Algorithms for computing the optimal Lipschitz constant of interpolants with Lipschitz derivative

TL;DR

This paper presents algorithms to efficiently compute the optimal Lipschitz constant for smooth interpolants with Lipschitz derivatives, improving the evaluation of interpolant quality in high-dimensional and large data scenarios.

Contribution

It introduces two algorithms for calculating the Lipschitz constant of smooth interpolants, one optimized for data dimension and the other for the number of data points.

Findings

Algorithms efficiently compute the Lipschitz constant for smooth interpolants.

The methods are optimal in either data dimension or number of points.

Facilitates better assessment of interpolant quality with smoothness constraints.

Abstract

One classical measure of the quality of an interpolating function is its Lipschitz constant. In this paper we consider interpolants with additional smoothness requirements, in particular that their derivatives be Lipschitz. We show that such a measure of quality can be easily computed, giving two algorithms, one optimal in the dimension of the data, the other optimal in the number of points to be interpolated.