Templates for Linear Algebra Problems

Abstract

The increasing availability of advanced-architecture computers is having a very signicant eect on all spheres of scientic 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 scientic computing. This chapter 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 advanced-architecture computers is motivated by the need to solve large problems on the fastest computers available. In this chapter, 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 chapter.