Barrett R. et al. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods

R.Barrett, M.Berry, T.F.Chan, J.Demmel, J.Donato, J.Dongarra, V.Eijkhout, R.Pozo, C.Romine, H.van der Vorst. — Society for Industrial and Applied Mathematics, 1994. — 143 p.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 specific 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-like methods, and row-projection 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.