Greedy-type approximation in Banach spaces and applications
type: Item
instance of: scholarly article
title: Greedy-type approximation in Banach spaces and applications
zbMATH Open document ID: 1070.41018
published in: Constructive Approximation
publication date: 2005-04-15T00:00:00Z
review text: This paper is based on the author's paper [Adv. Comput. Math. 14, No. 3, 277--292 (2001; Zbl 0988.41022)], where two greedy-type approximations methods, the Weak Chebyshev Greedy Algorithm (WCGA) and the Weak Relaxed Greedy Algorithm (WRGA), have been introduced. Here modifications of the WCGA and WRGA that are motivated by numerical applications are studied. The author develops the theory of the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) and the Approximate Weak Relaxed Greedy Algorithm (AWRGA) in general uniformly smooth Banach spaces. He also gives two applications of greedy type algorithms: (i) A constructive method for \(m\)-term trigonometric approximation in the uniform norm is obtained; (ii) A deterministic sets of points with small \(L_{p}\) discrepancy and with small symmetrized \(L_{p}\) discrepancy are constructed.
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 42A10
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 2157508
zbMATH Keywords: greedy approximation
zbMATH Keywords: greedy algorithms
zbMATH Keywords: uniformly smooth Banach spaces
zbMATH Keywords: trigonometric approximation
zbMATH Keywords: discrepancy
author: V. N. Temlyakov
reviewed by: Saulius Norvidas
MaRDI profile type: Publication
full work available at URL: s00365-004-0565-6
OpenAlex ID: W1972937048
DOI: 10.1007/S00365-004-0565-6
description: scientific article; zbMATH DE number 2157508