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How to Use This Book

We have divided this book into five main chapters. Chapter gives the motivation for this book and the use of templates.

Chapter 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 focuses on preconditioners. Many iterative methods depend in part on preconditioners to improve performance and ensure fast convergence.

Chapter 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 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.

The field of iterative methods for solving systems of linear equations is in constant flux, with new methods and approaches continually being created, modified, tuned, and some eventually discarded. We expect the material in this book to undergo changes from time to time as some of these new approaches mature and become the state-of-the-art. Therefore, we plan to update the material included in this book periodically for future editions. We welcome your comments and criticisms of this work to help us in that updating process. Please send your comments and questions by email to