Hermite type moving-least-squares approximations

The moving-least-squares approach, first presented by McLain [1], is a method for approximating multivariate functions using scattered data information. The method is using local polynomial approximations, incorporating weight functions of different types. Some weights, with certain singularities, induce C∞ interpolation approximation in n. In this work we present a way of generalizing the method to enable Hermite type interpolation, namely, interpolation to derivativesʹ data as well. The essence of the method is the use of an appropriate metric in the construction of the local polynomial approximations.