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.
EVALUATING LEBESGUE CONSTANTS BY CHEBYSHEV POLYNOMIAL MESHES ON CUBE, SIMPLEX, AND BALL
Sommariva A.;Vianello M.Investigation
2024
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.File in questo prodotto:
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