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Numerische Mathematik

, Volume 21, Issue 3, pp 220–222 | Cite as

Eine Bemerkung zur Konvergenz Hermitescher Interpolationsprozesse

  • H. Esser
  • K. Scherer
Article

Summary

LetH k,n (f; x) be the polynomial which interpolates ak-times continously differentiable functionf as well as its derivatives up to the orderk at the Chebyshevnodes. An estimate of the norm ofH k, n (f) is obtained which enables an estimate of the error of interpolation in terms of arbitrary moduli of continuity off (k) . Furthermore, by a more general result on projection operators, it is shown thatH k, n (k) (f; x) generally does not converge uniformly tof (k) .

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Literatur

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    Timan, A. F.: Theory of approximation of functions of a real variable. Oxford: Pergamon Press 1963Google Scholar
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Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • H. Esser
    • 1
  • K. Scherer
    • 2
  1. 1.Lehrstuhl A für Mathematik der RWTH AachenAachenBundesrepublik Deutschland
  2. 2.Institut für Geometrie und Praktische Mathematik der RWTH AachenAachenBundesrepublik Deutschland

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