On the extension of the Shepard-Bernoulli operators to higher dimensions

We present special extensions [5] to the bivariate case of the Shepard-Bernoulli opera- tors introduced in [1] and of several others univariate combined Shepard operators [2]. These new interpolation operators are realized by using bivariate three point extensions of univariate expansions formulas (see, for example, [3, 4]) in combination with bivariate Shepard operators [6] and do not require special partitions of the node convex hull. We study properties of the new operators and provide applications to the scattered data interpolation problem.