Abstract
We study the convergence of greedy algorithms in Banach spaces. We construct an example of a smooth Banach space, where the X-greedy algorithm converges not for all dictionaries and initial vectors. We also study the R-greedy algorithm, which, along with the X-greedy algorithm, is a generalization of the simple greedy algorithm in Hilbert space. We prove its convergence for a certain class of Banach spaces. In particular, this class contains, the spaces lp,p≥ 2.
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