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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
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
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
Linking options:
https://www.mathnet.ru/eng/zvmmf10277 https://www.mathnet.ru/eng/zvmmf/v55/i10/p1637
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Abstract page: | 309 | Full-text PDF : | 77 | References: | 67 | First page: | 15 |
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