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Cambridge Monographs on Applied and Computational Mathematic #10: Practical Extrapolation Methods: Theory and Applications

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Synopses & Reviews

Publisher Comments:

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 book is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. The methods it discusses are geared toward problems that commonly arise 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 the best numerical results. This state-of-the-art reference on the theory and practice of extrapolation methods will interest mathematicians interested in the theory of the relevant methods as well as giving applied scientists and engineers a practical guide to applying speed-up methods in the solution of difficult computational problems. Avram Sidi is Professor is Numerical Analysis in the Computer Science Department at the Technion-Israel Institute of Technology and holds the Technion Administration Chair in Computer Science. He has published extensively in various areas of numerical analysis and approximation theory and in journals such asMathematics of Computation, SIAM Review, SIAM Journal on Numerical Analysis, Journal of Approximation Theory, Journal of Computational and Applied Mathematics, Numerische Mathematik, and Journal of Scientific Computing. Professor Sidi's work has involved the development of novel me

Synopsis:

This book is concerned with the coherent treatment, including the derivation, analysis, and applications, of the most useful scalar extrapolation methods. Its importance is rooted in the fact that the methods it discusses are geared towards 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, and also shows how to apply these methods to obtain best results.

Synopsis:

This book is concerned with the coherent treatment, including the derivation, analysis, and applications, of the most useful scalar extrapolation methods. It differs from existing books by focusing 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. Finally, it shows how to apply these methods to obtain best results.

Synopsis:

Includes bibliographical references (p. 501-514) and index.

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 D2-process, and Lubkin W-transformation; 16. The Shanks transformation; 17. The Padétable; 18. Generalizations of Padéapproximants; 19. The Levin L- and S-transformations; 20. The Wynn r- and Brezinski q-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.

Product Details

ISBN:
9780521661591
Editor:
Ciarlet, P. G.
Editor:
Iserles, A.
Editor:
Ciarlet, P. G.
Editor:
Iserles, A.
Author:
Wright, M. H.
Author:
Iserles, A.
Author:
Kohn, R. V.
Author:
Sidi, Avram
Author:
Ciarlet, P. G.
Author:
Sidi, A.
Publisher:
Cambridge University Press
Location:
Cambridge
Subject:
General
Subject:
Mathematical Analysis
Subject:
Extrapolation.
Subject:
General Mathematics
Subject:
Mathematics-Analysis General
Edition Number:
1
Edition Description:
Hardback
Series:
Cambridge Monographs on Applied and Computational Mathematic
Series Volume:
5610
Publication Date:
20030631
Binding:
Hardcover
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Y
Pages:
519
Dimensions:
9.88x7.10x1.47 in. 2.67 lbs.

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Cambridge Monographs on Applied and Computational Mathematic #10: Practical Extrapolation Methods: Theory and Applications New Hardcover
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Product details 519 pages Cambridge University Press - English 9780521661591 Reviews:
"Synopsis" by , This book is concerned with the coherent treatment, including the derivation, analysis, and applications, of the most useful scalar extrapolation methods. Its importance is rooted in the fact that the methods it discusses are geared towards 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, and also shows how to apply these methods to obtain best results.
"Synopsis" by , This book is concerned with the coherent treatment, including the derivation, analysis, and applications, of the most useful scalar extrapolation methods. It differs from existing books by focusing 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. Finally, it shows how to apply these methods to obtain best results.
"Synopsis" by , Includes bibliographical references (p. 501-514) and index.
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