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A generalisation of de la Vallée-Poussin procedure to multivariate approximations

journal contribution
posted on 2022-01-01, 00:00 authored by N Sukhorukova, Julien UgonJulien Ugon
The theory of Chebyshev approximation has been extensively studied. In most cases, the optimality conditions are based on the notion of alternance or alternating sequence (that is, maximal deviation points with alternating deviation signs). There are a number of approximation methods for polynomial and polynomial spline approximation. Some of them are based on the classical de la Vallée-Poussin procedure. In this paper we demonstrate that under certain assumptions the classical de la Vallée-Poussin procedure, developed for univariate polynomial approximation, can be extended to the case of multivariate approximation. There are two main advantages of our approach. First of all, it provides an elegant geometrical interpretation of the procedure. Second, the corresponding basis functions are not restricted to be monomials and therefore can be extended to a larger family of functions.

History

Journal

Advances in Computational Mathematics

Volume

48

Article number

5

Pagination

1-19

Location

Berlin, Germany

ISSN

1019-7168

eISSN

1572-9044

Language

English

Publication classification

C1 Refereed article in a scholarly journal

Issue

5

Publisher

Springer