Cambridge Monographs on Applied and Computational Mathematics 10. Cambridge: Cambridge University Press (ISBN 0-521-66159-5/hbk). xxii, 519 p. £ 70.00; $ 95.00 (2003).
The book contains the following four parts:
I. The Richardson extrapolation method: the first generalization of the Richardson extrapolation process; the extrapolation method ; the D-transformation for infinite-range integrals; the d-transformation for infinite series and sequences; two recursive algorithms for : W-algorithm for and -algorithm for as well as an efficient algorithm, -algorithm, for a special case of an extension of ; the analytic study of ; acceleration of convergence of power series by d-transformation; acceleration of convergence of Fourier and generalized Fourier series by the d-transformation.
II. Sequence transformations: Euler transformation; Aitken process; Lubkin W-transformation; Shanks transformation; Padé table; Levin and Sidi transformations; Brezinsky -algorithm; the transformations of Overholt and Wimp; confluent forms of sequence transformations: confluent - algorithm, confluent - algorithm, confluent Overholt method, confluent - transformations.
III. Applications of the extrapolation methods and sequence transformations: multidimensional numerical quadrature, ordinary differential equations, the computation of the inverse Laplace transforms, convergence acceleration of infinite products, ill-posed problems.
IV. This part contains a review of several concepts and results required by the previous chapters and a Fortran 77 implementation for - transformation of real infinite series (via -algorithm) and this implementation can be adapted to complex series.
The book is an excellent support for the theoretical and practical studies of the speed-up methods based on extrapolation. It is an useful book for mathematicians interested in this field of research, but it can be used successfully by computer scientists and engineers.