Scattered data interpolation by Shepard’s like methods: classical results and recent advances

Interpolation problems arise in many areas where there is a need to construct a continuous surface from irregularly spaced data points. This problem has a number of solutions and, among them, the choice of interpolation technique depends on the distribution of points in the data set, the application domain, the approximating function or the method that is prevalent in the discipline. We discuss on Shepard’s interpolation method and some of its variations, which have been proposed in order to increase the accuracy of approximation of the original method, to improve its efficiency or even to solve specific interpolation problems. (joint work with Filomena Di Tommaso)