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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, Number 8, Pages 3–11
(Mi ivm9138)
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This article is cited in 6 scientific papers (total in 6 papers)
Iteratively regularized Gauss–Newton method for operator equations with normally solvable derivative at the solution
A. B. Bakushinskiia, M. Yu. Kokurinb a Federal Research Center "Information Science and Control", Institute for Systems Analysis, Russian Academy of Sciences, 9 60-Letiya Oktyabrya Ave., Moscow, 117312 Russia
b Mari State University, 1 Lenin sq., Ioshkar Ola, 424001 Russia
Abstract:
We study the iteratively regularized Gauss–Newton method in a Hilbert space for solving irregular nonlinear equations with smooth operators having normally solvable derivatives at the solution. We consider both a priori and a posteriori stopping criterions for the iterations and establish accuracy estimates for resulting approximations. In the case where the a priori stopping rule is used, the accuracy of approximations arises to be proportional to the error level in input data. The latter result generalizes well-known estimates of this kind obtained for linear equations with normally solvable operators.
Keywords:
operator equation, irregular operator, Hilbert space, normally solvable operator, Gauss–Newton method, iterative regularization, stopping rule, accuracy estimate.
Received: 01.01.2015
Citation:
A. B. Bakushinskii, M. Yu. Kokurin, “Iteratively regularized Gauss–Newton method for operator equations with normally solvable derivative at the solution”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 8, 3–11; Russian Math. (Iz. VUZ), 60:8 (2016), 1–8
Linking options:
https://www.mathnet.ru/eng/ivm9138 https://www.mathnet.ru/eng/ivm/y2016/i8/p3
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Abstract page: | 308 | Full-text PDF : | 112 | References: | 31 | First page: | 15 |
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