An efficient technique for the interpolation on compact triangulations

In this paper we present an efficient scheme for the computation of triangular Shepard method. More precisely, it is well known that the triangular Shepard method reaches an approximation order better than the Shepard one [4], but it needs to identify useful general triangulation of the node set. Here we propose a searching technique used to detect and select the nearest neighbor points in the interpolation scheme [2, 3]. It consists in determining the closest points belonging to the different neighborhoods and consequently applies to the triangulation-based approach. Numerical results show efficiency of the interpolation procedure.