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**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.