Bivariate Shepard-Bernoulli operators

In this paper we extend the Shepard-Bernoulli operators to the bivariate case. These new interpolation operators are realized by using local support basis functions instead of classical Shepard basis functions and the bivariate three point extension of the generalized Taylor polynomial introduced by F. Costabile. The new operators do not require either the use of special partitions of the node convex hull or special structured data. We deeply study their approximation properties and provide an application to the scattered data interpolation problem; the numerical results show that this new approach is comparable with the other well known bivariate schemes QSHEP2D and CSHEP2D by Renka.