Volume 60, pp. 428-445, 2024.

Evaluating Lebesgue constants by Chebyshev polynomial meshes on cube, simplex, and ball

L. Białas-Cież, D. J. Kenne, A. Sommariva, and M. Vianello

Abstract

We show that product Chebyshev polynomial meshes can be used, in a fully discrete way, to evaluate with rigorous error bounds the Lebesgue constant, i.e., the maximum of the Lebesgue function, for a class of polynomial projectors on cube, simplex, and ball, including interpolation, hyperinterpolation, and weighted least-squares approximation. Several examples are presented and possible generalizations outlined. A numerical software package implementing the method is freely available online.

Full Text (PDF) [438 KB], BibTeX

Key words

multivariate polynomial meshes, cube, simplex, ball, polynomial projectors, interpolation, least-squares, hyperinterpolation, polynomial optimization, Lebesgue constant

AMS subject classifications

65D05, 65D10, 65K05

Links to the cited ETNA articles

[52]	Vol. 42 (2014), pp. 41-63 Marc van Barel, Matthias Humet, and Laurent Sorber: Approximating optimal point configurations for multivariate polynomial interpolation

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