Bulletin of the Australian Mathematical Society

Table of Contents - December 2000 - Volume 62, Issue 03  

Research Article

On Lagrange interpolation with equally spaced nodes

Michael Reversa1

a1 Department of Mathematics, University of Salzburg, Hellbrunnerstrasse 34, A-5020 Slazburg, Austria e-mail: Michael.Revers@sbg.ac.at

Abstract

A well-known result due to S.N. Bernstein is that sequence of Lagrange interpolation polynomials for |x| at equally spaced nodes in [−1, 1] diverges everywhere, except at zero and the end-points. In this paper we present a quantitative version concerning the divergence behaviour of the Lagrange interpolants for |x|3 at equidistant nodes. Furthermore, we present the exact rate of convergence for the interpolatory parabolas at the point zero.

(Received November 15 1999)