Templates for the solution of linear systems: building blocks for iterative methods

Abstract

We have divided this book into five main chapters. Chapter 1 gives the motivation for this book and the use of templates. Chapter 2 describes stationary and nonstationary iterative methods. In this chapter we present both historical development and state-of-the-art methods for solving some of the most challenging computational problems facing researchers. Chapter 3 focuses on preconditioners. Many iterative methods depend in part on preconditioners to improve performance and ensure fast convergence. Chapter 4 provides a glimpse of issues related to the use of iterative methods. This chapter, like the preceding, is especially recommended for the experienced user who wishes to have further guidelines for tailoring a specic code to a particular machine. It includes information on complex systems, stopping criteria, data storage formats, and parallelism. Chapter 5 includes overviews of related topics such as the close connection between the Lanczos algorithm and the Conjugate Gradient algorithm, block iterative methods, red/black orderings, domain decomposition methods, multigrid-likemethods, and rowprojection schemes. The Appendices contain information on how the templates and BLAS software can be obtained. A glossary of important terms used in the book is also provided.