Skip to main content
Log in

Convergence and acceleration properties for the vector ε-algorithm

  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

In this paper we will give some acceleration properties for the vector ε-algorithm. We begin by recalling the rules and the fundamental result of exactness and by giving a complete description of the kernel of the algorithm. Based on these results we will obtain the speed of convergence of the algorithm for some classes of vector sequences.

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

Access this article

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. C. Brezinski, Généralisations de la transformation de Shanks, de la table de Padé et de l' ε-algorithm, Calcolo 12 (1975) 317–360.

    Google Scholar 

  2. F. Cordellier, Particular rules for the vector ε-algorithm, Numer. Math. 27 (197779 203–207.

  3. P. Graves-Morris, Vector valued rational interpolants I, Numer. Math. 42 (1983) 331–348.

    Article  Google Scholar 

  4. A.O. Guelfond,Calcul des Différences Finies (Dunod, Paris, 1963).

    Google Scholar 

  5. A.C. Matos, Construction de méthodes d'extrapolation à partir de développments asymptotiques, Thèse, Université des Sciences et Techniques de Lille (1989).

  6. H. Sadok, Accélération de la convergence de suites vectorielles et méthodes de point fixe, Thèse, Université des Sciences et Techniques de Lille (1988).

  7. A. Sidi, Convergence and stability analysis for some vector extrapolation in the presence of defective matrices, J. Comp. Appl. Math. 22 (1988) 35–61.

    Article  Google Scholar 

  8. A. Sidi, W. Ford and J. Smith, Acceleration of convergence of vector sequences, SIAM J. Numer. Anal. 23 (1986) 178–196.

    Article  Google Scholar 

  9. R. Tan, Computing derivatives of eigensystems by the vector ε-algorithm, IMA J. Numer. Anal. 7 (1987) 485–494.

    Google Scholar 

  10. P. Wynn, Acceleration techniques for iterated vector and matrix problems, Math. Comp. 16 (1962) 301–322.

    Google Scholar 

  11. P. Wynn, Upon a conjecture concerning a method for solving linear equations and certain other matters, MRC Technical Summary Report 626, University of Wisconsin (1966).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Matos, A.C. Convergence and acceleration properties for the vector ε-algorithm. Numer Algor 3, 313–319 (1992). https://doi.org/10.1007/BF02141939

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02141939

Keywords

Navigation