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ACM Transactions on Mathematical Software (TOMS), Volume 22 Issue 4, Dec. 1996

Algorithm 763: INTERVAL_ARITHMETIC: a Fortran 90 module for an interval data type
R. Baker Kearfott
Pages: 385-392
DOI: 10.1145/235815.235816
Interval arithmetic is useful in automatically verified computations, that is, in computations in which the algorithm itself rigorously proves that the answer must lie within certain bounds. In addition to rigor, interval...

The computation of elementary unitary matrices
R. B. Lehoucq
Pages: 393-400
DOI: 10.1145/235815.235817
The construction of elementary unitary matrices that transform a complex vector to a multiple of e1, the first column of the identity matrix, is studied. We present four variants and their software...

DESI methods for stiff initial-value problems
J. C. Butcher, J. R. Cash, M. T. Diamantakis
Pages: 401-422
DOI: 10.1145/235815.235818
Recently, the so-called DESI (diagonally extended singly implicit) Runge-Kutta methods were introduced to overcome some of the limitations of singly implicit methods. Preliminary experiments have shown that these methods are usually more...

Using the SLEDGE package on Sturm-Liouville problems having nonempty essential spectra
Michael S. P. Eastham, Charles T. Fulton, Steven Pruess
Pages: 423-446
DOI: 10.1145/235815.235819
We describe the performance of the Sturm-Liouville software package SLEDGE on a variety of problems having continuous spectra. The code's output is shown to be in good accord with a wide range of known theoretical results....

PYTHIA: a knowledge-based system to select scientific algorithms
Sanjiva Weerawarana, Elias N. Houstis, John R. Rice, Anupam Joshi, Catherine E. Houstis
Pages: 447-468
DOI: 10.1145/235815.235820
Problem-solving environments (PSEs) interact with the user in a language “natural” to the associated discipline, and they provide a high-level abstraction of the underlying, computationally complex model. The...

The quickhull algorithm for convex hulls
C. Bradford Barber, David P. Dobkin, Hannu Huhdanpaa
Pages: 469-483
DOI: 10.1145/235815.235821
The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm....

A composition-alias method for generating gamma variates with shape parameter greater than 1
Tapas K. Sarkar
Pages: 484-492
DOI: 10.1145/235815.235822
In this article the author describes a procedure for generating gamma variates with shape parameter >1. Given a supply of “good” uniform (0,1) variates, the procedure makes use of composition method, squeeze method, and aliasing...

A remark on Bartels and Conn's linearly constrained, discrete l1 problems
Roger W. Koenker, Pin T. Ng
Pages: 493-495
DOI: 10.1145/235815.235823
Two modifications of Bartels and Conn's algorithm for solving linearly constrained discrete l1 problems are described. The modifications are designed to improve performance of the algorithm under conditions...

Remark on “Fast floating-point processing in Common Lisp”
J. K. Reid
Pages: 496-497
DOI: 10.1145/235815.235824
We explain why we feel that the comparison betwen Common Lisp and Fortran in a recent article by Fateman et al. in this journal is not entirely fair....

Remark on algorithm 723: Fresnel integrals
W. Van Snyder
Pages: 498-500
DOI: 10.1145/235815.235825