Construction Techniques for Highly Accurate Quasi-Interpolation Operators

Abstract

Under mild additional assumptions this paper constructs quasi-interpolants in the form fh(x)=∑j=-∞+∞f(hj)φ h(xh-j),x∈R,h*0, ((0.1))with approximation order ℓ-1, whereφh(x) is a linear combination of translatesψ(x-jh) of a functionψinCℓ(R). Thus the order of convergence of such operators can be pushed up to a limit that only depends on the smoothness of the functionψ. This approach can be generalized to the multivariate setting by using discrete convolutions with tensor products of odd-degreeB-splines. © 1997 Academic Press.