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Matematicheskie Zametki, 2007, Volume 82, Issue 3, Pages 373–382
DOI: https://doi.org/10.4213/mzm3852 (Mi mzm3852) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On n-Term Approximation with Positive Coefficients

E. D. Livshits

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (491 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm3852
Abstract: In this paper, we consider algorithms for constructing n-terms approximations with nonnegative coefficients. The convergence theorem is proved for a “positive” analog of the Pure Greedy Algorithm. We establish a condition on the sequence of weakness coefficients which is sufficient for the convergence of the Positive Weak Greedy Algorithm. This condition is also necessary for the class of monotone sequences.
Keywords: polynomial approximation, greedy algorithm, approximation theory, positive dictionary, redundant system.
Received: 03.11.2006
Revised: 29.01.2007
English version:
Mathematical Notes, 2007, Volume 82, Issue 3, Pages 332–340
DOI: https://doi.org/10.1134/S0001434607090052
Bibliographic databases:
UDC: 517.518.8
Language: Russian
Citation: E. D. Livshits, “On n-Term Approximation with Positive Coefficients”, Mat. Zametki, 82:3 (2007), 373–382; Math. Notes, 82:3 (2007), 332–340
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    1. M. A. Valov, “Konicheskii dualnyi zhadnyi algoritm v banakhovom prostranstve”, Matem. zametki, 117:4 (2025), 485–493  mathnet  crossref
    2. M. A. Valov, “Conical Greedy Algorithm”, Math. Notes, 112:2 (2022), 171–176  mathnet  crossref  crossref
    3. P. A. Borodin, “Example of Divergence of a Greedy Algorithm with Respect to an Asymmetric Dictionary”, Math. Notes, 109:3 (2021), 379–385  mathnet  crossref  crossref  mathscinet  isi
    4. P. A. Borodin, “Greedy approximation by arbitrary set”, Izv. Math., 84:2 (2020), 246–261  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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