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ACM Transactions on Mathematical Software (TOMS), Volume 42 Issue 1, February 2016

A Sparse Symmetric Indefinite Direct Solver for GPU Architectures
Jonathan D. Hogg, Evgueni Ovtchinnikov, Jennifer A. Scott
Article No.: 1
DOI: 10.1145/2756548

In recent years, there has been considerable interest in the potential for graphics processing units (GPUs) to speed up the performance of sparse direct linear solvers. Efforts have focused on symmetric positive-definite systems for which no...

Replicated Computational Results (RCR) Report for A Sparse Symmetric Indefinite Direct Solver for GPU Architectures
Eric T. Bavier
Article No.: 2
DOI: 10.1145/2851489

A Sparse Symmetric Indefinite Direct Solver for GPU Architectures includes performance results and comparisons of the developed GPU direct solver against a CPU direct solver. New performance data were gathered using software provided by the...

Sampling Exactly from the Normal Distribution
Charles F. F. Karney
Article No.: 3
DOI: 10.1145/2710016

An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in the same...

Testing Matrix Function Algorithms Using Identities
Edvin Deadman, Nicholas J. Higham
Article No.: 4
DOI: 10.1145/2723157

Algorithms for computing matrix functions are typically tested by comparing the forward error with the product of the condition number and the unit roundoff. The forward error is computed with the aid of a reference solution, typically computed at...

ShearLab 3D: Faithful Digital Shearlet Transforms Based on Compactly Supported Shearlets
Gitta Kutyniok, Wang-Q Lim, Rafael Reisenhofer
Article No.: 5
DOI: 10.1145/2740960

Wavelets and their associated transforms are highly efficient when approximating and analyzing one-dimensional signals. However, multivariate signals such as images or videos typically exhibit curvilinear singularities, which wavelets are provably...

Parameterized Complexity of Discrete Morse Theory
Benjamin A. Burton, Thomas Lewiner, João Paixão, Jonathan Spreer
Article No.: 6
DOI: 10.1145/2738034

Optimal Morse matchings reveal essential structures of cell complexes that lead to powerful tools to study discrete geometrical objects, in particular, discrete 3-manifolds. However, such matchings are known to be NP-hard to compute on 3-manifolds...

Algorithm 955: Approximation of the Inverse Poisson Cumulative Distribution Function
Michael B. Giles
Article No.: 7
DOI: 10.1145/2699466

New approximations for the inverse of the incomplete gamma function are derived, which are used to develop efficient evaluations of the inverse Poisson cumulative distribution function. An asymptotic approximation based on the standard Normal...

Algorithm 956: PAMPAC, A Parallel Adaptive Method for Pseudo-Arclength Continuation
D. A. Aruliah, Lennaert Van Veen, Alex Dubitski
Article No.: 8
DOI: 10.1145/2714570

Pseudo-arclength continuation is a well-established method for generating a numerical curve approximating the solution of an underdetermined system of nonlinear equations. It is an inherently sequential predictor-corrector method in which new...

Algorithm 957: Evaluation of the Repeated Integral of the Coerror Function by Half-Range Gauss-Hermite Quadrature
Walter Gautschi
Article No.: 9
DOI: 10.1145/2735626

Nonstandard Gaussian quadrature is applied to evaluate the repeated integral inerfc x of the coerror function for n ∈ N0, x ∈ R in an appropriate domain of the (n, x)-plane....

Remark on “Algorithm 673: Dynamic Huffman Coding”
Alexander Novoselsky, Eugene Kagan
Article No.: 10
DOI: 10.1145/2740959

This remark presents a correction to Algorithm 673 (dynamic Huffman coding) [Vitter 1989] and its translation to MATLAB.