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Computing

, Volume 30, Issue 3, pp 275–278 | Cite as

The one-sided Remez algorithm

  • C. B. Dunham
Short Communications
  • 30 Downloads

Abstract

Best one-sided minimax approximations from above on an interval by alternating families have an alternating characterization and may be computed by a simple modification of the classical Remez algorithm for ordinary Chebyshev approximation.

AMS Subject Classification

41A50 

Key words

One-sided minimax alternation Remez algorithm 

Der einseitige Remez Algorithmus

Zusammenfassung

Beste einseitige Minimax-Approximationen von oben auf einem Intervall mit Hilfe von alternierenden Familien besitzen eine Charakterisierung als Alternanten. Die Approximationen können durch eine einfache Abänderung des klassischen Remez Algorithmus für gewöhnliche Tschebyscheff-Approximationen berechnet werden.

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References

  1. [1]
    Dunham, C. B.: Chebyshev approximation with respect to a weight function. J. Approximation Theory2, 223–232 (1969).CrossRefGoogle Scholar
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    Dunham, C. B.: Alternating Chebyshev approximation. Trans. Amer. Math. Soc.178, 95–109 (1973).Google Scholar
  3. [3]
    Dunham, C. B.: Alternating minimax approximation with unequal restraints. J. Approximation Theory10, 199–205 (1974).CrossRefGoogle Scholar
  4. [4]
    Dunham, C. B.: Diserete Chebyshev approximation: alternation and the Remez algorithm. Z. Angew. Math. Mech.58, 326–328 (1979).Google Scholar
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    Meinardus, G.: Approximation of functions. Berlin-Heidelberg-New York: Springer 1967.Google Scholar
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    Rice, J.: The approximation of functions, Vol. 2. Reading, Mass.: Addison-Wesley 1969.Google Scholar
  7. [7]
    Dunham, C. B.: Remez algorithm for Chebyshev approximation with interpolation. Computing28, 75–78 (1982).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • C. B. Dunham
    • 1
  1. 1.Computer Science DepartmentUniversity of Western OntarioLondonCanada

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