**A noniterative thinning algorithm**

Christian Neusius, Jan Olszewski

Pages: 5-20

DOI: 10.1145/174603.174604

Thinning algorithms are applied in image processing to compute a skeleton of an image. In this paper a new thinning method is presented which differs in its approach from other thinning algorithms. In the presented algorithm the minimal distance...

**Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules**

Walter Gautschi

Pages: 21-62

DOI: 10.1145/174603.174605

A collection of subroutines and examples of their uses, as well as the underlying numerical methods, are described for generating orthogonal polynomials relative to arbitrary weight functions. The object of these routines is to produce the...

**New NAG library software for first-order partial differential equations**

S. V. Pennington, M. Berzins

Pages: 63-99

DOI: 10.1145/174603.155272

New NAG Fortran Library routines are described for the solution of systems of nonlinear, first-order, time-dependent partial differential equations in one space dimension, with scope for coupled ordinary differential or algebraic equations. The...

**Algorithm 727: Quantile estimation using overlapping batch statistics**

Sherif Hashem, Bruce Schmeiser

Pages: 100-102

DOI: 10.1145/174603.174412

An efficient algorithm for estimating the qth quantile of a set of n data points is introduced. The standard error of the quantile estimate is estimated using overlapping batch statistics. A driver program is...

**Generating quadratic bilevel programming test problems**

Paul H. Calamai, Luis N. Vicente

Pages: 103-119

DOI: 10.1145/174603.174411

This paper describes a technique for generating sparse or dense quadratic bilevel programming problems with a selectable number of known global and local solutions. The technique described here does not require the solution of any subproblems....

**Algorithm 728: FORTRAN subroutines for generating quadratic bilevel programming test problems**

Paul H. Calamai, Luis N. Vicente

Pages: 120-123

DOI: 10.1145/174603.174410

This paper describes software for generating test problems for quadratic bilevel programming. The algorithm constructs problems with a number of favorable properties that can be selected and controlled by the user. The intention is to provide a...

**The evaluation of trigonometric integrals avoiding spurious discontinuities**

D. J. Jeffrey, A. D. Rich

Pages: 124-135

DOI: 10.1145/174603.174409

The tan(x/2) substitution, also called the Weierstrass substitution, is one method currently used by computer-algebra systems for the evaluation of trigonometric integrals. The method needs to be improved, because the expressions obtained using...

**Sparse QR factorization in MATLAB**

Pontus Matstoms

Pages: 136-159

DOI: 10.1145/174603.174408

In the recently presented sparse matrix extension of MATLAB, there is no routine for sparse QR factorization. Sparse linear least-squares problems are instead solved by the augmented system method. The accuracy in computed solutions is strongly...

**Corrigendum: Algorithm 729: FORTRAN subroutines for general Toeplitz systems**

Per Christian Hansen, Tony F. Chan

Page: 160

DOI: 10.1145/174603.174407

This paper presents FORTRAN 77 implementations of the lookahead Levinson algorithm of Chan and Hansen (7, 8) for solving symmetric indefinite and general Toeplitz systems. The algorithms are numerically stable for all Toeplitz matrices that do...

**Corrigendum: Algorithm 730: An implementation of a divide and conquer algorithm for the unitary eigenproblem**

G. S. Ammar, L. Reichel, D. C. Sorensen

Page: 161

DOI: 10.1145/174603.174406

We present a FORTRAN implementation of a divide-and-conquer method for computing the spectral resolution of a unitary upper Hessenberg matrix H. Any such matrix H of order n, normalized so that its subdiagonal elements are...