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ACM Transactions on Mathematical Software (TOMS), Volume 40 Issue 1, September 2013

ColPack: Software for graph coloring and related problems in scientific computing
Assefaw H. Gebremedhin, Duc Nguyen, Md. Mostofa Ali Patwary, Alex Pothen
Article No.: 1
DOI: 10.1145/2513109.2513110

We present a suite of fast and effective algorithms, encapsulated in a software package called ColPack, for a variety of graph coloring and related problems. Many of the coloring problems model partitioning needs arising in compression-based...

CHEBINT: A MATLAB/Octave toolbox for fast multivariate integration and interpolation based on chebyshev approximations over hypercubes
Koen Poppe, Ronald Cools
Article No.: 2
DOI: 10.1145/2513109.2513111

We present the fast approximation of multivariate functions based on Chebyshev series for two types of Chebyshev lattices and show how a fast Fourier transform (FFT) based discrete cosine transform (DCT) can be used to reduce the complexity of...

gHull: A GPU algorithm for 3D convex hull
Mingcen Gao, Thanh-Tung Cao, Ashwin Nanjappa, Tiow-Seng Tan, Zhiyong Huang
Article No.: 3
DOI: 10.1145/2513109.2513112

A novel algorithm is presented to compute the convex hull of a point set in ℝ3 using the graphics processing unit (GPU). By exploiting the relationship between the Voronoi diagram and the convex hull, the algorithm derives the...

Pivoting strategies for tough sparse indefinite systems
Jonathan D. Hogg, Jennifer A. Scott
Article No.: 4
DOI: 10.1145/2513109.2513113

The performance of a sparse direct solver is dependent upon the pivot sequence that is chosen before the factorization begins. In the case of symmetric indefinite systems, it may be necessary to modify this sequence during the factorization to...

Algorithm 931: An algorithm and software for computing multiplicity structures at zeros of nonlinear systems
Wenrui Hao, Andrew J. Sommese, Zhonggang Zeng
Article No.: 5
DOI: 10.1145/2513109.2513114

A Matlab implementation, multiplicity, of a numerical algorithm for computing the multiplicity structure of a nonlinear system at an isolated zero is presented. The software incorporates a newly developed equation-by-equation strategy that...

Algorithm 932: PANG: Software for nonmatching grid projections in 2D and 3D with linear complexity
Martin J. Gander, Caroline Japhet
Article No.: 6
DOI: 10.1145/2513109.2513115

We design and analyze an algorithm with linear complexity to perform projections between 2D and 3D nonmatching grids. This algorithm, named the PANG algorithm, is based on an advancing front technique and neighboring information. Its...

Algorithm 933: Reliable calculation of numerical rank, null space bases, pseudoinverse solutions, and basic solutions using suitesparseQR
Leslie V. Foster, Timothy A. Davis
Article No.: 7
DOI: 10.1145/2513109.2513116

The SPQR_RANK package contains routines that calculate the numerical rank of large, sparse, numerically rank-deficient matrices. The routines can also calculate orthonormal bases for numerical null spaces, approximate pseudoinverse solutions to...

Algorithm 934: Fortran 90 subroutines to compute Mathieu functions for complex values of the parameter
Danilo Erricolo, Giuseppe Carluccio
Article No.: 8
DOI: 10.1145/2513109.2513117

Software to compute angular and radial Mathieu functions is provided in the case that the parameter q is a complex variable and the independent variable x is real. After an introduction on the notation and the definitions of Mathieu...