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Title: Incoherent systems and coverings in finite dimensional Banach spaces

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
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 5; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; BANACH SPACE; CALCULATION METHODS; COMPARATIVE EVALUATIONS; MANY-DIMENSIONAL CALCULATIONS; MATHEMATICAL SOLUTIONS