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On the Divergence of Lagrange Interpolation to |x|

✍ Scribed by L. Brutman; E. Passow

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 227 KB
Volume: 81
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1995.1037

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✦ Synopsis

It is a classical result of Bernstein that the sequence of Lagrange interpolation polynomials to (|x|) at equally spaced nodes in ([-1,1]) diverges everywhere, except at zero and the end-points. In the present paper we show that the case of equally spaced nodes is not an exceptional one in this sense. Namely, we prove that the divergence everywhere in (0<|x|<1) of the Lagrange interpolation to (|x|) takes place for a broad family of nodes, including in particular the Newman nodes, which are known to be very efficient for rational interpolation. (1995 Academic Press, Inc.

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