Technical Report 10/94 (October, 5th 1994) Department of Pure and Applied Mathematics, University of Padova

Abstract: The Dyadic Iterative Interpolation Method (DIIM) (presented by S. Dubuc Journal of Math. An. and Appl. 1986, 185-204), concerns with the construction of an interpolating function on dyadic rationals. We characterize it in terms of Uniform Dyadic Subdivision Schemes (UDSS) (cfr. N. Dyn, J.A. Gregory and D. Levin, Constr. Approx. 7 1991, 127-147). We show that the DIIM is a 4-point subdivision scheme that generates almost twice differentiable functions. We also provide a proof to an unsolved problem left in the paper by S. Dubuc, related to the so called fundamental interpolation function , namely the existence of a unique minimum in the interval [1, 2].
We extend the method to a two dimensional setting proving interesting properties.