On Quasi-Interpolation with Non-uniformly Distributed Centers on Domains and Manifolds

The paper studies quasi interpolation by scaled shifts of a smooth and rapidly decaying function. The centers are images of a smooth mapping of the hZn lattice in Rs, s n, and the scaling parameters are proportional to h. We show that for a large class of generating functions the quasi interpolants provide high order approximations up to some prescribed accuracy. Although the approximants do not converge as h tends to zero, this is not feasible in computations if a scalar parameter is suitably chosen. The lack of convergence is compensated for by more exibility in the choice of generating functions used in numerical methods for solving operator equations.