Rate of convergence of multinode Shepard operators

The triangular Shepard method, introduced by Little in 1983 [7], is a convex combination of triangular basis functions with linear polynomials, based on the vertices of the triangles, that locally interpolate the given data at the vertices. The method has linear precision and reaches quadratic approximation order [3]. As specified by Little, the triangular Shepard method can be generalized to higher dimensions and to sets of more than three points. In this paper we introduce the multinode Shepard method as a generalization of the triangular Shepard method in the case of scattered points in ℝ s , s ∈ ℕ, and we study the remainder term and its asymptotic behavior.