A remark on covering
Metric Geometry
2013-01-15 v1 Functional Analysis
Numerical Analysis
Machine Learning
Abstract
We discuss construction of coverings of the unit ball of a finite dimensional Banach space. The well known technique of comparing volumes gives upper and lower bounds on covering numbers. This technique does not provide a construction of good coverings. Here we apply incoherent dictionaries for construction of good coverings. We use the following strategy. First, we build a good covering by balls with a radius close to one. Second, we iterate this construction to obtain a good covering for any radius. We mostly concentrate on the first step of this strategy.
Cite
@article{arxiv.1301.3043,
title = {A remark on covering},
author = {Vladimir Temlyakov},
journal= {arXiv preprint arXiv:1301.3043},
year = {2013}
}