Efficiency of weak greedy algorithms for m-term approximations

We investigate the efficiency of weak greedy algorithms for m-term expansional approximation with respect to quasi-greedy bases in general Banach spaces.We estimate the corresponding Lebesgue constants for the weak thresholding greedy algorithm（WTGA） and weak Chebyshev thresholding greedy algorithm....

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Bibliographic Details
Published in:Science China. Mathematics Vol. 59; no. 4; pp. 697 - 714
Main Authors: Ye, PeiXin, Wei, XiuJie
Format: Journal Article
Language:English
Published: Beijing Science China Press 01.04.2016
Subjects:
Applications of Mathematics
Approximation
Chebyshev approximation
Computational efficiency
Computing time
Constants
Functions (mathematics)
Greedy algorithms
Mathematical analysis
Mathematics
Mathematics and Statistics
TGA
一致有界
切比雪夫
勒贝格常数
巴拿赫空间
贪婪算法
贪心算法
逼近
quasi-greedy bases
41A46
46B15
41A25
weak thresholding greedy algorithm
term approximation
Lebesgue constants
weak Chebyshev greedy algorithm
ISSN:1674-7283, 1869-1862
Online Access:Get full text
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Summary:We investigate the efficiency of weak greedy algorithms for m-term expansional approximation with respect to quasi-greedy bases in general Banach spaces.We estimate the corresponding Lebesgue constants for the weak thresholding greedy algorithm（WTGA） and weak Chebyshev thresholding greedy algorithm.Then we discuss the greedy approximation on some function classes.For some sparse classes induced by uniformly bounded quasi-greedy bases of L_p,12 the WCGA is better than the TGA.
Bibliography:m-term approximation Lebesgue constants weak thresholding greedy algorithm weak Chebyshev greedy algorithm quasi-greedy bases
We investigate the efficiency of weak greedy algorithms for m-term expansional approximation with respect to quasi-greedy bases in general Banach spaces.We estimate the corresponding Lebesgue constants for the weak thresholding greedy algorithm（WTGA） and weak Chebyshev thresholding greedy algorithm.Then we discuss the greedy approximation on some function classes.For some sparse classes induced by uniformly bounded quasi-greedy bases of L_p,12 the WCGA is better than the TGA.
11-5837/O1
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-015-5106-1