A study of the uniform accuracy of univariate thin plate spline interpolation
For researchers in approximation theory and spline interpolation, this work provides a corrected error analysis for a specific univariate case, but it is incremental as it focuses on a narrow problem.
The paper addresses the mismatch between standard power function error estimates and the actual uniform accuracy of univariate thin plate spline interpolation for smooth functions. It introduces a new power function that yields error estimates matching the expected order, validated through numerical experiments.
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.