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Algebra i Analiz, 2016, Volume 28, Issue 6, Pages 20–69 (Mi aa1513)  
This article is cited in 11 scientific papers (total in 11 papers)

Research Papers

Approximation by sums of ridge functions with fixed directions

V. E. Ismailov

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan
Full-text PDF (410 kB) Citations (11)
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Abstract: The paper contains a survey of some results about approximation of functions of several variables by sums of ridge functions with fixed directions. Also, some new theorems are proved, both for uniform approximation and for approximation in $L_2$ . These theorems generalize some results by the author known previously. The paper is finished by the study of the role of ridge functions in a problem of approximation by neural networks.
Keywords: Ridge function, best approximation, superposition, cycle, path, neural network.
Funding agency Grant number
Science Development Foundation under the President of the Republic of Azerbaijan EIF-2013-9(15)-46/11/1
Received: 08.02.2015
English version:
St. Petersburg Mathematical Journal, 2017, Volume 28, Issue 6, Pages 741–772
DOI: https://doi.org/10.1090/spmj/1471
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. E. Ismailov, “Approximation by sums of ridge functions with fixed directions”, Algebra i Analiz, 28:6 (2016), 20–69; St. Petersburg Math. J., 28:6 (2017), 741–772
Citation in format AMSBIB
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\vol 28
\issue 6
\pages 20--69
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\pages 741--772
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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    Abstract page:392
    Full-text PDF :98
    References:58
    First page:38
     
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