This article is cited in 2 papers

The convergence of the greedy algorithm with respect to the Haar system in the space $L_p(0,1)$

E. D. Livshits

Evernote Corporation

Abstract: The approximation properties of the $X$-greedy algorithm in the space $L_p(0,1)$ are studied. For $1<p<2$ estimates for the rate of convergence of the $X$-greedy algorithm with respect to the Haar system are obtained that are close to optimal.
Bibliography: 18 titles.

Keywords: greedy algorithms, $m$-term approximations, the Haar system, rate of convergence.

UDC: 517.518.8

MSC: Primary 41A65; Secondary 41A25, 41A30

Received: 29.12.2008 and 02.07.2009

DOI: 10.4213/sm7517

 English version: Sbornik: Mathematics, 2010, 201:2, 253–288

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