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ACM Transactions on Mathematical Software (TOMS), Volume 39 Issue 2, February 2013

NLEVP: A Collection of Nonlinear Eigenvalue Problems
Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder, Françoise Tisseur
Article No.: 7
DOI: 10.1145/2427023.2427024

We present a collection of 52 nonlinear eigenvalue problems in the form of a MATLAB toolbox. The collection contains problems from models of real-life applications as well as ones constructed specifically to have particular properties. A...

Accelerating Linear System Solutions Using Randomization Techniques
Marc Baboulin, Jack Dongarra, Julien Herrmann, Stanimire Tomov
Article No.: 8
DOI: 10.1145/2427023.2427025

We illustrate how linear algebra calculations can be enhanced by statistical techniques in the case of a square linear system Ax = b. We study a random transformation of A that enables us to avoid pivoting and...

Level-3 Cholesky Factorization Routines Improve Performance of Many Cholesky Algorithms
Fred G. Gustavson, Jerzy Waśniewski, Jack J. Dongarra, José R. Herrero, Julien Langou
Article No.: 9
DOI: 10.1145/2427023.2427026

Four routines called DPOTF3i, i = a,b,c,d, are presented. DPOTF3i are a novel type of level-3 BLAS for use by BPF (Blocked Packed Format) Cholesky factorization and LAPACK routine DPOTRF. Performance of routines DPOTF3i are...

Finite Element Integration on GPUs
Matthew G. Knepley, Andy R. Terrel
Article No.: 10
DOI: 10.1145/2427023.2427027

We present a novel finite element integration method for low-order elements on GPUs. We achieve more than 100GF for element integration on first order discretizations of both the Laplacian and Elasticity operators on an NVIDIA GTX285, which has a...

A Runge-Kutta BVODE Solver with Global Error and Defect Control
Jason J. Boisvert, Paul H. Muir, Raymond J. Spiteri
Article No.: 11
DOI: 10.1145/2427023.2427028

Boundary value ordinary differential equations (BVODEs) are systems of ODEs with boundary conditions imposed at two or more distinct points. The global error (GE) of a numerical solution to a BVODE is the amount by which the numerical solution...

Variants of Mersenne Twister Suitable for Graphic Processors
Mutsuo Saito, Makoto Matsumoto
Article No.: 12
DOI: 10.1145/2427023.2427029

This article proposes a type of pseudorandom number generator, Mersenne Twister for Graphic Processor (MTGP), for efficient generation on graphic processessing units (GPUs). MTGP supports large state sizes such as 11213 bits, and uses the...

Elemental: A New Framework for Distributed Memory Dense Matrix Computations
Jack Poulson, Bryan Marker, Robert A. van de Geijn, Jeff R. Hammond, Nichols A. Romero
Article No.: 13
DOI: 10.1145/2427023.2427030

Parallelizing dense matrix computations to distributed memory architectures is a well-studied subject and generally considered to be among the best understood domains of parallel computing. Two packages, developed in the mid 1990s, still enjoy...

Algorithm 926: Incomplete Gamma Functions with Negative Arguments
Ian Thompson
Article No.: 14
DOI: 10.1145/2427023.2427031

An algorithm for accurately computing the lower incomplete gamma function γ(a, t) in the case where a = n + 1/2, n ∈ Z and t < 0 is described. Series expansions and analytic...

Algorithm 927: The MATLAB Code bvptwp.m for the Numerical Solution of Two Point Boundary Value Problems
J. R. Cash, D. Hollevoet, F. Mazzia, A. M. Nagy
Article No.: 15
DOI: 10.1145/2427023.2427032

In this article we describe the code bvptwp.m, a MATLAB code for the solution of two point boundary value problems. This code is based on the well-known Fortran codes, twpbvp.f, twpbvpl.f and acdc.f, that employ a mesh selection strategy based on...