Local approximation of functions over points scattered in Rm Original Research Article

Given points {View the MathML source} scattered in View the MathML sourcem and a real valued function f that is Cn+2 on a neighborhood of the convex hull of the points {View the MathML source}, we define an interpolant Fn which has polynomial precision of order n + 1, and Fn − f = O(hn+2), where h is determined by the distribution of the data sites View the MathML source. We also discuss the application of this interpolant to the scattered data interpolation problem in the plane, where we know the function values View the MathML source but have no information concerning the partial derivatives of f. We also present the results of numerical experiments.