Greedy Algorithms with Prescribed Coefficients |
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Authors: | Vladimir Temlyakov |
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Institution: | (1) Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA |
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Abstract: | We study greedy algorithms in a Banach space from the point of view of convergence and rate of convergence. We concentrate
on studying algorithms that provide expansions into a series. We call such expansions greedy expansions. It was pointed out
in our previous article that there is a great flexibility in choosing coefficients of greedy expansions. In that article this
flexibility was used for constructing a greedy expansion that converges in any uniformly smooth Banach space. In this article
we push the flexibility in choosing the coefficients of greedy expansions to the extreme. We make these coefficients independent
of an element f ∈ X. Surprisingly, for a properly chosen sequence of coefficients we obtain results similar to the previous
results on greedy expansions when the coefficients were determined by an element f. |
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Keywords: | |
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