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 Mat. Tr., 2018, Volume 21, Number 2, Pages 117–135 (Mi mt341)

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.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 02.A03.21.0006 Russian Foundation for Basic Research 16-51-50064_ßÔ_à Ural Branch of the Russian Academy of Sciences 18-1-1-8 The work was supported by the Government of the Russian Federation (contract 02. A03.21.0006), the Russian Foundation for Basic Research (project 16-51-50064), and, partially, by a Program of the Ural Branch of RAS (project 18-1-1-8).

DOI: https://doi.org/10.17377/mattrudy.2018.21.205

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English version:
Siberian Advances in Mathematics, 2019, 29, 217–229

UDC: 517.988.68

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

Citation in format AMSBIB
\Bibitem{Vas18} \by V.~V.~Vasin \paper Iterative processes for ill-posed problems with a monotone operator \jour Mat. Tr. \yr 2018 \vol 21 \issue 2 \pages 117--135 \mathnet{http://mi.mathnet.ru/mt341} \crossref{https://doi.org/10.17377/mattrudy.2018.21.205} \transl \jour Siberian Adv. Math. \yr 2019 \vol 29 \pages 217--229 \crossref{https://doi.org/10.3103/S1055134419030076} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85071447984}