Practical Extrapolation Methods: Theory and Applications(10 Cambridge Monographs on Applied and Computational Mathematics)

An important problem that arises in many scientific and engineering applications is that of approximating limits of infinite sequences which in most instances converge very slowly. Thus, to approximate limits with reasonable accuracy, it is necessary to compute a large number of terms, and this is in general costly. These limits can be approximated economically and with high accuracy by applying suitable extrapolation (or convergence acceleration) methods to a small number of terms. This book is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. The methods it discusses are geared toward problems that commonly arise in scientific and engineering disciplines. It differs from existing books on the subject in that it concentrates on the most powerful nonlinear methods, presents in-depth treatments of them, and shows which methods are most effective for different classes of practical nontrivial problems; it also shows how to fine-tune these methods to obtain the best numerical results. This state-of-the-art reference on the theory and practice of extrapolation methods will interest mathematicians interested in the theory of the relevant methods as well as giving applied scientists and engineers a practical guide to applying speed-up methods in the solution of difficult computational problems. Avram Sidi is Professor is Numerical Analysis in the Computer Science Department at the Technion-Israel Institute of Technology and holds the Technion Administration Chair in Computer Science. He has published extensively in various areas of numerical analysis and approximation theory and in journals such as Mathematics of Computation, SIAM Review, SIAM Journal on Numerical Analysis, Journal of Approximation Theory, Journal of Computational and Applied Mathematics, Numerische Mathematik, and Journal of Scientific Computing. Professor Sidi's work has involved the development of novel methods, their detailed mathematical analysis, design of efficient algorithms for their implementation, and their application to difficult practical problems. His methods and algorithms are successfully used in various scientific and engineering disciplines.

Review :
"This book should be an excellent reference for practicing scientists and engineers who need in depth information about extrapolation methods and their applications." Mathematical Reviews 'The book is an excellent support for the theoretical and practical studies of the speed-up methods based on extrapolation. It is a useful book for mathematicians interested in this field of research, but it can be used successfully by computer scientists and engineers.' Zentralblatt MATH "This book, written by a leading expert in the field, is an excellent up-to-date account of the most useful extrapolation methods for sequences of scalars. The author has produced a book that is in complete agreement with its title: the methods it deals with are practical, and so are the problems they are applied to. Everything taken into account, this book will benefit both the theoretician and the practitioner. This book is quite pleasant to read. ...an excellent research monograph... The reviewer recommends Practical Extrapolation Methods very highly to all those interested in applying and/or learning the subject. He believes that it will remain that state-of-the-art reference in extrapolation methods and their applications for many years to come." David Levin, Tel Aviv University, Mathematics of Computation