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ACM Transactions on Mathematical Software (TOMS), Volume 37 Issue 2, April 2010

EFCOSS: An interactive environment facilitating optimal experimental design
Arno Rasch, H. Martin Bücker
Article No.: 13
DOI: 10.1145/1731022.1731023

An interactive software environment is proposed that combines numerical simulation codes with optimization software packages in an automated and modular way. It simplifies the experimentation with varying objective functions for common...

Efficient controls for finitely convergent sequential algorithms
Wei Chen, Gabor T. Herman
Article No.: 14
DOI: 10.1145/1731022.1731024

Finding a feasible point that satisfies a set of constraints is a common task in scientific computing; examples are the linear feasibility problem and the convex feasibility problem. Finitely convergent sequential algorithms can be used for...

Stepsize selection for ordinary differential equations
Fred T. Krogh
Article No.: 15
DOI: 10.1145/1731022.1731025

This note offers a new approach based on a least squares fit to past data in order to select the stepsize when solving an ordinary differential equation. The approach used may have applicability to other situations where one wants to repeatedly...

Efficient and formally proven reduction of large integers by small moduli
Luc Rutten, Marko Van Eekelen
Article No.: 16
DOI: 10.1145/1731022.1731026

On w-bit processors which are much faster at multiplying two w-bit integers than at dividing 2w-bit integers by w-bit integers, reductions of large integers by moduli M smaller than 2w-1 are...

A fast and robust mixed-precision solver for the solution of sparse symmetric linear systems
J. D. Hogg, J. A. Scott
Article No.: 17
DOI: 10.1145/1731022.1731027

On many current and emerging computing architectures, single-precision calculations are at least twice as fast as double-precision calculations. In addition, the use of single precision may reduce pressure on memory bandwidth. The penalty for...

Rectangular full packed format for cholesky's algorithm: factorization, solution, and inversion
Fred G. Gustavson, Jerzy Waśniewski, Jack J. Dongarra, Julien Langou
Article No.: 18
DOI: 10.1145/1731022.1731028

We describe a new data format for storing triangular, symmetric, and Hermitian matrices called Rectangular Full Packed Format (RFPF). The standard two-dimensional arrays of Fortran and C (also known as full format) that are used to...

Scaling and pivoting in an out-of-core sparse direct solver
Jennifer A. Scott
Article No.: 19
DOI: 10.1145/1731022.1731029

Out-of-core sparse direct solvers reduce the amount of main memory needed to factorize and solve large sparse linear systems of equations by holding the matrix data, the computed factors, and some of the work arrays in files on disk. The...

DOLFIN: Automated finite element computing
Anders Logg, Garth N. Wells
Article No.: 20
DOI: 10.1145/1731022.1731030

We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with...

PRIMME: preconditioned iterative multimethod eigensolver—methods and software description
Andreas Stathopoulos, James R. McCombs
Article No.: 21
DOI: 10.1145/1731022.1731031

This article describes the PRIMME software package for solving large, sparse Hermitian standard eigenvalue problems. The difficulty and importance of these problems have increased over the years, necessitating the use of preconditioning and near...

Algorithm 902: GPOPS, A MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method
Anil V. Rao, David A. Benson, Christopher Darby, Michael A. Patterson, Camila Francolin, Ilyssa Sanders, Geoffrey T. Huntington
Article No.: 22
DOI: 10.1145/1731022.1731032

An algorithm is described to solve multiple-phase optimal control problems using a recently developed numerical method called the Gauss pseudospectral method. The algorithm is well suited for use in modern vectorized programming languages...

Algorithm 903: FRB--Fortran routines for the exact computation of free rigid body motions
Elena Celledoni, Antonella Zanna
Article No.: 23
DOI: 10.1145/1731022.1731033

We present two algorithms and their corresponding Fortran routines for the exact computation of free rigid body motions. The methods use the same description of the angular momentum part m by Jacobi elliptic functions, and suitably...