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On Lagrange interpolation with equally spaced nodes

Published online by Cambridge University Press:  17 April 2009

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

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 3 , December 2000 , pp. 357 - 368
Copyright
Copyright © Australian Mathematical Society 2000

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