A remark on covering

01/10/2013

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by   Vladimir Temlyakov, et al.

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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.