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We present a software toolbox for symmetric band reduction via orthogonal transformations, together with a testing and timing program. The toolbox contains drivers and computational routines for the reduction of full symmetric matrices to banded form and the reduction of banded matrices to...
In this paper we explain some of the changes that have been incorporated in the latest version of the LAPACK subroutine for reducing a symmetric banded matrix to tridiagonal form. These modifications improve the performance for larger-bandwidth problems and reduce the number of operations when...
In this article we present background, rationale, and a description of the Scalable Parallel Random Number Generators (SPRNG) library. We begin by presenting some methods for parallel pseudorandom number generation. We will focus on methods based on parameterization, meaning that we will not...
A recurring theme in mathematical software evaluation is the generalization of rankings of algorithms on test problems to build knowledge-based recommender systems for algorithm selection. A key issue is to profile algorithms in terms of the qualitative characteristics of benchmark problems. In...
We develop an algorithmic framework for reducing the bandwidth of symmetric matrices via orthogonal similarity transformations. This framework includes the reduction of full matrices to banded or tridiagonal form and the reduction of banded matrices to narrower banded or tridiagonal form,...
A software suite consisting of 17 MATLAB functions for solving differential equations by the spectral collocation (i.e., pseudospectral) method is presented. It includes functions for computing derivatives of arbitrary order corresponding to Chebyshev, Hermite, Laguerre, Fourier, and sinc...
In this article we discuss a small modification of the bisection routines in EISPACK and LAPACK for finding a few of the eigenvalues of a symmetric tridiagonal matrix A . When the principal minors of the matrix A yield good approximations to the desired eigenvalues, these modifications can yield...
Many computationally intensive problems in engineering and science give rise to the solution of large, sparse, linear systems of equations. Fast and efficient methods for their soltion are very important because these systems usually occur in the innermost loop of the computational scheme....
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