A link between Lebesgue constants and Hermite-Fejér interpolation-Reference-Cited by-同舟云学术

A link between Lebesgue constants and Hermite-Fejér interpolation

Published:1986-04 Issue:2 Volume:33 Page:207-218
ISSN:0004-9727
Container-title:Bulletin of the Australian Mathematical Society
language:en
Short-container-title:Bull. Austral. Math. Soc.

Author:

Goodenough S. J.

Abstract

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).

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

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1. Error estimates for the approximation of functions by certain interpolation polynomials;Bulletin of the Australian Mathematical Society;1986-02