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ACM Transactions on Mathematical Software (TOMS), Volume 40 Issue 3, April 2014

Restructuring the Tridiagonal and Bidiagonal QR Algorithms for Performance
Field G. Van Zee, Robert A. van de Geijn, Gregorio Quintana-Ortí
Article No.: 18
DOI: 10.1145/2535371

We show how both the tridiagonal and bidiagonal QR algorithms can be restructured so that they become rich in operations that can achieve near-peak performance on a modern processor. The key is a novel, cache-friendly algorithm for applying...

A Pthreads Wrapper for Fortran 2003
Omar Awile, Ivo F. Sbalzarini
Article No.: 19
DOI: 10.1145/2558889

With the advent of multicore processors, numerical and mathematical software relies on parallelism in order to benefit from hardware performance increases. We present the design and use of a Fortran 2003 wrapper for POSIX threads, called...

Algorithm 939: Computation of the Marcum Q-Function
Amparo Gil, Javier Segura, Nico M. Temme
Article No.: 20
DOI: 10.1145/2591004

Methods and an algorithm for computing the generalized Marcum Q–function (Qμ(x,y)) and the complementary function (Pμ(x,y)) are described. These functions appear in...

Algorithm 940: Optimal Accumulator-Based Expression Evaluation through the Use of Expression Templates
Blake Nelson, Robert M. Kirby, Steven Parker
Article No.: 21
DOI: 10.1145/2591005

In this article we present a compile-time algorithm, implemented using C++ template metaprogramming techniques, that minimizes the use of temporary storage when evaluating expressions. We present the basic building blocks of our...

Algorithm 941: htucker---A Matlab Toolbox for Tensors in Hierarchical Tucker Format
Daniel Kressner, Christine Tobler
Article No.: 22
DOI: 10.1145/2538688

The hierarchical Tucker format is a storage-efficient scheme to approximate and represent tensors of possibly high order. This article presents a Matlab toolbox, along with the underlying methodology and algorithms, which provides a...

Algorithm 942: Semi-Stencil
Raúl de la Cruz, Mauricio Araya-Polo
Article No.: 23
DOI: 10.1145/2591006

Finite Difference (FD) is a widely used method to solve Partial Differential Equations (PDE). PDEs are the core of many simulations in different scientific fields, such as geophysics, astrophysics, etc. The typical FD solver performs stencil...