Rational Hermite interpolation on six-tuples and scattered data

摘要

The main objective of this paper is to construct an approximant, with cubic precision and quartic approximation order, which interpolates functional values and first order derivatives on a set of scattered data. This approximant is a combination of six-point Shepard basis functions with rational interpolants based on six-tuples of nodes. The numerical results show the efficiency and the accuracy of the proposed method, which is implemented by a fast algorithm that makes it useful in several domains of application.