iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://doi.org/10.1007/BF02521609
A general extrapolation procedure revisited | Advances in Computational Mathematics Skip to main content
Log in

A general extrapolation procedure revisited

  • Published:
Advances in Computational Mathematics Aims and scope Submit manuscript

Abstract

TheE-algorithm is the most general extrapolation algorithm actually known. The aim of this paper is to provide a new approach to this algorithm. This approach gives a deeper insight into theE-algorithm, and allows one to obtain new properties and to relate it to other algorithms. Some extensions of the procedure are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. B. Beckermann, A connection between theE-algorithm and the epsilon-algorithm, in:Numerical and Applied Mathematics, ed. C. Brezinski (Baltzer, Basel, 1989) pp. 443–446.

    Google Scholar 

  2. C. Brezinski, A general extrapolation algorithm, Numer. Math. 35(1980)175–187.

    Article  MATH  MathSciNet  Google Scholar 

  3. C. Brezinski, The Mühlbach-Neville-Aitken algorithm and some extensions, BIT 20(1980) 444–451.

    Article  MATH  MathSciNet  Google Scholar 

  4. C. Brezinski, A survey of iterative extrapolation by theE-algorithm, Det Kong. Norske Vid. Selsk. skr. 2(1989)1–26.

    MATH  Google Scholar 

  5. C. Brezinski, Algebraic properties of theE-transformation, in:Numerical Analysis and Mathematical Modelling, Banach Center Publications, Vol. 24 (PWN, Warsaw, 1990) pp. 85–90.

    Google Scholar 

  6. C. Brezinski and A.C. Matos, A derivation of extrapolation algorithms based on error estimates, J. Comput. Appl. Math., to appear.

  7. C. Brezinski and M. Redivo-Zaglia,Extrapolation Methods. Theory and Practice (North-Holland, Amsterdam, 1991).

    MATH  Google Scholar 

  8. C. Brezinski and A. Salam, Matrix and vector sequence transformations revisited, submitted.

  9. C. Brezinski and G. Walz, Sequences of transformations and triangular recursion schemes with applications in numerical analysis, J. Comput. Appl. Math. 34(1991)361–383.

    Article  MATH  MathSciNet  Google Scholar 

  10. C. Carstensen, On a general epsilon algorithm, in:Numerical and Applied Mathematics, ed. C. Brezinski (Baltzer, Basel, 1989) pp. 437–441.

    Google Scholar 

  11. W.F. Ford and A. Sidi, An algorithm for a generalization of the Richardson extrapolation process, SIAM J. Numer. Anal. 24(1987)1212–1232.

    Article  MATH  MathSciNet  Google Scholar 

  12. T. Håvie, Generalized Neville type extrapolation schemes, BIT 19(1979)204–213.

    Article  MATH  MathSciNet  Google Scholar 

  13. A.C. Matos and M. Prévost, Acceleration property of theE-algorithm, Numer. Algor. 2(1992) 393–408.

    Article  MATH  Google Scholar 

  14. G. Meinardus and G.D. Taylor, Lower estimates for the error of best uniform approximation, J. Approx. Theory 16(1976)150–161.

    Article  MATH  MathSciNet  Google Scholar 

  15. G. Mühlbach, A recurrence formula for generalized divided differences and some applications, J. Approx. Theory 9(1973)165–172.

    Article  MATH  Google Scholar 

  16. G. Mühlbach, Newton- und Hermite-Interpolation mit Čebyšev-Systemen, Z. Angew. Math. Mech. 54(1974)541–550.

    MATH  MathSciNet  Google Scholar 

  17. G. Mühlbach, Neville-Aitken algorithms for interpolation by functions of Čebyšev-systems in the sense of Newton and in a generalized sense of Hermite, in:Theory of Approximation, with Applications, ed. A.G. Law and B.N. Sahney(Academic Press, New York, 1967) pp. 200–212.

    Google Scholar 

  18. G. Mühlbach, The general Neville-Aitken algorithm and some applications, Numer. Math. 31(1978)97–110.

    Article  MATH  MathSciNet  Google Scholar 

  19. G. Mühlbach, The general recurrence relation for divided differences and the general Newton-interpolation-algorithm with applications to trigonometric interpolation, Numer. Math. 32(1979) 393–408.

    Article  MATH  MathSciNet  Google Scholar 

  20. M. Prévost, Acceleration property for theE-algorithm and an application to the summation of series, Adv. Comput. Math. 2(1994)319–341.

    MATH  MathSciNet  Google Scholar 

  21. C. Schneider, Vereinfachte Rekursionen zur Richardson-Extrapolation in Spezialfällen, Numer. Math. 24(1975)177–184.

    Article  MATH  MathSciNet  Google Scholar 

  22. D. Shanks, Non linear transformations of divergent and slowly convergent sequences, J. Math. Phys. 34(1951)1–42.

    MathSciNet  Google Scholar 

  23. A. Sidi, An algorithm for a special case of a generalization of the Richardson extrapolation process, Numer. Math. 38(1982)299–307.

    Article  MATH  MathSciNet  Google Scholar 

  24. A. Sidi, On a generalization of the Richardson extrapolation process, Numer. Math. 57(1990) 365–377.

    Article  MATH  MathSciNet  Google Scholar 

  25. E.J. Weniger, Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series, Comput. Phys. Rep. 10(1989)189–371.

    Article  Google Scholar 

  26. P. Wynn, On a device for computing theS n) transformation, MTAC 10(1956)91–96.

    MATH  MathSciNet  Google Scholar 

  27. P. Wynn, Confluent forms of certain nonlinear algorithms. Arch. Math. 11(1960)223–234.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brezinski, C., Redivo-Zaglia, M. A general extrapolation procedure revisited. Adv Comput Math 2, 461–477 (1994). https://doi.org/10.1007/BF02521609

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02521609

Keywords

AMS(MOS) subject classification

Navigation