Quasi-interpolation in the Absence of Polynomial Reproduction
Rick K. Beatson, Will Light · Birkhäuser Basel eBooks · 1992
This paper discusses approximation by quasi-interpolants K h which are constructed using the usual scaling and translation operations on a one-parameter family of functions {ψ λ } λ>0. A particular feature of the analysis is the fact that we do not require K h to reproduce low degree polynomials. In the first part of the paper, estimates are obtained for |(f − K h f)(x)| as h → 0, when ψ λ decays polynomially at infinity. These estimates are then used to analyse quasi-interpolation to functions in W ∞ k (ℝ n ) based on Gaussians and Exponentials.