Practical Extrapolation Methods by Avram Sidi

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. 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. 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. 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. 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. The methods it discusses are geared toward problems that commonly arise in scientific and engineering disciplines. This book is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. These limits can be approximated economically and with high accuracy by applying suitable extrapolation (or convergence acceleration) methods to a small number of terms. Thus, to approximate limits with reasonable accuracy, it is necessary to compute a large number of terms, and this is in general costly. 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.

Practical Extrapolation Methods by Avram Sidi