Lebesgue constants for Chebyshev thresholding greedy algorithms

We investigate the efficiency of Chebyshev Thresholding Greedy Algorithm (CTGA) for an n -term approximation with respect to general bases in a Banach space. We show that the convergence property of CTGA is better than TGA for non-quasi-greedy bases. Then we determine the exact rate of the Lebesgue...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2018; no. 1; pp. 1 - 23
Main Authors: Shao, Chunfang, Ye, Peixin
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 27.04.2018
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Banach spaces
Chebyshev approximation
Chebyshev thresholding greedy algorithm
Convergence
Convergence property
Greedy algorithms
Lebesgue constants
Mathematics
Mathematics and Statistics
Parameter estimation
Quasi-greedy basis
Summing basis
Trigonometric system
41A46
Trigonometric system
41A25
Chebyshev thresholding greedy algorithm
Convergence property
42A10
Quasi-greedy basis
Summing basis
Lebesgue constants
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:We investigate the efficiency of Chebyshev Thresholding Greedy Algorithm (CTGA) for an n -term approximation with respect to general bases in a Banach space. We show that the convergence property of CTGA is better than TGA for non-quasi-greedy bases. Then we determine the exact rate of the Lebesgue constants L n ch for two examples of such bases: the trigonometric system and the summing basis. We also establish the upper estimates for L n ch with respect to general bases in terms of quasi-greedy parameter, democracy parameter and A-property parameter. These estimates do not involve an unconditionality parameter, therefore they are better than those of TGA. In particular, for conditional quasi-greedy bases, a faster convergence rate is obtained.
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content type line 14
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-018-1694-y