**Algorithm 687: a decision tree for the numerical solution of initial value ordinary differential equations**

C. A. Addison, W. H. Enright, P. W. Gaffney, I. Gladwell, P. M. Hanson

Pages: 1-10

DOI: 10.1145/103147.103148

**Reliable solution of special event location problems for ODEs**

L. F. Shampine, I. Gladwell, R. W. Brankin

Pages: 11-25

DOI: 10.1145/103147.103149

Computing the solution of the initial value problem in ordinary differential equations (ODEs) may be only part of a larger task. One such task is finding where an algebraic function of the solution (an event function) has a root (an event...

**An accurate elementary mathematical library for the IEEE floating point standard**

Shmuel Gal

Pages: 26-45

DOI: 10.1145/103147.103151

The algorithms used by the IBM Israel Scientific Center for the elementary mathematical library using the IEEE standard for binary floating point arithmetic are described. The algorithms are based on the “accurate tables method.”...

**Performance evaluation of programs related to the real gamma function**

W. J. Cody

Pages: 46-54

DOI: 10.1145/103147.103153

Methods are presented for evaluating the performance of programs for the functions &Ggr;(x), ln &Ggr;(x), and &psgr;(x). Accuracy estimates are based on comparisons using the manipulation...

**The use of Taylor series to test accuracy of function programs**

W. J. Cody, L. Stoltz

Pages: 55-63

DOI: 10.1145/103147.103154

This paper discusses the use of local Taylor series expansions for determining the accuracy of computer programs for special functions. The main example is testing of programs for exponential integrals. Additional applicaitons include testing of...

**On computational aspects of bounded linear least squares problems**

Achiya Dax

Pages: 64-73

DOI: 10.1145/103147.103155

The paper describes numerical experiments with active set methods for solving bounded linear least squares problems. It concentrates on two problems that arise in the implementation of the active set method. One problem is the choice of a good...

**Construction of test problems in quadratic bivalent programming**

Panos M. Pardalos

Pages: 74-87

DOI: 10.1145/103147.103156

A method of constructing test problems for constrained bivalent quadratic programming is presented. For any feasible integer point for a given domain, the method generates quadratic functions whose minimum over the given domain occurs at the...

**On finding the closest bitwise matches in a fixed set**

Peter Klier, Richard J. Fateman

Pages: 88-97

DOI: 10.1145/103147.103157

In a given large fixed table of bit-vectors, we would like to find, as rapidly as possible, those bit-vectors which have the least Hamming distances from a newly-presented arbitrary bit-vector.

**Implementing a random number package with splitting facilities**

Pierre L'Ecuyer, Serge Côté

Pages: 98-111

DOI: 10.1145/103147.103158

A portable set of software tools is described for uniform random
variates generation. It provides for multiple generators running
simultaneously, and each generator has its sequence of numbers
partitioned into many long (disjoint) substreams....

**A generalized envelope method for sparse factorization by rows**

Joseph W. H. Liu

Pages: 112-129

DOI: 10.1145/103147.103159

A generalized form of the envelope method is proposed for the solution of large sparse symmetric and positive definite matrices by rows. The method is demonstated to have practical advantages over the conventional column-oriented factorization...

**On recursive calculation of the generalized inverse of a matrix**

Saleem Mohideen, Vladimir Cherkassky

Pages: 130-147

DOI: 10.1145/103147.103160

The generalized inverse of a matrix is an extension of the ordinary square matrix inverse which applies to any matrix (e.g., singular, rectangular). The generalized inverse has numerous important applications such as regression analysis,...