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https://dx.doi.org/10.48550/ar...
Article . 2021
License: CC BY NC ND
Data sources: Datacite
CNR ExploRA
Article . 2021
Data sources: CNR ExploRA
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Some remarks on filtered polynomial interpolation at Chebyshev nodes

Authors: Occorsio D; Themistoclakis W;

Some remarks on filtered polynomial interpolation at Chebyshev nodes

Abstract

The present paper concerns filtered de la Vall��e 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 H��lder--Zygmund spaces where several integro--differential models are uniquely and stably solvable.

Keywords

De la Valleé Poussin filtered interpolation, Sobolev and Hölder-Zygmund spaces, Chebyshev nodes, Simultaneous approximation, Sobolev and Hölder-Zygmund spaces, De la Valleé Poussin filtered interpolation, Numerical Analysis (math.NA), 510, 004, FOS: Mathematics, Mathematics - Numerical Analysis, Lebsgue constants, Uniform error estimates

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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