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Chebyshev Multivariate Polynomial Approximation and Point Reduction Procedure

journal contribution
posted on 2021-06-01, 00:00 authored by N Sukhorukova, Julien UgonJulien Ugon, D Yost
We apply the methods of nonsmooth and convex analysis to extend the study of Chebyshev (uniform) approximation for univariate polynomial functions to the case of general multivariate functions (not just polynomials). First of all, we give new necessary and sufficient optimality conditions for multivariate approximation, and a geometrical interpretation of them which reduces to the classical alternating sequence condition in the univariate case. Then, we present a procedure for verification of necessary and sufficient optimality conditions that is based on our generalization of the notion of alternating sequence to the case of multivariate polynomials. Finally, we develop an algorithm for fast verification of necessary optimality conditions in the multivariate polynomial case.

History

Journal

Constructive Approximation

Volume

53

Pagination

529-544

Location

New York, N.Y.

ISSN

0176-4276

eISSN

1432-0940

Language

English

Publication classification

C1 Refereed article in a scholarly journal

Issue

3

Publisher

SPRINGER