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Implementation of hierarchical bases in FEMLAB for simplicial elements
Jianguo Xin, Katia Pinchedez, Joseph E. Flaherty
We present the implementation of well-conditioned hierarchical bases for one-dimensional, triangular and tetrahedral elements in finite element FEMLAB software. Using the domain mesh information provided by FEMLAB, we found an easy way to maintain...
A fully portable high performance minimal storage hybrid format Cholesky algorithm
Bjarne S. Andersen, John A. Gunnels, Fred G. Gustavson, John K. Reid, Jerzy Waśniewski
We consider the efficient implementation of the Cholesky solution of symmetric positive-definite dense linear systems of equations using packed storage. We take the same starting point as that of LINPACK and LAPACK, with the upper (or lower)...
Algorithm 842: A set of GMRES routines for real and complex arithmetics on high performance computers
Valérie Frayssé, Luc Giraud, Serge Gratton, Julien Langou
In this article we describe our implementations of the GMRES algorithm for both real and complex, single and double precision arithmetics suitable for serial, shared memory and distributed memory computers. For the sake of portability, simplicity,...
Algorithm 843: Improvements to the Schwarz-Christoffel toolbox for MATLAB
Tobin A. Driscoll
The Schwarz--Christoffel Toolbox (SC Toolbox) for MATLAB, first released in 1994, made possible the interactive creation and visualization of conformal maps to regions bounded by polygons. The most recent release supports new features, including an...
Algorithm 844: Computing sparse reduced-rank approximations to sparse matrices
Michael W. Berry, Shakhina A. Pulatova, G. W. Stewart
In many applications---latent semantic indexing, for example---it is required to obtain a reduced rank approximation to a sparse matrix A. Unfortunately, the approximations based on traditional decompositions, like the singular value and QR...
Algorithm 845: EIGIFP: a MATLAB program for solving large symmetric generalized eigenvalue problems
James H. Money, Qiang Ye
eigifp is a MATLAB program for computing a few extreme eigenvalues and eigenvectors of the large symmetric generalized eigenvalue problem Ax = λ Bx. It is a black-box implementation of an inverse free preconditioned Krylov...