Greedy Algorithms with Prescribed Coefficients

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.