zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Practical extrapolation methods. Theory and applications. (English) Zbl 1041.65001
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 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.

II. Sequence transformations: Euler transformation; Aitken process; Lubkin W-transformation; Shanks transformation; Padé table; Levin and Sidi transformations; Brezinsky θ-algorithm; the transformations of Overholt and Wimp; confluent forms of sequence transformations: confluent ε- algorithm, confluent ρ- algorithm, confluent Overholt method, confluent D (m) - 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 d (m) - transformation of real infinite series (via W (m) -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.


MSC:
65B05Extrapolation to the limit, deferred corrections
65-02Research monographs (numerical analysis)
65B10Summation of series (numerical analysis)
65D25Numerical differentiation
65D32Quadrature and cubature formulas (numerical methods)
65R10Integral transforms (numerical methods)
44A10Laplace transform
42A20Convergence and absolute convergence of Fourier and trigonometric series
65T40Trigonometric approximation and interpolation (numerical methods)