Local Convergence Of Lagrange Interpolation Associated With Equidistant Nodes

    Authors

    X. Li;E. B. Saff

    Comments

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    Abbreviated Journal Title

    J. Approx. Theory

    Keywords

    Mathematics

    Abstract

    Under the assumption that the function f is bounded on [- 1, 1] and analytic at x = 0 we prove the local convergence of Lagrange interpolating polynomials of f associated with equidistant nodes on [- 1, 1]. The classical results concerning the convergence of such interpolants assume the stronger condition that f is analytic on [- 1, 1]. A de Montessus de Ballore type theorem for interpolating rationals associated with equidistant nodes is also established without assuming the global analyticity of f on [- 1, 1]. (C) 1994 Academic Press, Inc.

    Journal Title

    Journal of Approximation Theory

    Volume

    78

    Issue/Number

    2

    Publication Date

    1-1-1994

    Document Type

    Article

    Language

    English

    First Page

    213

    Last Page

    225

    WOS Identifier

    WOS:A1994PA23100004

    ISSN

    0021-9045

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