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

الملخص EN

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.