On approximation by Lagrange interpolating polynomials for a subset of the space of continuous functions

S. Zhou

Colloquium Mathematicae (1998)

  • Volume: 75, Issue: 1, page 1-5
  • ISSN: 0010-1354

Abstract

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We construct a C k piecewise differentiable function that is not C k piecewise analytic and satisfies a Jackson type estimate for approximation by Lagrange interpolating polynomials associated with the extremal points of the Chebyshev polynomials.

How to cite

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Zhou, S.. "On approximation by Lagrange interpolating polynomials for a subset of the space of continuous functions." Colloquium Mathematicae 75.1 (1998): 1-5. <http://eudml.org/doc/210526>.

@article{Zhou1998,
abstract = {We construct a $C^k$ piecewise differentiable function that is not $C^k$ piecewise analytic and satisfies a Jackson type estimate for approximation by Lagrange interpolating polynomials associated with the extremal points of the Chebyshev polynomials.},
author = {Zhou, S.},
journal = {Colloquium Mathematicae},
keywords = {interpolation; Lagrange interpolating operators; extremal points; Chebyshev polynomials; rate of convergence},
language = {eng},
number = {1},
pages = {1-5},
title = {On approximation by Lagrange interpolating polynomials for a subset of the space of continuous functions},
url = {http://eudml.org/doc/210526},
volume = {75},
year = {1998},
}

TY - JOUR
AU - Zhou, S.
TI - On approximation by Lagrange interpolating polynomials for a subset of the space of continuous functions
JO - Colloquium Mathematicae
PY - 1998
VL - 75
IS - 1
SP - 1
EP - 5
AB - We construct a $C^k$ piecewise differentiable function that is not $C^k$ piecewise analytic and satisfies a Jackson type estimate for approximation by Lagrange interpolating polynomials associated with the extremal points of the Chebyshev polynomials.
LA - eng
KW - interpolation; Lagrange interpolating operators; extremal points; Chebyshev polynomials; rate of convergence
UR - http://eudml.org/doc/210526
ER -

References

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  1. [MS] G. Mastroianni and J. Szabados, Jackson order of approximation by Lagrange interpolation, in: Proc. Second Internat. Conf. in Functional Analysis and Approximation Theory (Aquafredda di Maratea, 1992), Rend. Circ. Mat. Palermo (2) Suppl. 1993, no. 33, 375-386. Zbl0837.41003
  2. [Li] X. Li, On the Lagrange interpolation for a subset of C^k functions, Constr. Approx. 11 (1995), 287-297. Zbl0830.41001

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