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