Practical extrapolation methods : theory and applications [E-Book] / Avram Sidi.
Sidi, Avram, (author)
Cambridge : Cambridge University Press, 2003
1 online resource (xxii, 519 pages)
englisch
9780511546815
9780521661591
Cambridge monographs on applied and computational mathematics ; 10
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 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.