article, Vitter's reservoir-sampling algorithm, algorithm Z,...

Programs to generate Niederreiter's low-discrepancy sequences
Paul Bratley, Bennett L. Fox, Harald Niederreiter
Pages: 494-495
DOI: 10.1145/198429.198436
This note points out programs to implement Niederreiter's low-discrepancy sequences.

Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods
Kjell Gustafsson
Pages: 496-517
DOI: 10.1145/198429.198437
The problem of stepsize selection in implicit Runge-Kutta schemes is analyzed from a feedback control point of view. This approach leads to a better understanding of the relation between stepsize and error. A new dynamical model describing this...

Algorithm 738: a software package for unconstrained optimization using tensor methods
T. Chow, E. Eskow, R. Schnabel
Pages: 518-530
DOI: 10.1145/198429.198438
This paper describes a software package for finding the unconstrained minimizer of a nonlinear function of n variables. The package is intended for problems where n is not too large—say, n...

A data-level parallel linear-quadratic penalty algorithm for multicommodity network flows
Mustafa Ç. Pinar, Stavros A. Zenios
Pages: 531-552
DOI: 10.1145/198429.198439
We describe the development of a data-level, massively parallel, software system for the solution of multicommodity network flow problems. Using a smooth linear-quadratic penalty (LQP) algorithm we transform the multicommodity network flow...