On the Convergence of a Weak Greedy Algorithm for the Multivariate Haar Basis

We define a family of weak thresholding greedy algorithms for the multivariate Haar basis for L 1 [0,1] d ( d ≥1). We prove convergence and uniform boundedness of the weak greedy approximants for all f ∈ L 1 [0,1] d .

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Bibliographic Details
Published in:Constructive approximation Vol. 39; no. 2; pp. 343 - 366
Main Authors: Dilworth, S. J., Gogyan, S., Kutzarova, Denka
Format: Journal Article
Language:English
Published: Boston Springer US 01.04.2014
Subjects:
Analysis
Mathematics
Mathematics and Statistics
Numerical Analysis
Greedy algorithms
Multivariate Haar system
Multivariate Haar wavelet
42A10
Branch-greedy
41A65
46B20
Thresholding greedy algorithm
Weak thresholding
Nonlinear approximation
ISSN:0176-4276, 1432-0940
Online Access:Get full text
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Summary:We define a family of weak thresholding greedy algorithms for the multivariate Haar basis for L 1 [0,1] d ( d ≥1). We prove convergence and uniform boundedness of the weak greedy approximants for all f ∈ L 1 [0,1] d .
ISSN:0176-4276
1432-0940
DOI:10.1007/s00365-013-9212-4