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

    Authors

    X. Li

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    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

    Share

    COinS