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.
