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Zbl 1041.65001
Sidi, Avram
Practical extrapolation methods. Theory and applications. (English)
[B] Cambridge Monographs on Applied and Computational Mathematics 10. Cambridge: Cambridge University Press. xxii, 519~p. \sterling~70.00; \$~95.00 (2003). ISBN 0-521-66159-5/hbk

The book contains the following four parts:\par I. The Richardson extrapolation method: the first generalization of the Richardson extrapolation process; the extrapolation method $GREP$; the D-transformation for infinite-range integrals; the d-transformation for infinite series and sequences; two recursive algorithms for $GREP$: W-algorithm for $GREP^{(1)}$ and $W^{(m)}$-algorithm for $GREP^{(m)}$ as well as an efficient algorithm, $EW$-algorithm, for a special case of an extension of $GREP$; the analytic study of $GREP^{(1)}$; acceleration of convergence of power series by d-transformation; acceleration of convergence of Fourier and generalized Fourier series by the d-transformation.\par II. Sequence transformations: Euler transformation; Aitken process; Lubkin W-transformation; Shanks transformation; Padé table; Levin and Sidi transformations; Brezinsky $\theta$-algorithm; the transformations of Overholt and Wimp; confluent forms of sequence transformations: confluent $\varepsilon$- algorithm, confluent $\rho$- algorithm, confluent Overholt method, confluent $D^{(m)}$- transformations.\par 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.\par IV. This part contains a review of several concepts and results required by the previous chapters and a Fortran 77 implementation for $d^{(m)}$- transformation of real infinite series (via $W^{(m)}$-algorithm) and this implementation can be adapted to complex series.\par 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.
[N. Ţăndăreanu (Craiova)]

MSC 2000:: *65B05 Extrapolation to the limit
65-02 Research monographs (numerical analysis)
65B10 Summation of series
65D25 Numerical differentiation
65D32 Quadrature formulas (numerical methods)
65R10 Integral transforms (numerical methods)
44A10 Laplace transform
42A20 Convergence trigonometric series
65T40 Trigonometric approximation and interpolation

Keywords: extrapolation; convergence acceleration; sequence transformation; textbook; Richardson extrapolation; GREP; $W$-algorithm; Fourier series; Euler transformation; Aitken process; $W$-transformation; Padé table; $\theta$-algorithm; cubature; inverse Laplace transform; ill-posed problems

Cited in: Zbl 1108.65044

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