A study of the uniform accuracy of univariate thin plate spline interpolation

TL;DR

This paper introduces a new power function for univariate thin plate spline interpolation that accurately predicts the uniform error order, supported by numerical experiments and analysis of its relation to the Peano kernel.

Contribution

It proposes a novel power function that better captures the true uniform accuracy of thin plate spline interpolation for smooth data functions in one variable.

Findings

New power function matches the expected error order

Numerical experiments confirm the accuracy of the error estimate

Analysis links the power function to the Peano kernel

Abstract

The usual power function error estimates do not capture the true order of uniform accuracy for thin plate spline interpolation to smooth data functions in one variable. In this paper we propose a new type of power function and we show, through numerical experiments, that the error estimate based upon it does match the expected order. We also study the relationship between the new power function and the Peano kernel for univariate thin plate spline interpolation.