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:
File Dimensione Formato  
Lebesgue.pdf

accesso aperto

Tipologia: Published (Publisher's Version of Record)
Licenza: Accesso libero
Dimensione 438.31 kB
Formato Adobe PDF
438.31 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3535869
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? ND
  • OpenAlex ND
social impact