Some remarks on filtered polynomial interpolation at Chebyshev nodes

TitleSome remarks on filtered polynomial interpolation at Chebyshev nodes
Publication TypeJournal Article
Year of Publication2021
AuthorsOccorsio, D, Themistoclakis, W
JournalDolomites Research Notes on Approximation
Date Published04/2021
PublisherPadova University Press
Place PublishedPadova, IT
ISSN Number20356803

The present paper concerns filtered de la Vallée Poussin (VP) interpolation at the Chebyshev nodes of the four kinds. This approximation model is interesting for applications because it combines the advantages of the classical Lagrange polynomial approximation (interpolation and polynomial preserving) with the ones of filtered approximation (uniform boundedness of the Lebesgue constants and reduction of the Gibbs phenomenon). Here we focus on some additional features that are useful in the applications of filtered VP interpolation. In particular, we analyze the simultaneous approximation provided by the derivatives of the VP interpolation polynomials. Moreover, we state the uniform boundedness of VP approximation operators in some Sobolev and Hölder–Zygmund spaces where several integro–differential models are uniquely and stably solvable.