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ACM Transactions on Mathematical Software (TOMS), Volume 39 Issue 3, April 2013

High-performance bidiagonal reduction using tile algorithms on homogeneous multicore architectures
Hatem Ltaief, Piotr Luszczek, Jack Dongarra
Article No.: 16
DOI: 10.1145/2450153.2450154

This article presents a new high-performance bidiagonal reduction (BRD) for homogeneous multicore architectures. This article is an extension of the high-performance tridiagonal reduction implemented by the same authors [Luszczek et al., IPDPS...

An efficient overloaded method for computing derivatives of mathematical functions in MATLAB
Michael A. Patterson, Matthew Weinstein, Anil V. Rao
Article No.: 17
DOI: 10.1145/2450153.2450155

An object-oriented method is presented that computes without truncation the error derivatives of functions defined by MATLAB computer codes. The method implements forward-mode automatic differentiation via operator overloading in a manner that...

An algorithm for the complete solution of quadratic eigenvalue problems
Sven Hammarling, Christopher J. Munro, Françoise Tisseur
Article No.: 18
DOI: 10.1145/2450153.2450156

We develop a new algorithm for the computation of all the eigenvalues and optionally the right and left eigenvectors of dense quadratic matrix polynomials. It incorporates scaling of the problem parameters prior to the computation of eigenvalues,...

Efficient generalized Hessenberg form and applications
Nela Bosner, Zvonimir Bujanović, Zlatko Drmač
Article No.: 19
DOI: 10.1145/2450153.2450157

This article proposes an efficient algorithm for reducing matrices to generalized Hessenberg form by unitary similarity, and recommends using it as a preprocessor in a variety of applications. To illustrate its usefulness, two cases from control...

The Tapenade automatic differentiation tool: Principles, model, and specification
Laurent Hascoet, Valérie Pascual
Article No.: 20
DOI: 10.1145/2450153.2450158

Tapenade is an Automatic Differentiation (AD) tool which, given a Fortran or C code that computes a function, creates a new code that computes its tangent or adjoint derivatives. Tapenade puts particular emphasis on adjoint differentiation, which...

Algorithm 928: A general, parallel implementation of Dantzig--Wolfe decomposition
Joseph Rios
Article No.: 21
DOI: 10.1145/2450153.2450159

Dantzig--Wolfe Decomposition is recognized as a powerful, algorithmic tool for solving linear programs of block-angular form. While use of the approach has been reported in a wide variety of domains, there has not been a general implementation of...