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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Vydané v:Constructive approximation Ročník 39; číslo 2; s. 343 - 366
Hlavní autori: Dilworth, S. J., Gogyan, S., Kutzarova, Denka
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Boston Springer US 01.04.2014
Predmet:
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
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Popis
Shrnutí: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