Templates for linear algebra problems

Abstract

The increasing availability of advanced-architecture computers is having a very significant effect on all spheres of scientific computation, including algorithm research and software development in numerical linear algebra. Linear algebra -in particular, the solution of linear systems of equations and eigenvalue problems — lies at the heart of most calculations in scientific computing. This paper discusses some of the recent developments in linear algebra designed to help the user on advanced-architecture computers.Much of the work in developing linear algebra software for advancedarchitecture computers is motivated by the need to solve large problems on the fastest computers available. In this paper, we focus on four basic issues: (1) the motivation for the work; (2) the development of standards for use in linear algebra and the building blocks for a library; (3) aspects of templates for the solution of large sparse systems of linear algorithm; and (4) templates for the solution of large sparse eigenvalue problems. This last project is under development and we will pay more attention to it in this paper.KeywordsEigenvalue ProblemLinear AlgebraSingular Value DecompositionMemory HierarchyMatrix PencilThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.