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