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ACM Transactions on Mathematical Software (TOMS), Volume 31 Issue 4, December 2005

FEMSTER: An object-oriented class library of high-order discrete differential forms
Paul Castillo, Robert Rieben, Daniel White
Pages: 425-457
DOI: 10.1145/1114268.1114269
FEMSTER is a modular finite element class library for solving three-dimensional problems arising in electromagnetism. The library was designed using a modern geometrical approach based on differential forms (or p-forms) and can be used for...

A differentiation-enabled Fortran 95 compiler
Uwe Naumann, Jan Riehme
Pages: 458-474
DOI: 10.1145/1114268.1114270
The availability of first derivatives of vector functions is crucial for the robustness and efficiency of a large number of numerical algorithms. An upcoming new version of the differentiation-enabled NAGWare Fortran 95 compiler is described that...

DFTI---a new interface for Fast Fourier Transform libraries
Ping Tak Peter Tang
Pages: 475-507
DOI: 10.1145/1114268.1114271
The Fast Fourier Transform (FFT) algorithm that calculates the Discrete Fourier Transform (DFT) is one of the major breakthroughs in scientific computing and is now an indispensable tool in a vast number of fields. Unfortunately, software...

PDE.Mart: A network-based problem-solving environment for PDEs
Mo Mu
Pages: 508-531
DOI: 10.1145/1114268.1114272
PDE.Mart is a network-based problem-solving environment (PSE) for solving partial differential equations (PDEs) in numerical simulations and academic research, as well as in educational settings. The client-server protocol consists of a...

MATSLISE: A MATLAB package for the numerical solution of Sturm-Liouville and Schrödinger equations
V. Ledoux, M. Van Daele, G. Vanden Berghe
Pages: 532-554
DOI: 10.1145/1114268.1114273
MATSLISE is a graphical MATLAB software package for the interactive numerical study of regular Sturm-Liouville problems, one-dimensional Schrödinger equations, and radial Schrödinger equations with a distorted Coulomb potential. It allows...

Algorithm 846: MixedVol: a software package for mixed-volume computation
Tangan Gao, T. Y. Li, Mengnien Wu
Pages: 555-560
DOI: 10.1145/1114268.1114274
MixedVol is a C++ software package that computes the mixed volume of n finite subsets of ℤn or the support of a system of n polynomials in n variables. The software produces the mixed volume as...

Algorithm 847: Spinterp: piecewise multilinear hierarchical sparse grid interpolation in MATLAB
Andreas Klimke, Barbara Wohlmuth
Pages: 561-579
DOI: 10.1145/1114268.1114275
To recover or approximate smooth multivariate functions, sparse grids are superior to full grids due to a significant reduction of the required support nodes. The order of the convergence rate in the maximum norm is preserved up to a logarithmic...

Algorithm 848: A recursive fixed-point algorithm for the infinity-norm case
Spencer Shellman, K. Sikorski
Pages: 580-586
DOI: 10.1145/1114268.1114276
We present the PFix algorithm for approximating a fixed point of a function f that has arbitrary dimensionality, is defined on a rectangular domain, and is Lipschitz continuous with respect to the infinity norm with constant 1. PFix has applications...

Algorithm 849: A concise sparse Cholesky factorization package
Timothy A. Davis
Pages: 587-591
DOI: 10.1145/1114268.1114277
The LDL software package is a set of short, concise routines for factorizing symmetric positive-definite sparse matrices, with some applicability to symmetric indefinite matrices. Its primary purpose is to illustrate much of the basic theory of...