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Izvestiya: Mathematics, 2009, Volume 73, Issue 6, Pages 1197–1215
DOI: https://doi.org/10.1070/IM2009v073n06ABEH002478 (Mi im2742) 		 
This article is cited in 19 scientific papers (total in 19 papers)

Lower bounds for the rate of convergence of greedy algorithms

E. D. Livshits

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (309 kB) Citations (19)
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DOI: https://doi.org/10.1070/IM2009v073n06ABEH002478
Abstract: We obtain a lower bound for the rate of convergence of a pure greedy algorithm in the spaces $\mathcal A_0(\mathcal D)$ and $\mathcal A_1(\mathcal D)$, and this bound turns out to be very close to the best known upper bound. We also obtain a precise lower bound for the rate of convergence of the orthogonal greedy algorithm in the space $\mathcal A_0(\mathcal D)$.
Keywords: pure greedy algorithm, best $n$-term approximation, interpolation classes, rate of convergence.
Received: 02.11.2007
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2009, Volume 73, Issue 6, Pages 125–144
DOI: https://doi.org/10.4213/im2742
Bibliographic databases:
UDC: 517.518.8+519.651.3
MSC: Primary 41A25; Secondary 41A65, 65D15
Language: English
Original paper language: Russian
Citation: E. D. Livshits, “Lower bounds for the rate of convergence of greedy algorithms”, Izv. RAN. Ser. Mat., 73:6 (2009), 125–144; Izv. Math., 73:6 (2009), 1197–1215
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v73/i6/p125
    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:597
    Russian version PDF:235
    English version PDF:34
    References:58
    First page:13
     
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