
handle: 20.500.14243/443268 , 11563/152627
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.
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
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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