Complete Hermite-Birkhoff interpolation on scattered data by combined Shepard operators

摘要

The problem of Hermite-Birkhoff interpolation on scattered data under certain conditions of completeness is considered by using Shepard basis functions in combination with local interpolating polynomials based on the vertices of triangles. This approach allows the construction of interpolation operators with nontrivial polynomial reproduction and a good accuracy of approximation. (C) 2015 Elsevier B.V. All rights reserved.