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ACM Transactions on Mathematical Software (TOMS), Volume 35 Issue 2, July 2008

SNOBFIT -- Stable Noisy Optimization by Branch and Fit
Waltraud Huyer, Arnold Neumaier
Article No.: 9
DOI: 10.1145/1377612.1377613

The software package SNOBFIT for bound-constrained (and soft-constrained) noisy optimization of an expensive objective function is described. It combines global and local search by branching and local fits. The program is made robust and flexible...

Benchmarking Domain-Specific Compiler Optimizations for Variational Forms
Robert C. Kirby, Anders Logg
Article No.: 10
DOI: 10.1145/1377612.1377614

We examine the effect of using complexity-reducing relations [Kirby et al. 2006] to generate optimized code for the evaluation of finite-element variational forms. The optimizations are implemented in a prototype code named FErari, which has been...

Updating an LU Factorization with Pivoting
Enrique S. Quintana-Ortí, Robert A. Van De Geijn
Article No.: 11
DOI: 10.1145/1377612.1377615

We show how to compute an LU factorization of a matrix when the factors of a leading principle submatrix are already known. The approach incorporates pivoting akin to partial pivoting, a strategy we call incremental pivoting. An...

On the Failure of Rank-Revealing QR Factorization Software -- A Case Study
Zlatko Drmač, Zvonimir Bujanović
Article No.: 12
DOI: 10.1145/1377612.1377616

This article reports an unexpected and rather erratic behavior of the LAPACK software implementation of the QR factorization with Businger-Golub column pivoting. It is shown that, due to finite precision arithmetic, the software implementation of...

Algorithm 881: A Set of Flexible GMRES Routines for Real and Complex Arithmetics on High-Performance Computers
Valérie Frayssé, Luc Giraud, Serge Gratton
Article No.: 13
DOI: 10.1145/1377612.1377617

In this article we describe our implementations of the FGMRES algorithm for both real and complex, single and double precision arithmetics suitable for serial, shared-memory, and distributed-memory computers. For the sake of portability,...

Algorithm 882: Near-Best Fixed Pole Rational Interpolation with Applications in Spectral Methods
Joris van Deun, Karl Deckers, Adhemar Bultheel, J. A. C. Weideman
Article No.: 14
DOI: 10.1145/1377612.1377618

We present a numerical procedure to compute the nodes and weights in rational Gauss-Chebyshev quadrature formulas. Under certain conditions on the poles, these nodes are near best for rational interpolation with prescribed poles (in the same sense...

Algorithm 883: SparsePOP---A Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems
Hayato Waki, Sunyoung Kim, Masakazu Kojima, Masakazu Muramatsu, Hiroshi Sugimoto
Article No.: 15
DOI: 10.1145/1377612.1377619

SparsePOP is a Matlab implementation of the sparse semidefinite programming (SDP) relaxation method for approximating a global optimal solution of a polynomial optimization problem (POP) proposed by Waki et al. [2006]. The sparse SDP relaxation...

Algorithm 884: A Simple Matlab Implementation of the Argyris Element
Víctor Domínguez, Francisco-Javier Sayas
Article No.: 16
DOI: 10.1145/1377612.1377620

In this work we propose a new algorithm to evaluate the basis functions of the Argyris finite element and their derivatives. The main novelty here is an efficient way to calculate the matrix which gives the change of coordinates between the bases...