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-Coverings of Hölder-Zygmund Type Spaces on Data-Defined Manifolds

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  • Martin Ehler
  • Frank Filbir

Abstract

We first determine the asymptotes of the -covering numbers of Hölder-Zygmund type spaces on data-defined manifolds. Secondly, a fully discrete and finite algorithmic scheme is developed providing explicit -coverings whose cardinality is asymptotically near the -covering number. Given an arbitrary Hölder-Zygmund type function, the nearby center of a ball in the -covering can also be computed in a discrete finite fashion.

Suggested Citation

  • Martin Ehler & Frank Filbir, 2014. "-Coverings of Hölder-Zygmund Type Spaces on Data-Defined Manifolds," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, June.
    • Handle: RePEc:hin:jnlaaa:402918
    DOI: 10.1155/2014/402918
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