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Practical Extrapolation Methods

Practical Extrapolation Methods
Theory and Applications

£108.00

Part of Cambridge Monographs on Applied and Computational Mathematics

  • Author: Avram Sidi, Technion - Israel Institute of Technology, Haifa
  • Date Published: June 2003
  • availability: In stock
  • format: Hardback
  • isbn: 9780521661591

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  • An important problem that arises in many scientific and engineering applications is that of approximating limits of infinite sequences which in most instances converge very slowly. Thus, to approximate limits with reasonable accuracy, it is necessary to compute a large number of 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. This state-of-the art reference for mathematicians, scientists and engineers is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. The methods discussed are geared toward common problems in scientific and engineering disciplines. It differs from existing books by concentrateing on the most powerful nonlinear methods, presenting in-depth treatments of them, and showing which methods are most effective for different classes of practical nontrivial problems.

    • Concentrates on nontrivial problems
    • Shows that divergent processes can be treated on an equal footing with convergent ones
    • Gives the theory of the methods with complete proofs in most places
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    Reviews & endorsements

    'The book is an excellent support for the theoretical and practical studies of the speed-up methods based on extrapolation. It is a useful book for mathematicians interested in this field of research, but it can be used successfully by computer scientists and engineers.' Zentralblatt MATH

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    Product details

    • Date Published: June 2003
    • format: Hardback
    • isbn: 9780521661591
    • length: 542 pages
    • dimensions: 255 x 179 x 38 mm
    • weight: 1.22kg
    • availability: In stock
  • Table of Contents

    Preface
    Introduction
    Part I. The Richardson Extrapolation Process and Its Generalizations:
    1. The richardson extrapolation process
    2. Additional topics in Richardson extrapolation
    3. First generalization of the Richardson extrapolation process
    4. GREP: further generalization of the Richardson extrapolation process
    5. The d-transformation: a GREP for infinite-range integrals
    6. The d-transformation: a GREP for infinite series and sequences
    7. Recursive algorithms for GREP
    8. Analytic study of GREP (1): slowly varying A(y) ∈ F(1)
    9. Analytic study of GREP(1): quickly varying A(y) ∈ F(1)
    10: Efficient use of GREP(1): applications to the D(1)-, d(1)- and d(m)-transformations
    11. Reduction of the d-transformation for oscillatory infinite-range integrals: the D-, D-, W-, and mW-transformations
    12. Acceleration of convergence of power series by the d-transformation: rational d-approximants
    13. Acceleration of convergence of Fourier and generalized Fourier series by the d-transformation: the complex series approach with APS
    14. Special topics in Richardson extrapolation
    Part II. Sequence Transformations:
    15. The Euler transformation, Aitken Δ2-process, and Lubkin W-transformation
    16. The Shanks transformation
    17. The Padé table
    18. Generalizations of Padé approximants
    19. The Levin L- and S-transformations
    20. The Wynn ρ- and Brezinski θ-algorithms
    21. The g-transformation and its generalizations
    22. The transformations of Overholt and Wimp
    23. Confluent transformations
    24. Formal theory of sequence transformations
    Part III. Further Applications:
    25. Further applications of extrapolation methods and sequence transformations
    Part IV. Appendices: A. review of basic asymptotics
    B. The Laplace transform and Watson's lemma
    C. The gamma function
    D. Bernoulli numbers and polynomials and the Euler-Maclaurin formula
    E. The Riemann zeta function
    F. Some highlights of polynomial approximation theory
    G. A compendium of sequence transformations
    H. Efficient application of sequence transformations: Summary
    I. FORTRAN 77 program for the d(m)-transformation.

  • Author

    Avram Sidi, Technion - Israel Institute of Technology, Haifa

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