Evaluating Lebesgue constants by Chebyshev polynomial meshes on cube, simplex and ball
Numerical Analysis
2023-12-01 v1 Numerical Analysis
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. Several examples are presented and possible generalizations outlined. A numerical software package implementing the method is freely available online.
Keywords
Cite
@article{arxiv.2311.18656,
title = {Evaluating Lebesgue constants by Chebyshev polynomial meshes on cube, simplex and ball},
author = {L. Bialas-Ciez and D. J. Kenne and A. Sommariva and M. Vianello},
journal= {arXiv preprint arXiv:2311.18656},
year = {2023}
}