- De la Vallée Poussin filtered polynomial approximation on the half line
Authors: Occorsio Donatella, Woula Themistoclakis
Summary: On the half line we introduce a brand new sequence of close to — finest uniform approximation polynomials, simply computable by the values of the approximated perform at a truncated variety of Laguerre zeros. Such approximation polynomials come from a discretization of filtered Fourier — Laguerre partial sums, that are filtered by utilizing a de la Vallée Poussin (VP) filter. They’ve the peculiarity of relying on two parameters: a truncation parameter that determines how most of the n Laguerre zeros are thought-about, and a localization parameter, which determines the vary of motion of the VP filter that we’re going to apply. As n→∞, underneath easy assumptions on such parameters and on the Laguerre exponents of the concerned weights, we show that the brand new VP filtered approximation polynomials have uniformly bounded Lebesgue constants and uniformly convergence at a close to — finest approximation fee, for any regionally steady perform on the semiaxis. newline The theoretical outcomes have been validated by the numerical experiments. Specifically, they present a greater efficiency of the proposed VP filtered approximation versus the truncated Lagrange interpolation on the identical nodes, particularly for features a.e. very easy with remoted singularities. In such instances we see a extra localized approximation in addition to an excellent discount of the Gibbs phenomenon.
