This article is cited in 18 papers

Generalized Approximate Weak Greedy Algorithms

V. V. Galatenko^a, E. D. Livshits<sup>b

a</sup> M. V. Lomonosov Moscow State University
^b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We study generalized approximate weak greedy algorithms. The main difference of these algorithms from approximate weak greedy algorithms proposed by R. Gribonval and M. Nielsen consists in that errors in the calculation of the coefficients can be prescribed in terms of not only their relative values, but also their absolute values. We present conditions on the parameters of generalized approximate weak greedy algorithms which are sufficient for the expansions resulting from the use of this algorithm to converge to the expanded element. It is shown that these conditions cannot be essentially weakened. We also study some questions of the convergence of generalized approximate weak greedy expansions with respect to orthonormal systems.

UDC: 517.518+517.988+519.651

Received: 08.04.2004

DOI: 10.4213/mzm2581

 English version: Mathematical Notes, 2005, 78:2, 170–184

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