Numerische Mathematik

, Volume 7, Issue 4, pp 322–330 | Cite as

Rational chebyshev approximation by Remes' algorithms

  • Anthony Ralston


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Achieser, N. I.: Theory of Approximation (translated byC. J. Hyman). New York: Frederick Ungar Publ. Co. 1956.MATHGoogle Scholar
  2. [2]
    Fraser, W., andJ. F. Hart: On the Computation of Rational Approximations to Continuous Functions. Comm. ACM5, 401–403 (1962).CrossRefMATHGoogle Scholar
  3. [3]
    Novodvorskii, E. N., andI. S. Pinsker: On a Process of Equalization of Maxima. Uspehi Mat. Nauk.6, 174–181 (1951) (translation byA. Shenitzer available from New York University library).MathSciNetGoogle Scholar
  4. [4]
    Remes, E.: Sur le Calcul Effectif des Polynomes d'Approximation de Tchebichef. C. R. Acad. Sci. Paris96, 337–340 (1934).MATHGoogle Scholar
  5. [5]
    Rice, J. R.: The Characterization of Best Nonlinear Approximations. Trans. Amer. Math. Soc.96, 322–340 (1960).MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    —: The Approximation of Functions, vol. 1. Reading, Mass.: Addison-Wesley 1964.MATHGoogle Scholar
  7. [7]
    Stoer, J.: A Direct Method for Chebyshev Approximation by Rational Functions. J. Assoc. Comput. Mach.11, 59–69 (1964).MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    Tornheim, L.: Onn-parameter Families of Functions and Associated Convex Functions. Trans. Amer. Math. Soc.69, 457–467 (1950).MathSciNetMATHGoogle Scholar
  9. [9]
    Werner, H.: Tschebyscheff-Approximationen im Bereich der rationalen Funktionen bei Vorliegen einer guten Ausgangsnäherung. Arch. Rat. Mech. Anal.10, 205–219 (1962).CrossRefMATHGoogle Scholar
  10. [10]
    —: Die konstruktive Ermittlung der Tschebyscheff-Approximierenden im Bereich der rationalen Funktionen. Arch. Rat. Mech. Anal.11, 368–384 (1962).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1965

Authors and Affiliations

  • Anthony Ralston
    • 1
  1. 1.Mathematics Department Stevens Institute of TechnologyCastle Point StationHobokenUSA

Personalised recommendations