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ACM Transactions on Mathematical Software (TOMS), Volume 43 Issue 1, August 2016

General Template Units for the Finite Volume Method in Box-Shaped Domains
Luis M. De La Cruz, Eduardo Ramos
Article No.: 1
DOI: 10.1145/2835175

In this work, we develop an extension of the Curiously Recurring Template Pattern (CRTP), which allows us to organize three related concepts in a class hierarchy. Generalizations, specializations and special procedures are the concepts that we use...

WorkStream -- A Design Pattern for Multicore-Enabled Finite Element Computations
Bruno Turcksin, Martin Kronbichler, Wolfgang Bangerth
Article No.: 2
DOI: 10.1145/2851488

Many operations that need to be performed in modern finite element codes can be described as an operation that needs to be done independently on every cell, followed by a reduction of these local results into a global data structure....

On BLAS Level-3 Implementations of Common Solvers for (Quasi-) Triangular Generalized Lyapunov Equations
Martin Köhler, Jens Saak
Article No.: 3
DOI: 10.1145/2850415

The solutions of Lyapunov and generalized Lyapunov equations are a key player in many applications in systems and control theory. Their stable numerical computation, when the full solution is sought, is considered solved since the seminal work of...

A Nonlinear QR Algorithm for Banded Nonlinear Eigenvalue Problems
C. Kristopher Garrett, Zhaojun Bai, Ren-Cang Li
Article No.: 4
DOI: 10.1145/2870628

A variation of Kublanovskaya's nonlinear QR method for solving banded nonlinear eigenvalue problems is presented in this article. The new method is iterative and specifically designed for problems too large to use dense linear algebra techniques....

Modular SIMD arithmetic in Mathemagix
Joris Van Der Hoeven, Grégoire Lecerf, Guillaume Quintin
Article No.: 5
DOI: 10.1145/2876503

Modular integer arithmetic occurs in many algorithms for computer algebra, cryptography, and error correcting codes. Although recent microprocessors typically offer a wide range of highly optimized arithmetic functions, modular integer operations...

A High Performance QDWH-SVD Solver Using Hardware Accelerators
Dalal Sukkari, Hatem Ltaief, David Keyes
Article No.: 6
DOI: 10.1145/2894747

This article describes a new high performance implementation of the QR-based Dynamically Weighted Halley Singular Value Decomposition (QDWH-SVD) solver on multicore architecture enhanced with multiple GPUs. The standard QDWH-SVD algorithm was...

A Robust and Scalable Implementation of the Parks-McClellan Algorithm for Designing FIR Filters
Silviu-Ioan Filip
Article No.: 7
DOI: 10.1145/2904902

With a long history dating back to the beginning of the 1970s, the Parks-McClellan algorithm is probably the most well known approach for designing finite impulse response filters. Despite being a standard routine in many signal processing...

Algorithm 965: RIDC Methods: A Family of Parallel Time Integrators
Benjamin W. Ong, Ronald D. Haynes, Kyle Ladd
Article No.: 8
DOI: 10.1145/2964377

Revisionist integral deferred correction methods are a family of parallel-in-time methods to solve systems of initial values problems. The approach is able to bootstrap lower-order time integrators to provide high-order approximations in...