New book by Prof. Avram Sidi

Cambridge University Press just published a new book by Prof. Avram Sidi titled: Practical Extrapolation Methods: Theory and Applications. The book is No. 10 in Cambridge Monographs in Applied and Computational Mathematics, 2003.

An important problem that arises in many scientific and engineering applications is that of approximating limits of infinite sequences. In most cases, these sequences converge very slowly. Thus, to approximate their limits with reasonable accuracy, one needs to compute a large number of their 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 of the sequences in question.

This book is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. Its importance and relevance follow from the fact that the methods it discusses are geared toward problems that arise commonly 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 best numerical results.

This book is intended to serve as a state-of-the-art reference on the theory and practice of extrapolation methods. It should be of interest to mathematicians interested in the theory of the relevant methods and serve applied scientists and engineers as a practical guide for applying speed-up methods in the solution of difficult computational problems.