BIT Numerical Mathematics

, Volume 24, Issue 4, pp 647–655 | Cite as

An asymptotically orthonormal polynomial family

  • Lothar Reichel


Given a Jordan curve Г in the complex plane, we describe a polynomial family which is asymptotically orthonormal on Г. The polynomials have some similarities with the Faber polynomials but are simpler to compute with. Numerical examples are presented.

AMS (MOS) Subject Classifications

65E05 30E10 41A10 

Key Words

complex polynomial approximation 


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  1. 1.
    J. H. Curtiss,Faber polynomials and the Faber series. Amer. Math. Monthly 78 (1971), 577–596.Google Scholar
  2. 2.
    B. Fornberg,A numerical method for conformal mappings. SIAM J. Sci. Stat. Comp. 1 (1980), 386–400.Google Scholar
  3. 3.
    D. Gaier,Vorlesungen über Approximation im Komplexen. Birkhäuser, Basel (1980).Google Scholar
  4. 4.
    M. H. Gutknecht,Solving Theodorsen's integral equation for conformal maps with the fast Fourier transform and various nonlinear iterative methods. Numer. Math. 36 (1981), 405–429.Google Scholar
  5. 5.
    L. Reichel,A fast method for solving certain integral equations of the first kind with application to conformal mappings. Report TRITA-NA-8118„ Dept. of Numer. Anal. and Comp. Sci., Royal Institute of Technology, Stockholm, (1981).Google Scholar

Copyright information

© BIT Foundations 1984

Authors and Affiliations

  • Lothar Reichel
    • 1
  1. 1.Forschungsinstitut für Mathematik, ETH-ZentrumZürichSwitzerland

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