Title

On The Lagrange Interpolation For A Subset Of CK Functions

Keywords

AMS classification: 41A05, 41A25, Key words and phrases, Interpolation, Optimal order of approximation

Abstract

We study the optimal order of approximation for Ckpiecewise analytic functions (cf. Definition 1.2) by Lagrange interpolation associated with the Chebyshev extremal points. It is proved that the Jackson order of approximation is attained, and moreover, if x is away from the singular points, the local order of approximation at x can be improved by O(n-1). Such improvement of the local order of approximation is also shown to be sharp. These results extend earlier results of Mastroianni and Szabados on the order of approximation for continuous piecewise polynomial functions (splines) by the Lagrange interpolation, and thus solve a problem of theirs (about the order of approximation for |x|3) in a much more general form. © 1995 Springer-Verlag New York, Inc.

Publication Date

9-1-1995

Publication Title

Constructive Approximation

Volume

11

Issue

3

Number of Pages

287-297

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/BF01208556

Socpus ID

26444602944 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/26444602944

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