Thin plate spline interpolation on the unit interval.

Abstract  It is known that the unique thin plate spline interpolant to a function f ∈ C 3 IR sampled at the scaled integers h Z converges at an optimal rate of h 3. In this paper we present results from a recent numerical investigation of the case where the function is sampled at equally spaced points on the unit interval. In this setting the known theoretical error bounds predict a drop in the convergence rate from h 3 to h. However, numerical experiments show that the usual rate of convergence is h 3/2 and that the deterioration occurs near the end points of the interval. We will examine the effect of the boundary on the accuracy of the interpolant and also the effect of the smoothness of the target function. We will show that there exists functions which enjoy an even faster order of convergence of h 5/2. [ABSTRACT FROM AUTHOR]