**Superconvergent interpolants for collocation methods applied to mixed-order BVODEs**

Wayne H. Enright, Ramanan Sivasothinathan

Pages: 323-351

DOI: 10.1145/358407.358410

Continuous approximations to boundary value problems in ordinary differential equations (BVODEs), constructed using collocation at Gauss points, are more accurate at the mesh points than at off-mesh points. From these approximations, it is...

**Remark on algorithm 746**: new features of PCOMP, a Fortran code for automatic differentiation

Michael Liepelt, Klaus Schittkowski

Pages: 352-362

DOI: 10.1145/358407.358412

The software system PCOMP uses automatic differentiation to calculate derivatives of functions that are defined by the user in a modeling language similar to Fortran. This symbolical representation is converted into an intermediate code, which...

**A simple method for generating gamma variables**

George Marsaglia, Wai Wan Tsang

Pages: 363-372

DOI: 10.1145/358407.358414

We offer a procedure for generating a gamma variate as the cube of a suitably scaled normal variate. It is fast and simple, assuming one has a fast way to generate normal variables. In brief: generate a normal variate x and a...

**On stopping criteria in verified nonlinear systems or optimization algorithms**

R. B. Kearfott, G. W. Walster

Pages: 373-389

DOI: 10.1145/358407.358418

Traditionally, iterative methods for nonlinear systems use heuristic domain and range stopping criteria to determine when accuracy tolerances have been met. However, such heuristics can cause stopping at points far from actual solutions, and can...

**Algorithms for the computation of all Mathieu functions of integer orders**

Fayez A. Alhargan

Pages: 390-407

DOI: 10.1145/358407.358420

The article presents methods for the computation of all Mathieu functions of integer order, which cover a large range of n and h; previous algorithms were limited to small values of n. The...

**Algorithm 804**: subroutines for the computation of Mathieu functions of integer orders

Fayez A. Alhargan

Pages: 408-414

DOI: 10.1145/358407.358422

Computer subroutines in C++ for computing Mathieu functions of integer orders are described. The routines can handle a large range of the order n and the parameter h. Sample test results and graphs are...

**Algorithm 805**: computation and uses of the semidiscrete matrix decomposition

Tamara G. Kolda, Dianne P. O'Leary

Pages: 415-435

DOI: 10.1145/358407.358424

We present algorithms for computing a semidiscrete approximation to a matrix in a weighted norm, with the Frobenius norm as a special case. The approximation is formed as a weighted sum of outer products of vectors whose elements are ±1...

**Algorithm 806: SPRNG**: a scalable library for pseudorandom number generation

Michael Mascagni, Ashok Srinivasan

Pages: 436-461

DOI: 10.1145/358407.358427

In this article we present background, rationale, and a description of the Scalable Parallel Random Number Generators (SPRNG) library. We begin by presenting some methods for parallel pseudorandom number generation. We will focus on methods...