Practical extrapolation methods : theory and applications [EBook] / Avram Sidi.
Practical extrapolation methods : theory and applications [EBook] / Avram Sidi.
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...
Personal Name(s):  Sidi, Avram, (author) 

Imprint: 
Cambridge :
Cambridge University Press,
2003

Physical Description: 
1 online resource (xxii, 519 pages) 
Note: 
englisch 
ISBN: 
9780511546815 9780521661591 
Series Title: 
Cambridge monographs on applied and computational mathematics ;
10 
Subject (LOC):  
Full Text 
Table of Contents:
 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 Dtransformation: A GREP for infiniterange integrals
 6. The dtransformation: 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 Dtransformation for oscillatory infiniterange integrals
 12. Acceleration of convergence of power series by the dtransformation: Rational dapproximants
 13. Acceleration of convergence of Fourier and generalized Fourier series by the dtransformation: The complex series approach with APS
 14. Special topics in Richardson extrapolation
 II. Sequence transformations
 15. The Euler transformation, Aitken [delta]²process, and Lubkin Wtransformation
 16. The Shanks transformation
 17. The Padé table
 18. Generalizations of Padé approximants
 19. The Levin L and Sidi Stransformations
 20. The Wynn and Brezinski algorithms
 21. The Gtransformation 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 EulerMaclaurin 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.