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

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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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Linking options:

https://www.mathnet.ru/eng/aa1513

https://www.mathnet.ru/eng/aa/v28/i6/p20

This publication is cited in the following 11 articles:

I. G. Kazantsev, R. Z. Turebekov, M. A. Sultanov, “Modeling regular textures in images using the Radon transform”, J. Appl. Industr. Math., 15:2 (2021), 223–233
P. Jorgensen, D. E. Stewart, “Approximation properties of ridge functions and extreme learning machines”, SIAM J. Math. Data Sci., 3:3 (2021), 815–832
R. A. Aliev, A. A. Asgarova, V. E. Ismailov, “On the representation by bivariate ridge functions”, Ukr. Math. J., 73:5 (2021), 675–685
A. M. B. Babayev, I. K. Maharov, “On the error of approximation by rbf neural networks with two hidden nodes”, Proc. Inst. Math. Mech., 47:2 (2021), 226–231
R. A. Aliev, A. A. Asgarova, V. E. Ismailov, “On the representation by bivariate ridge functions”, Ukr. Mat. Zhurn., 73:5 (2021), 579
R. A. Aliev, V. E. Ismailov, “A representation problem for smooth sums of ridge functions”, J. Approx. Theory, 257 (2020), 105448
A. V. Chernov, “Gaussian functions combined with Kolmogorov's theorem as applied to approximation of functions of several variables”, Comput. Math. Math. Phys., 60:5 (2020), 766–782
R. A. Aliev, A. A. Asgarova, V. E. Ismailov, “A note on continuous sums of ridge functions”, J. Approx. Theory, 237 (2019), 210–221
R. A. Aliev, A. A. Asgarova, V. E. Ismailov, “On the Holder continuity in ridge function representation”, Proc. Inst. Math. Mech., 45:1 (2019), 31–40
N. J. Guliyev, V. E. Ismailov, “On the approximation by single hidden layer feedforward neural networks with fixed weights”, Neural Netw., 98 (2018), 296–304
N. G. Polson, V. Rockova, “Posterior concentration for sparse deep learning”, NIPS 2018, Advances in Neural Information Processing Systems, 31, eds. S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, R. Garnett, 2018

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	433
Full-text PDF :	106
References:	69
First page:	39

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