Relaxation in greedy approximation
type: Item
instance of: scholarly article
title: Relaxation in greedy approximation
zbMATH Open document ID: 1167.41006
published in: Constructive Approximation
publication date: 2008-09-12T00:00:00Z
review text: The author studies greedy algorithms in a Banach space from the point of view of convergence and rate of convergence. There are two well-studied approximation methods: the Weak Chebyshev Greedy Algorithm (WCGA) and the Weak Relaxed Greedy Algorithm (WRGA). The WRGA is simpler than the WCGA in the sense of computational complexity. However, the WRGA has limited applicability. It converges only for elements of the closure of the convex hull of a dictionary. In this paper he studies algorithms that combine good features of both algorithms, the WRGA and the WCGA. In the construction of such algorithms he uses different forms of relaxation. First results on such algorithms have been obtained in a Hilbert space by A. Barron, A. Cohen, W. Dahmen, and R. DeVore. Their paper was a motivation for the research reported here.
reviewed by: Francisco Pérez Acosta
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 5343897
zbMATH Keywords: algorithms
zbMATH Keywords: greedy algorithms
zbMATH Keywords: Banach space
zbMATH Keywords: convergence
zbMATH Keywords: rate of convergence
zbMATH Keywords: approximation methods
zbMATH Keywords: forms of relaxation
author: V. N. Temlyakov
MaRDI profile type: Publication
full work available at URL: s00365-006-0652-5
OpenAlex ID: W2027161466
DOI: 10.1007/S00365-006-0652-5
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description: scientific article; zbMATH DE number 5343897