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This article is cited in 4 scientific papers (total in 4 papers)
Iterative processes for ill-posed problems with a monotone operator
V. V. Vasinab a Krasovskiĭ Institute of Mathematics, Ekaterinburg, 620990 Russia
b Ural Federal University, Ekaterinburg, 620000 Russia
Abstract:
We consider the problem on constructing a stable approximate solution of an inverse problem formulated as a nonlinear irregular equation with a monotone operator. We suggest a two-stage method based on Lavrentiev's regularization scheme and iterative approximation with the use of either modified Newton's method or a regularized $\kappa$-process. We prove that the iterative processes converge and the iterations possess the Fejér property. We show that our method generates a regularization algorithm under a certain adjustment of control parameters. On the set of source-like representable solutions, we find an optimal-order error estimate for the algorithm.
Key words:
ill-posed problem, Lavrentiev's regularization scheme, Newton's method, $\kappa$-processes, error estimation.
Received: 18.12.2017
Citation:
V. V. Vasin, “Iterative processes for ill-posed problems with a monotone operator”, Mat. Tr., 21:2 (2018), 117–135; Siberian Adv. Math., 29 (2019), 217–229
Linking options:
https://www.mathnet.ru/eng/mt341 https://www.mathnet.ru/eng/mt/v21/i2/p117
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