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\(\varepsilon\)-coverings of Hölder-Zygmund type spaces on data-defined manifolds. (English) Zbl 1470.41026

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

MSC:

41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
41A30 Approximation by other special function classes
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