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A link between Lebesgue constants and Hermite-Fejér interpolation

Published online by Cambridge University Press:  17 April 2009

S. J. Goodenough
S. J. Goodenough
Affiliation:
Department of Mathematics, Statistics, Computer Science, University of Newcastle, N.S.W. 2308.
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Abstract

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A review of the development of estimates for Lebesgue constants associated with Lagrange interpolation on the one hand, and estimates for the rate of convergence of Hermite-Fejér interpolation on the other hand, provides a historical perspective for the following surprising, close link between these apparently diverse concepts. Denoting by Λn (T) the Lebesgue constant of order n and by Δn (T) the maximum interpolation error for functions of class Lip 1 by Hexmite-Fejér interpolation polynomials of degree not exceeding 2n − 1, based on the zeros of the Chebyshev polynomial of first kind, we discover that, for even values of n, Λn(T) = n Δn(T).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 2 , April 1986 , pp. 207 - 218
Copyright
Copyright © Australian Mathematical Society 1986

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