Advertisement

Computing with the faber transform

  • S. W. Ellacott
  • E. B. Saff
Numerical Methods
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)

Abstract

Some theoretical and computational aspects of Faber-Padé approximants are discussed. In particular, a Montessus type theorem is proved and a new method for computing the approximants is presented. Results of numerical tests for the latter are included.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. M. Anderson, "The Faber operator." This volume.Google Scholar
  2. 2.
    G. A. Baker and P. Graves-Morris, "Padé approximants. Part 1: Basic Theory." Encyclopedia of Mathematics and its Applications, vol. 13. Addison-Wesley. Massachusetts, 1981.Google Scholar
  3. 3.
    S. W. Ellacott, "Computation of Faber series with application to numerical polynomial approximation in the complex plane." Math. Comp. vol. 40, no. 162, 1984, pp. 575–587.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    S. W. Ellacott, "On the Faber Transform and efficient numerical rational approximation." SIAM J. Numer. Anal., vol. 20, no. 5, October 1983, pp. 989–1000.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    T. Ganelius, Degree of rational approximation. In: Lectures on Approximation and Value Distribution, Les Presses de l'Université de Montréal, Montréal, Canada (1982).Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • S. W. Ellacott
    • 1
  • E. B. Saff
    • 2
  1. 1.Department of MathematicsBrighton PolytechnicBrightonEngland
  2. 2.Department of MathematicsUniversity of South FloridaTampaUSA

Personalised recommendations