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On the continuity of multivariate Lagrange interpolation at natural lattices

Part of: Numerical approximation and computational geometry Approximations and expansions

Published online by Cambridge University Press:  10 April 2013

J.-P. Calvi  and
V. M. Phung
J.-P. Calvi
Affiliation:
Institut de MathématiquesUniversité de Toulouse III and CNRS (UMR 5219)31062, Toulouse Cedex 9, France email jean-paul.calvi@math.univ-toulouse.fr
V. M. Phung
Affiliation:
Department of MathematicsHanoi University of Education136 Xuan Thuy StreetCaugiay, Hanoi, Vietnam email manhlth@gmail.com

Abstract

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We give a natural geometric condition that ensures that sequences of interpolation polynomials (of fixed degree) of sufficiently differentiable functions with respect to the natural lattices introduced by Chung and Yao converge to a Taylor polynomial.

MSC classification

Secondary: 41A05: Interpolation 41A63: Multidimensional problems (should also be assigned at least one other classification number in this section) 41A80: Remainders in approximation formulas 65D05: Interpolation
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 16 , October 2013 , pp. 45 - 60
Copyright
© The Author(s) 2013 

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