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Vector Extrapolation Methods with Applications

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by Avram Sidi


2017 / xiv + 433 pages / Softcover / ISBN 978-1-611974-95-9 / List Price $104.00 / SIAM Member Price $72.80 / Order Code: CS17

Keywords: convergence acceleration, vector extrapolation methods, Krylov subspace methods, large sparse linear and nonlinear systems, vector iterative processes

SIREV Book Review

"This is the first book fully dedicated to the comprehensive study of this intriguing topic, to which Sidi has made many significant contributions since the early 1980s. It reviews all the known vector extrapolation methods that have proved to be effective accelerators. It also unifies and broadens the theoretical as well as practical studies of vector extrapolation methods. Given its extensive scope, the book thus constitutes an up-to-date encyclopedic rendering of the area that is also self-contained. ... To conclude, overall, Sidi has given us an excellent state-of-the-art book on a fascinating area of computational science that is also of practical importance. This reviewer warmly recommends it to readers interested in advanced computational methods and non-standard numerical analysis." --David Levin,Tel Aviv University, Mathematics Today 54(3):117–118, 2018

An important problem that arises in different disciplines of science and engineering is that of computing limits of sequences of vectors of very large dimension. Such sequences arise, for example, in the numerical solution of systems of linear and nonlinear equations by fixed-point iterative methods, and their limits are simply the required solutions to these systems. The convergence of these sequences, which is very slow in many cases, can be accelerated successfully by using suitable vector extrapolation methods.

Vector Extrapolation Methods with Applications is the first book fully dedicated to the subject of vector extrapolation methods. It is a self-contained, up-to-date, and state-of-the-art reference on the theory and practice of the most useful methods. It covers all aspects of the subject, including development of the methods, their convergence study, numerically stable algorithms for their implementation, and their various applications. It also provides complete proofs in most places. As an interesting application, the author shows how these methods give rise to rational approximation procedures for vector-valued functions in the complex plane, a subject of importance in model reduction problems among others.

This book is intended for numerical analysts, applied mathematicians, and computational scientists and engineers in fields such as computational fluid dynamics, structures, and mechanical and electrical engineering, to name a few. Since it provides complete proofs in most places, it can also serve as a textbook in courses on acceleration of convergence of iterative vector processes, for example.

About the Author
Avram Sidi is Professor Emeritus of Numerical Analysis in the Computer Science Department at the Technion-Israel Institute of Technology and the former holder of the Technion Administration Chair in Computer Science. He has published extensively in various areas of numerical analysis and approximation theory, such as convergence acceleration, numerical integration, rational approximation, and asymptotic analysis, convergence acceleration being a major area. He is also the author of the book Practical Extrapolation Methods: Theory and Applications (Cambridge University Press, 2003), which deals exclusively with the acceleration of convergence of scalar sequences. His research has involved the development of novel numerical methods of high accuracy, their rigorous mathematical analysis, design of efficient algorithms for their implementation, and their application to difficult problems. His methods and algorithms are being used successfully in various scientific and engineering disciplines.


ISBN 9781611974959

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