Polynomial generation and quasi-interpolation in stationary non-uniform subdivision Original Research Article

We study the necessary and sufficient conditions for the generation of polynomials by stationary subdivision schemes, and we show how to derive appropriate quasi-interpolation rules that have the optimal approximation order. We show that these conditions hold in the context of non-uniform subdivision as well, and we demonstrate how they can be used for the construction of stationary non-uniform subdivision schemes that have a prescribed approximation power.