This article is cited in 4 papers

On $n$-Term Approximation with Positive Coefficients

E. D. Livshits

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In this paper, we consider algorithms for constructing $n$-terms approximations with nonnegative coefficients. The convergence theorem is proved for a “positive” analog of the Pure Greedy Algorithm. We establish a condition on the sequence of weakness coefficients which is sufficient for the convergence of the Positive Weak Greedy Algorithm. This condition is also necessary for the class of monotone sequences.

Keywords: polynomial approximation, greedy algorithm, approximation theory, positive dictionary, redundant system.

UDC: 517.518.8

Received: 03.11.2006
Revised: 29.01.2007

DOI: 10.4213/mzm3852

 English version: Mathematical Notes, 2007, 82:3, 332–340

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