RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Tr.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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_ЯФ_а
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

Full text: PDF file (244 kB)
References: PDF file   HTML file

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

UDC: 517.988.68
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

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}


Linking options:
  • http://mi.mathnet.ru/eng/mt341
  • http://mi.mathnet.ru/eng/mt/v21/i2/p117

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математические труды Siberian Advances in Mathematics
    Number of views:
    This page:126
    Full text:22
    References:9
    First page:9

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020