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ACM Transactions on Mathematical Software (TOMS), Volume 33 Issue 3, August 2007

An accurate nonuniform fourier transform for SPRITE magnetic resonance imaging data
J. Rioux, M. Halse, E. Aubanel, B. J. Balcom, J. Kaffanke, S. Romanzetti, T. Dierkes, N. J. Shah
Article No.: 16
DOI: 10.1145/1268769.1268770

A new algorithm is proposed for computing the discrete Fourier Transform (DFT) of purely phase encoded data acquired during Magnetic Resonance Imaging (MRI) experiments. These experiments use the SPRITE (Single Point Ramped Imaging with...

Efficient compilation of a class of variational forms
Robert C. Kirby, Anders Logg
Article No.: 17
DOI: 10.1145/1268769.1268771

We investigate the compilation of general multilinear variational forms over affines simplices and prove a representation theorem for the representation of the element tensor (element stiffness matrix) as the contraction of a constant reference...

Experiences of sparse direct symmetric solvers
Jennifer A. Scott, Yifan Hu
Article No.: 18
DOI: 10.1145/1268769.1268772

We recently carried out an extensive comparison of the performance of state-of-the-art sparse direct solvers for the numerical solution of symmetric linear systems of equations. Some of these solvers were written primarily as research codes while...

Efficient Gauss-related quadrature for two classes of logarithmic weight functions
James S. Ball, Nelson H. F. Beebe
Article No.: 19
DOI: 10.1145/1268769.1268773

Integrals with logarithmic singularities are often difficult to evaluate by numerical methods. In this work, a quadrature method is developed that allows the exact evaluation (up to machine accuracy) of integrals of polynomials with two general...

Algorithm 867: QUADLOG—a package of routines for generating Gauss-related quadrature for two classes of logarithmic weight functions
Nelson H. F. Beebe, James S. Ball
Article No.: 20
DOI: 10.1145/1268769.1268774

A collection of subroutines and examples of their uses are described for the quadrature method developed in the companion article. These allow the exact evaluation (up to computer truncation and rounding errors) of integrals of polynomials with...

Algorithm 868: Globally doubly adaptive quadrature—reliable Matlab codes
Terje O. Espelid
Article No.: 21
DOI: 10.1145/1268769.1268775

We discuss how to modify a recently published Matlab code, coteglob, so that the excellent performance this code demonstrates for low and intermediate accuracy requests is retained while the performance is improved for high accuracy requests....