Algorithm 763: INTERVAL_ARITHMETIC: a Fortran 90 module for an interval data type
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 arithmetic also provides a ...
The computation of elementary unitary matrices
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 implementation, including a discussion onthe LAPACK ...
DESI methods for stiff initial-value problems
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 efficient than ...
Using the SLEDGE package on Sturm-Liouville problems having nonempty essential spectra
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
Problem-solving e*nvironments (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 knowledge-based system PYTHIA addresses the ...
The quickhull algorithm for convex hulls
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. It ...
A composition-alias method for generating gamma variates with shape parameter greater than 1
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 to generate gamma ...
A remark on Bartels and Conn's linearly constrained, discrete l1 problems
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 of degeneracy.
Remark on “Fast floating-point processing in Common Lisp”
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.