ε-Coverings of Hölder-Zygmund Type Spaces on Data-Defined Manifolds
We first determine the asymptotes of the ε-covering numbers of Hölder-Zygmund type spaces on data-defined manifolds. Secondly, a fully discrete and finite algorithmic scheme is developed providing explicit ε-coverings whose cardinality is asymptotically near the ε-covering number. Given an arbitrary...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/402918 |
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| Summary: | We first determine the asymptotes of the ε-covering numbers of Hölder-Zygmund type spaces
on data-defined manifolds. Secondly, a fully discrete and finite algorithmic scheme is developed providing explicit ε-coverings whose cardinality is asymptotically near the ε-covering number. Given an arbitrary Hölder-Zygmund type function, the nearby center of a ball in the ε-covering can also be computed in a discrete finite fashion. |
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| ISSN: | 1085-3375 1687-0409 |