A high order method using MAX-ENT approximation schemes

In this work we present a combined technique using Maximun-Entropy approximation [1] and De Boor’s Algorithm [2]. The goal of this approach is to generate higher-order consistency max-ent interpolants, based on the successive application of the de Boor’s algorithm. In fact, splines can be constructed by successively applying the de Boor’s algorithm over linear interpolants in one di- mension. Since maximum entropy approximation can be considered as a generalization of linear interpolation to arbitrary dimensions, it seems therefore natural to apply the de Boor’s algorithm to Max-Entropy interpolation to obtain spline-like interpolation with arbitrary consistency.