Email this article A remark on constructive covering of a ball of finite dimensional Banach space
- Authors: Temlyakov V.N.1,2,3,4
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
- Lomonosov Moscow State University, Moscow, Russia
- Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
- University of South Carolina, Columbia, SC, USA
- Issue: Vol 216, No 7 (2025)
- Pages: 96-108
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/306721
- DOI: https://doi.org/10.4213/sm10140
- ID: 306721
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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 a good covering. Here we study incoherent systems and apply them to the construction of good coverings. We use the following strategy. First, we build a good covering by balls of radius close to one. Second, we iterate this construction to obtain a good covering for any radius. We provide a greedy-type algorithm for such constructions.
About the authors
Vladimir Nikolaevich Temlyakov
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia; Lomonosov Moscow State University, Moscow, Russia; Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia; University of South Carolina, Columbia, SC, USA
Author for correspondence.
Email: temlyakovv@gmail.com
Doctor of physico-mathematical sciences, Professor
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