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ACM Transactions on Mathematical Software (TOMS), Volume 33 Issue 4, August 2007

TestU01: A C library for empirical testing of random number generators
Pierre L'Ecuyer, Richard Simard
Article No.: 22
DOI: 10.1145/1268776.1268777

We introduce TestU01, a software library implemented in the ANSI C language, and offering a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). It provides general implementations of the...

hpGEM---A software framework for discontinuous Galerkin finite element methods
Lars Pesch, Alexander Bell, Henk Sollie, Vijaya R. Ambati, Onno Bokhove, Jaap J. W. Van Der Vegt
Article No.: 23
DOI: 10.1145/1268776.1268778

hpGEM, a novel framework for the implementation of discontinuous Galerkin finite element methods (FEMs), is described. We present data structures and methods that are common for many (discontinuous) FEMs and show how we have implemented the...

deal.II—A general-purpose object-oriented finite element library
W. Bangerth, R. Hartmann, G. Kanschat
Article No.: 24
DOI: 10.1145/1268776.1268779

An overview of the software design and data abstraction decisions chosen for deal.II, a general purpose finite element library written in C++, is given. The library uses advanced object-oriented and data encapsulation techniques to break...

A parallel symmetric block-tridiagonal divide-and-conquer algorithm
Yihua Bai, Robert C. Ward
Article No.: 25
DOI: 10.1145/1268776.1268780

We present a parallel implementation of the block-tridiagonal divide-and-conquer algorithm that computes eigensolutions of symmetric block-tridiagonal matrices to reduced accuracy. In our implementation, we use mixed data/task parallelism to...

Accurate numerical derivatives in MATLAB
L. F. Shampine
Article No.: 26
DOI: 10.1145/1268776.1268781

Complex step differentiation (CSD) is a technique for computing very accurate numerical derivatives in languages that support complex arithmetic. We describe here the development of a CSD package in MATLAB called PMAD. We have extended work...

Algorithm 869: ODRPACK95: A weighted orthogonal distance regression code with bound constraints
Jason W. Zwolak, Paul T. Boggs, Layne T. Watson
Article No.: 27
DOI: 10.1145/1268776.1268782

ODRPACK (TOMS Algorithm 676) has provided a complete package for weighted orthogonal distance regression for many years. The code is complete with user selectable reporting facilities, numerical and analytic derivatives, derivative checking, and...

Remark on Algorithm 644
Masao Kodama
Article No.: 28
DOI: 10.1145/1268776.1268783

This remark details correction for errors in the functions which compute the modified Bessel function of the second kind and the log of the gamma function. In both cases these errors cause a loss of precision for a small range of values of the...