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ACM Transactions on Mathematical Software (TOMS), Volume 38 Issue 2, December 2011

Partial factorization of a dense symmetric indefinite matrix
John K. Reid, Jennifer A. Scott
Article No.: 10
DOI: 10.1145/2049673.2049674

At the heart of a frontal or multifrontal solver for the solution of sparse symmetric sets of linear equations, there is the need to partially factorize dense matrices (the frontal matrices) and to be able to use their factorizations in subsequent...

Validated computation of certain hypergeometric functions
Michel Colman, Annie Cuyt, Joris Van Deun
Article No.: 11
DOI: 10.1145/2049673.2049675

We present an efficient algorithm for the validated high-precision computation of real continued fractions, accurate to the last digit. The algorithm proceeds in two stages. In the first stage, computations are done in double precision. A forward...

A note on shifted Hessenberg systems and frequency response computation
Christopher Beattie, Zlatko Drmavč, Serkan Gugercin
Article No.: 12
DOI: 10.1145/2049673.2049676

In this article, we propose a numerical algorithm for efficient and robust solution of a sequence of shifted Hessenberg linear systems. In particular, we show how the frequency response &calG;(σ) = d-C(A...

Design, implementation, and analysis of maximum transversal algorithms
Iain S. Duff, Kamer Kaya, Bora Uçcar
Article No.: 13
DOI: 10.1145/2049673.2049677

We report on careful implementations of seven algorithms for solving the problem of finding a maximum transversal of a sparse matrix. We analyze the algorithms and discuss the design choices. To the best of our knowledge, this is the most...

Algorithms and data structures for massively parallel generic adaptive finite element codes
Wolfgang Bangerth, Carsten Burstedde, Timo Heister, Martin Kronbichler
Article No.: 14
DOI: 10.1145/2049673.2049678

Today's largest supercomputers have 100,000s of processor cores and offer the potential to solve partial differential equations discretized by billions of unknowns. However, the complexity of scaling to such large machines and problem sizes has so...

Algorithm 916: Computing the Faddeyeva and Voigt Functions
Mofreh R. Zaghloul, Ahmed N. Ali
Article No.: 15
DOI: 10.1145/2049673.2049679

We present a MATLAB function for the numerical evaluation of the Faddeyeva function w(z). The function is based on a newly developed accurate algorithm. In addition to its higher accuracy, the software provides a flexible accuracy vs...