Skip to main content
SpringerLink
Log in

The mühlbach-neville-aitken algorithm and some extensions

  • Part II Numerical Mathematics
  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

A new proof of the Mühlbach-Neville-Aitken algorithm for interpolation by a linear family of functions forming a Chebyshev system is given. This proof is based on Sylvester's identity for determinants. The algorithm is then applied to the general interpolation problem, and applications to orthogonal polynomials and Padé-type approximants are treated. Finally the extension to rational interpolation is also studied.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. Brezinski:Rational approximation to formal power series, J. Approx. Theory 25 (1979), 295–317.

    Google Scholar 

  2. id. : Padé-type approximation and general orthogonal polynomials, ISNM vol. 50, Birkhäuser-Verlag, Basel, 1980.

    Google Scholar 

  3. id.: A general extrapolation algorithm, Numer. Math. to appear.

  4. id.: Subroutines for the general interpolation and extrapolation problems, ACM Trans. Math. Soft. to appear.

  5. F. Cordellier:Démonstration algébrique de l'extension de l'identité de Wynn aux tables de Padé non normales in Padé Approximation and its Applications, L. Wuytack ed., Lecture Notes in Mathematics 765, Springer-Verlag, Heidelberg, 1979.

    Google Scholar 

  6. P. J. Davis:Interpolation and Approximation, Blaisdell Publ. Co., New York, 1961.

    Google Scholar 

  7. A. Draux: To appear.

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

    Google Scholar 

  9. S. J. Karlin and W. J. Studden:Tchebycheff Systems: With Applications in Analysis and Statistics, Interscience Publ., New York, 1966.

    Google Scholar 

  10. F. M. Larkin:Some techniques for rational interpolation, Computer J. 10 (1967), 178–187.

    Google Scholar 

  11. id.: A class of methods for tabular interpolation, Proc. Camb. Phil. Soc. 63 (1967), 1101–1114.

    Google Scholar 

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

    Google Scholar 

  13. id.: 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, A. G. Law and B. N. Sahney eds., Academic Press, New York, 1976.

    Google Scholar 

  14. id.: The general Neville-Aitken algorithm and some applications, Nümer. Math. 31 (1978), 97–110.

    Google Scholar 

  15. P. Wynn:Singular rules for certain nonlinear algorithms, BIT 3 (1963), 175–195.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université De Lille 1, 59655, Villeneuve D'Ascq-Cédex, France

    C. Brezinski

Authors
  1. C. Brezinski
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brezinski, C. The mühlbach-neville-aitken algorithm and some extensions. BIT 20, 443–451 (1980). https://doi.org/10.1007/BF01933638

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01933638

Keywords

Search

Navigation