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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 10, Pages 1637–1645
DOI: https://doi.org/10.7868/S0044466915100051 (Mi zvmmf10277) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Iterative methods of stochastic approximation for solving non-regular nonlinear operator equations

A. B. Bakushinskiia, M. Yu. Kokurinb

a Institute of System Analysis, Russian Academy of Sciences, pr. 60-letiya Oktyabrya 9, Moscow, 117312, Russia
b Mari State University, pl. Lenina 1, Yoshkar-Ola, 424001, Russia
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DOI: https://doi.org/10.7868/S0044466915100051
Abstract: Iterative methods for solving non-regular nonlinear operator equations in a Hilbert space under random noise are constructed and examined. The methods use the averaging of the input data. It is not assumed that the noise dispersion is known. An iteratively regularized method of order zero for equations with monotone operators and iteratively regularized methods of the Gauss–Newton type for equations with arbitrary smooth operators are used as the basic procedures. It is shown that the generated approximations converge in the mean-square sense to the desired solution or stabilize (again in the mean-square sense) in a small neighborhood of the solution.
Key words: non-regular equation, nonlinear operator, iterative methods, iterative regularization, random errors, averaging, mean-square convergence, stability.
Received: 20.01.2015
Revised: 28.03.2015
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 10, Pages 1597–1605
DOI: https://doi.org/10.1134/S096554251510005X
Bibliographic databases:
Document Type: Article
UDC: 519.642.8
Language: Russian
Citation: A. B. Bakushinskii, M. Yu. Kokurin, “Iterative methods of stochastic approximation for solving non-regular nonlinear operator equations”, Zh. Vychisl. Mat. Mat. Fiz., 55:10 (2015), 1637–1645; Comput. Math. Math. Phys., 55:10 (2015), 1597–1605
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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