On the generalized Approximate Weak Chebyshev Greedy Algorithm

In this paper we study greedy approximation in Banach spaces. We discuss a modification of the Weak Chebyshev Greedy Algorithm, in which steps of the algorithm can be executed imprecisely. Such inaccuracies are represented by both absolute and relative errors, which provides more flexibility for num...

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Bibliographic Details
Published in:arXiv.org
Main Author: Dereventsov, Anton
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 29.09.2016
Subjects:
Algorithms
Banach spaces
Chebyshev approximation
Convergence
Error analysis
Greedy algorithms
ISSN:2331-8422
Online Access:Get full text
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Summary:In this paper we study greedy approximation in Banach spaces. We discuss a modification of the Weak Chebyshev Greedy Algorithm, in which steps of the algorithm can be executed imprecisely. Such inaccuracies are represented by both absolute and relative errors, which provides more flexibility for numerical applications. We obtain the conditions on the error parameters that guarantee convergence of the algorithm in all uniformly smooth Banach spaces and prove that these conditions are sharp. Additionally, we discuss the conditions that need to be imposed on a Banach space to guarantee convergence of the Chebyshev Greedy Algorithm, and construct a smooth Banach space in which the algorithm diverges.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1603.09006