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Title: Incoherent systems and coverings in finite dimensional Banach spaces

Abstract

We discuss the construction of coverings of the unit ball of a finite dimensional Banach space. There is a well-known technique based on comparing volumes which gives upper and lower bounds on covering numbers. However, this technique does not provide a method for constructing good coverings. Here we study incoherent systems and apply them to construct good coverings. We use the following strategy. First, we build a good covering using balls with a radius close to one. Second, we iterate this construction to obtain a good covering for any radius. We shall concentrate mainly on the first step of this strategy. Bibliography: 14 titles.

Authors:
 [1]
  1. Steklov Mathematical Institute of the Russian Academy of Sciences (Russian Federation)
Publication Date:
OSTI Identifier:
22365155
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 205; Journal Issue: 5; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; BANACH SPACE; CALCULATION METHODS; COMPARATIVE EVALUATIONS; MANY-DIMENSIONAL CALCULATIONS; MATHEMATICAL SOLUTIONS

Citation Formats

Temlyakov, V N. Incoherent systems and coverings in finite dimensional Banach spaces. United States: N. p., 2014. Web. doi:10.1070/SM2014V205N05ABEH004395.
Temlyakov, V N. Incoherent systems and coverings in finite dimensional Banach spaces. United States. https://doi.org/10.1070/SM2014V205N05ABEH004395
Temlyakov, V N. 2014. "Incoherent systems and coverings in finite dimensional Banach spaces". United States. https://doi.org/10.1070/SM2014V205N05ABEH004395.
@article{osti_22365155,
title = {Incoherent systems and coverings in finite dimensional Banach spaces},
author = {Temlyakov, V N},
abstractNote = {We discuss the construction of coverings of the unit ball of a finite dimensional Banach space. There is a well-known technique based on comparing volumes which gives upper and lower bounds on covering numbers. However, this technique does not provide a method for constructing good coverings. Here we study incoherent systems and apply them to construct good coverings. We use the following strategy. First, we build a good covering using balls with a radius close to one. Second, we iterate this construction to obtain a good covering for any radius. We shall concentrate mainly on the first step of this strategy. Bibliography: 14 titles.},
doi = {10.1070/SM2014V205N05ABEH004395},
url = {https://www.osti.gov/biblio/22365155}, journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 5,
volume = 205,
place = {United States},
year = {Sat May 31 00:00:00 EDT 2014},
month = {Sat May 31 00:00:00 EDT 2014}
}