Ε-Coverings of Hölder-Zygmund Type Spaces on Data-Defined Manifolds. (17th June 2014)

• Record Type: Journal Article
• Authors: Ehler, Martin; Filbir, Frank
• Other Names: Cattani Carlo Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-06-17
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/402918
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : 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.