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ACM Transactions on Mathematical Software (TOMS), Volume 34 Issue 1, January 2008

Block variants of Hammarling's method for solving Lyapunov equations
Daniel Kressner
Article No.: 1
DOI: 10.1145/1322436.1322437

This article is concerned with the efficient numerical solution of the Lyapunov equation AT X + XA &equls; −C with a stable matrix A and a symmetric positive semidefinite matrix...

A grid-free abstraction of the Navier-Stokes equations in Fortran 95/2003
Damian W. I. Rouson, Robert Rosenberg, Xiaofeng Xu, Irene Moulitsas, Stavros C. Kassinos
Article No.: 2
DOI: 10.1145/1322436.1322438

Computational complexity theory inspires a grid-free abstraction of the Navier-Stokes equations in Fortran 95/2003. A novel complexity analysis estimates that structured programming time grows at least quadratically with the number of program...

Computing sparse Hessians with automatic differentiation
Andrea Walther
Article No.: 3
DOI: 10.1145/1322436.1322439

A new approach for computing a sparsity pattern for a Hessian is presented: nonlinearity information is propagated through the function evaluation yielding the nonzero structure. A complexity analysis of the proposed algorithm is given. Once the...

Algorithm 870: A static geometric Medial Axis domain decomposition in 2D Euclidean space
Leonidas Linardakis, Nikos Chrisochoides
Article No.: 4
DOI: 10.1145/1322436.1322440

We present a geometric domain decomposition method and its implementation, which produces good domain decompositions in terms of three basic criteria: (1) The boundary of the subdomains create good angles, that is, angles no smaller than a given...

Algorithm 871: A C/C++ precompiler for autogeneration of multiprecision programs
Walter Schreppers, Annie Cuyt
Article No.: 5
DOI: 10.1145/1322436.1322441

In the past decade a number of libraries for multiprecision floating-point arithmetic have been developed. We describe an easy to use, generic C/C++ transcription program or precompiler for the conversion of C or C++ source...

Algorithm 872: Parallel 2D constrained Delaunay mesh generation
Andrey N. Chernikov, Nikos P. Chrisochoides
Article No.: 6
DOI: 10.1145/1322436.1322442

Delaunay refinement is a widely used method for the construction of guaranteed quality triangular and tetrahedral meshes. We present an algorithm and a software for the parallel constrained Delaunay mesh generation in two dimensions. Our approach...