Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations

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Zhang, Kewei, Crooks, Elaine and Orlando, Antonio (2016) Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations. SIAM Journal on Mathematical Analysis, 48 (6). pp. 4126-4154. ISSN 1095-7154

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Abstract

We introduce Lipschitz continuous and C¹,¹ geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in Rn by using compensated convex transforms. Error estimates are provided for the approximations of bounded uniformly continuous functions, of Lipschitz functions, and of C1,1 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.

Item Type: Article
Additional Information: First published in SIAM Journal on Mathematical Analysis in vol. 48, no. 6, published by the Society for Industrial and Applied Mathematics. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
Keywords: interpolation, approximation, compensated convex transforms, Lipschitz functions, local-Lipschitz approximation, Hausdorff stability, error estimates
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1137/15M1045673
Depositing User: Eprints, Support
Date Deposited: 28 Feb 2017 09:14
Last Modified: 12 Oct 2017 19:34
URI: https://eprints.nottingham.ac.uk/id/eprint/40889

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