Bivariate Shepard-Bernoulli operators

We extend the Shepard-Bernoulli operators introduced in [1] to the bivariate case. These new interpolation operators are realized by using local support basis functions introduced in [2] instead of classical Shepard basis functions and the bivariate three point extension [3] of the generalized Taylor polynomial introduced by F. Costabile in [4]. The new operators do not require either the use of special partitions of the node convex hull or special structured data as in [5]. 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 [6,7].