English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The paper deals with a special filtered approximation method, whichoriginates interpolation polynomials at Chebyshev zeros by using de la Vall\'eePoussin filters. These polynomials can be an useful device for many theoreticaland applicative problems since they combine the advantages of the classicalLagrange interpolation, with the uniform convergence in spaces of locallycontinuous functions equipped with suitable, Jacobi--weighted, uniform norms.The uniform boundedness of the related Lebesgue constants, which equals to theuniform convergence and is missing from Lagrange interpolation, has beenalready proved in literature under different, but only sufficient, assumptions.Here, we state the necessary and sufficient conditions to get it. Theseconditions are easy to check since they are simple inequalities on theexponents of the Jacobi weight defining the norm. Moreover, they are necessaryand sufficient to get filtered interpolating polynomials with a near bestapproximation error, which tends to zero as the number $n$ of nodes tends toinfinity. In addition, the convergence rate is comparable with the error ofbest polynomial approximation of degree $n$, hence the approximation orderimproves with the smoothness of the sought function. Several numericalexperiments are given in order to test the theoretical results, to make acomparison with the Lagrange interpolation at the same nodes and to show howthe Gibbs phenomenon can be strongly reduced.

On the filtered polynomial interpolation at Chebyshev nodes