http://dx.doi.org/10.1007/bf01208556

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Title

On The Lagrange Interpolation For A Subset Of C-K Functions

Authors

Authors

X. Li

Comments

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Abbreviated Journal Title

Constr. Approx.

Keywords

INTERPOLATION; OPTIMAL ORDER OF APPROXIMATION; Mathematics

Abstract

We study the optimal order of approximation for C-k piecewise 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.

Journal Title

Constructive Approximation

Volume

11

Issue/Number

3

Publication Date

1-1-1995

Document Type

Article

Language

English

First Page

287

Last Page

297

WOS Identifier

WOS:A1995RV64900001

ISSN

0176-4276

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