Incoherent systems and coverings in finite dimensional Banach spaces
Journal Article
·
· Sbornik. Mathematics
- Steklov Mathematical Institute of the Russian Academy of Sciences (Russian Federation)
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.
- OSTI ID:
- 22365155
- Journal Information:
- Sbornik. Mathematics, Vol. 205, Issue 5; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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