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Practical extrapolation methods : = theory and applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Practical extrapolation methods :/ Avram Sidi.
其他題名:	theory and applications /
作者:	Sidi, Avram,
面頁冊數:	1 online resource (xxii, 519 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Extrapolation. -
電子資源:	https://doi.org/10.1017/CBO9780511546815
ISBN:	9780511546815 (ebook)

Practical extrapolation methods : = theory and applications /
Sidi, Avram,

Practical extrapolation methods :theory and applications /Avram Sidi. - 1 online resource (xxii, 519 pages) :digital, PDF file(s). - Cambridge monographs on applied and computational mathematics ;10. - Cambridge monographs on applied and computational mathematics ;16..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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 ... -- 9. Analytic study of GREP(¹): Quickly varying ... -- 10. Efficient use of GREP(¹): Applications to the ... -- 11. Reduction of the D-transformation for oscillatory infinite-range integrals -- 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 -- II. Sequence transformations -- 15. The Euler transformation, Aitken [delta]²-process, and Lubkin W-transformation -- 16. The Shanks transformation -- 17. The Padé table -- 18. Generalizations of Padé approximants -- 19. The Levin L- and Sidi S-transformations -- 20. The Wynn and Brezinski algorithms -- 21. The G-transformation and its generalizations -- 22. The transformations of Overholt and Wimp -- 23. Confluent transformations -- 24. Formal theory of sequence transformations -- III. Further applications -- 25. Further applications of extrapolation methods and sequence transformations -- 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 and the generalized 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.

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.

ISBN: 9780511546815 (ebook)Subjects--Topical Terms:

591916
Extrapolation.

LC Class. No.: QA281 / .S555 2003

Dewey Class. No.: 511/.42

Practical extrapolation methods : = theory and applications /
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490 1 $a Cambridge monographs on applied and computational mathematics ; $v 10
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 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 ... -- 9. Analytic study of GREP(¹): Quickly varying ... -- 10. Efficient use of GREP(¹): Applications to the ... -- 11. Reduction of the D-transformation for oscillatory infinite-range integrals -- 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 -- II. Sequence transformations -- 15. The Euler transformation, Aitken [delta]²-process, and Lubkin W-transformation -- 16. The Shanks transformation -- 17. The Padé table -- 18. Generalizations of Padé approximants -- 19. The Levin L- and Sidi S-transformations -- 20. The Wynn and Brezinski algorithms -- 21. The G-transformation and its generalizations -- 22. The transformations of Overholt and Wimp -- 23. Confluent transformations -- 24. Formal theory of sequence transformations -- III. Further applications -- 25. Further applications of extrapolation methods and sequence transformations -- 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 and the generalized 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.
520 $a 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.
650 0 $a Extrapolation. $3 591916
776 0 8 $i Print version: $z 9780521661591
830 0 $a Cambridge monographs on applied and computational mathematics ; $v 16. $3 746415
856 4 0 $u https://doi.org/10.1017/CBO9780511546815