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arXiv · 1609.09015

Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Theoretical Foundations

Kewei Zhang·Elaine Crooks·Antonio Orlando
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Abstract

We introduce Lipschitz continuous and $C^{1,1}$ geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in $\mathbb{R}^n$ by using compensated convex transforms. Error estimates are provided for the approximations of bounded uniformly continuous functions, of Lipschitz functions, and of $C^{1,1}$ functions. We also prove that our approximation methods, which are differentiation and integration free and not sensitive to sample type, are stable with respect to the Hausdorff distance between samples.

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Kewei Zhang, Elaine Crooks, Antonio Orlando. 2016-09-28. Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Theoretical Foundations. https://arxiv.org/abs/1609.09015

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