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ACM Transactions on Mathematical Software (TOMS), Volume 30 Issue 3, September 2004

ProtoMol, an object-oriented framework for prototyping novel algorithms for molecular dynamics
Thierry Matthey, Trevor Cickovski, Scott Hampton, Alice Ko, Qun Ma, Matthew Nyerges, Troy Raeder, Thomas Slabach, Jesús A. Izaguirre
Pages: 237-265
DOI: 10.1145/1024074.1024075
ProtoMol is a high-performance framework in C++ for rapid prototyping of novel algorithms for molecular dynamics and related applications. Its flexibility is achieved primarily through the use of inheritance and design patterns (object-oriented...

Jacobian code generated by source transformation and vertex elimination can be as efficient as hand-coding
Shaun A. Forth, Mohamed Tadjouddine, John D. Pryce, John K. Reid
Pages: 266-299
DOI: 10.1145/1024074.1024076
This article presents the first extended set of results from EliAD, a source-transformation implementation of the vertex-elimination Automatic Differentiation approach to calculating the Jacobians of functions defined by Fortran code (Griewank and...

A numerical evaluation of HSL packages for the direct solution of large sparse, symmetric linear systems of equations
Nicholas I. M. Gould, Jennifer A. Scott
Pages: 300-325
DOI: 10.1145/1024074.1024077
In recent years, a number of new direct solvers for the solution of large sparse, symmetric linear systems of equations have been added to the mathematical software library HSL. These include solvers that are designed for the solution of...

Block tridiagonalization of "effectively" sparse symmetric matrices
Yihua Bai, Wilfried N. Gansterer, Robert C. Ward
Pages: 326-352
DOI: 10.1145/1024074.1024078
A block tridiagonalization algorithm is proposed for transforming a sparse (or "effectively" sparse) symmetric matrix into a related block tridiagonal matrix, such that the eigenvalue error remains bounded by some prescribed accuracy tolerance. It is...

A column approximate minimum degree ordering algorithm
Timothy A. Davis, John R. Gilbert, Stefan I. Larimore, Esmond G. Ng
Pages: 353-376
DOI: 10.1145/1024074.1024079
Sparse Gaussian elimination with partial pivoting computes the factorization PAQ = LU of a sparse matrix A, where the row ordering P is selected during factorization using standard partial pivoting with row interchanges....

Algorithm 836: COLAMD, a column approximate minimum degree ordering algorithm
Timothy A. Davis, John R. Gilbert, Stefan I. Larimore, Esmond G. Ng
Pages: 377-380
DOI: 10.1145/1024074.1024080
Two codes are discussed, COLAMD and SYMAMD, that compute approximate minimum degree orderings for sparse matrices in two contexts: (1) sparse partial pivoting, which requires a sparsity preserving column pre-ordering prior to numerical factorization,...

Algorithm 837: AMD, an approximate minimum degree ordering algorithm
Patrick R. Amestoy, Timothy A. Davis, Iain S. Duff
Pages: 381-388
DOI: 10.1145/1024074.1024081
AMD is a set of routines that implements the approximate minimum degree ordering algorithm to permute sparse matrices prior to numerical factorization. There are versions written in both C and Fortran 77. A MATLAB interface is included....