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

S. J. Dilworth; S. Gogyan; Denka Kutzarova

doi:10.1007/s00365-013-9212-4

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

S. J. Dilworth, S. Gogyan, Denka Kutzarova

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	343-366
Number of pages	24
Journal	Constructive Approximation
Volume	39
Issue number	2
DOIs	https://doi.org/10.1007/s00365-013-9212-4
State	Published - Apr 2014

Keywords

Branch-greedy
Greedy algorithms
Multivariate Haar system
Multivariate Haar wavelet
Nonlinear approximation
Thresholding greedy algorithm
Weak thresholding

ASJC Scopus subject areas

Analysis
General Mathematics
Computational Mathematics

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10.1007/s00365-013-9212-4

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title = "On the Convergence of a Weak Greedy Algorithm for the Multivariate Haar Basis",

abstract = "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.",

keywords = "Branch-greedy, Greedy algorithms, Multivariate Haar system, Multivariate Haar wavelet, Nonlinear approximation, Thresholding greedy algorithm, Weak thresholding",

author = "Dilworth, {S. J.} and S. Gogyan and Denka Kutzarova",

note = "Funding Information: The first author was partially supported by NSF grant DMS1101490. All authors were participants at the NSF supported Workshop in Analysis and Probability at Texas A&M University in 2011. ",

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AU - Dilworth, S. J.

AU - Gogyan, S.

AU - Kutzarova, Denka

N1 - Funding Information: The first author was partially supported by NSF grant DMS1101490. All authors were participants at the NSF supported Workshop in Analysis and Probability at Texas A&M University in 2011.

PY - 2014/4

Y1 - 2014/4

N2 - 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.

AB - 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.

KW - Branch-greedy

KW - Greedy algorithms

KW - Multivariate Haar system

KW - Multivariate Haar wavelet

KW - Nonlinear approximation

KW - Thresholding greedy algorithm

KW - Weak thresholding

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JO - Constructive Approximation

JF - Constructive Approximation

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

Abstract

Keywords

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