Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations
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 approximation...
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| Format: | Article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2016
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| Online Access: | https://eprints.nottingham.ac.uk/40889/ |
| _version_ | 1848796156100870144 |
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| author | Zhang, Kewei Crooks, Elaine Orlando, Antonio |
| author_facet | Zhang, Kewei Crooks, Elaine Orlando, Antonio |
| author_sort | Zhang, Kewei |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:43:30Z |
| format | Article |
| id | nottingham-40889 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T19:43:30Z |
| publishDate | 2016 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-408892017-10-12T19:34:51Z https://eprints.nottingham.ac.uk/40889/ Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations Zhang, Kewei Crooks, Elaine Orlando, Antonio 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. Society for Industrial and Applied Mathematics 2016-12-08 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/40889/1/ZOC-M104567.pdf 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 interpolation approximation compensated convex transforms Lipschitz functions local-Lipschitz approximation Hausdorff stability error estimates http://epubs.siam.org/doi/10.1137/15M1045673 doi:10.1137/15M1045673 doi:10.1137/15M1045673 |
| spellingShingle | interpolation approximation compensated convex transforms Lipschitz functions local-Lipschitz approximation Hausdorff stability error estimates Zhang, Kewei Crooks, Elaine Orlando, Antonio Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations |
| title | Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations |
| title_full | Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations |
| title_fullStr | Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations |
| title_full_unstemmed | Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations |
| title_short | Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations |
| title_sort | compensated convexity methods for approximations and interpolations of sampled functions in euclidean spaces: theoretical foundations |
| topic | interpolation approximation compensated convex transforms Lipschitz functions local-Lipschitz approximation Hausdorff stability error estimates |
| url | https://eprints.nottingham.ac.uk/40889/ https://eprints.nottingham.ac.uk/40889/ https://eprints.nottingham.ac.uk/40889/ |