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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 504, Pages 47–50
DOI: https://doi.org/10.31857/S2686954322030110 (Mi danma263) 		 
MATHEMATICS

Solving nonlinear inverse problems based on the regularized modified Gauss–Newton method

V. V. Vasinab

a N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
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DOI: https://doi.org/10.31857/S2686954322030110
Abstract: A nonlinear operator equation is investigated in the case when the Hadamard correctness conditions are violated. A two-stage method is proposed for constructing a stable method for solving the equation. It includes modified Tikhonov regularization and a modified iterative Gauss–Newton process for approximating the solution of the regularized equation. The convergence of the iterations and the strong Fejér property of the process are proved. An order optimal estimate for the error of the two-stage method is established in the class of sourcewise representable functions.
Keywords: ill-posed problem, modified Tikhonov method, modified Gauss–Newton method.
Funding agency Grant number
Russian Science Foundation 18-11-00024-П
This work was supported in part by the Russian Science Foundation, project no. 18-11-00024-P.
Received: 11.01.2022
Revised: 28.03.2022
Accepted: 01.04.2022
English version:
Doklady Mathematics, 2022, Volume 105, Issue 3, Pages 175–177
DOI: https://doi.org/10.1134/S1064562422030103
Bibliographic databases:
Document Type: Article
UDC: 517.988.68
Language: Russian
Citation: V. V. Vasin, “Solving nonlinear inverse problems based on the regularized modified Gauss–Newton method”, Dokl. RAN. Math. Inf. Proc. Upr., 504 (2022), 47–50; Dokl. Math., 105:3 (2022), 175–177
Citation in format AMSBIB
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\by V.~V.~Vasin
\paper Solving nonlinear inverse problems based on the regularized modified Gauss--Newton method
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 504
\pages 47--50
\mathnet{http://mi.mathnet.ru/danma263}
\crossref{https://doi.org/10.31857/S2686954322030110}
\elib{https://elibrary.ru/item.asp?id=48649155}
\transl
\jour Dokl. Math.
\yr 2022
\vol 105
\issue 3
\pages 175--177
\crossref{https://doi.org/10.1134/S1064562422030103}
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