**Practical experience in the numerical dangers of heterogeneous computing**

L. S. Blackford, A. Cleary, A. Petitet, R. C. Whaley, J. Demmel, I. Dhillon, H. Ren, K. Stanley, J. Dongarra, S. Hammarling

Pages: 133-147

DOI: 10.1145/264029.264030

Special challenges exist in writing reliable numerical library software for heterogeneous computing environments. Although a lot of software for distributed-memory parallel computers has been written, porting this software to a network of...

**Distributed nested decomposition of staircase linear programs**

James K. Ho, R. P. Sundarraj

Pages: 148-173

DOI: 10.1145/264029.264031

This article considers the application of a primal nested-decomposition method to solve staircase linear programs (SLPs) on distributed-memory, multiple-instruction-multiple-data computers. Due to the coupling that exists among the stages of an...

**Algorithm 768: TENSOLVE**: a software package for solving systems of nonlinear equations and nonlinear least-squares problems using tensor methods

Ali Bouaricha, Robert B. Schnabel

Pages: 174-195

DOI: 10.1145/264029.264032

This article describes a modular solftware package for solving systems of nonlinear equations and nonlinear problems, using a new class of methods called tensor methods. It is intended for small- to medium-sized problems, say with up to 100...

**Algorithm 769**: Fortran subroutines for approximate solution of sparse quadratic assignment problems using GRASP

Panos M. Pardalos, Leonidas S. Pitsoulis, Mauricio G. C. Resende

Pages: 196-208

DOI: 10.1145/264029.264038

We describe Fortran subroutines for finding approximate solutions of sparse instances of the Quadratic Assignment Problem (QAP) using a Greedy Randomized Adaptive Search Procedure (GRASP). The design and implementation of the code are described...

**Enhanced simulated annealing for globally minimizing functions of many-continuous variables**

Patrick Siarry, Gérard Berthiau, François Durdin, Jacques Haussy

Pages: 209-228

DOI: 10.1145/264029.264043

A new global optimization algorithm for functions of many continuous variables is presented, derived from the basic Simulated annealing method. Our main contribution lies in dealing with high-dimensionality minimization problems, which are often...

**Boundary-valued shape-preserving interpolating splines**

P. Costantini

Pages: 229-251

DOI: 10.1145/264029.264050

This article describes a general-purpose method for computing interpolating polynomial splines with arbitrary constraints on their shape and satisfying separable or nonseparable boundary conditions. Examples of applications of the related...

**Algorithm 770: BVSPIS—a package for computing boundary-valued shape-preserving interpolating splines**

P. Costantini

Pages: 252-254

DOI: 10.1145/264029.264059

This article describes a software package for computing interpolating polynomial splines with arbitrary constraints on their shape and satisfying separable or nonseparable boundary conditions.

**Multiplicative, congruential random-number generators with multiplier ± 2**^{k1} ± 2^{k2} and modulus 2^{p} - 1

Pei-Chi Wu

Pages: 255-265

DOI: 10.1145/264029.264056

The demand for random numbers in scientific applications is increasing. However, the most widely used multiplicative, congruential random-number generators with modulus 231 − 1 have a cycle length of about 2.1 ×...

**Computational investigations of low-discrepancy sequences**

Ladislav Kocis, William J. Whiten

Pages: 266-294

DOI: 10.1145/264029.264064

The Halton, Sobol, and Faure sequences and the Braaten-Weller construction of the generalized Halton sequence are studied in order to assess their applicability for the quasi Monte Carlo integration with large number of variates. A modification...

**Remark on Algorithm 745**

Michele Goano

Pages: 295-295

DOI: 10.1145/264029.643581