English

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.

Keywords

Cite

@article{arxiv.1301.3043,
  title  = {A remark on covering},
  author = {Vladimir Temlyakov},
  journal= {arXiv preprint arXiv:1301.3043},
  year   = {2013}
}
R2 v1 2026-06-21T23:09:02.128Z