Author:Richard Barrett, Michael Berry, Tony Chan, James Demmel, June Donato, Jack Dongarra, Victor Eijkhout, Roldan Pozo, Charles Romine, and Henk van der Vorst
Pages:125
Summary:This book provides a comprehensive guide to iterative methods for solving large sparse systems of linear equations. It is divided into five main chapters, each focusing on different aspects of iterative methods and their applications. Chapter 1 introduces the motivation for using templates and the structure of the book. Chapter 2 covers stationary and nonstationary iterative methods, including historical development and state-of-the-art techniques. Chapter 3 focuses on preconditioners, which are crucial for improving the performance and convergence of iterative methods. Chapter 4 addresses related issues such as complex systems, stopping criteria, data storage formats, and parallelism. Chapter 5 provides overviews of related topics like Lanczos and Conjugate Gradient algorithms, block iterative methods, domain decomposition methods, multigrid methods, and row-projection schemes. The appendices include information on obtaining the templates and BLAS software, as well as a glossary of important terms. The book aims to provide users with the tools and knowledge to choose, implement, and tailor iterative methods to specific problems, while also offering insights into the algorithms and numerical techniques involved.