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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2004, Volume 7, Number 1, Pages 1–12 (Mi sjvm140)  

This article is cited in 1 scientific paper (total in 1 paper)

Continuous methods for stable approximation of solutions to nonlinear equations in the Banach space based on the regularized Newton–Kantarovich scheme

A. B. Bakushinskiia, M. Yu. Kokurinb

a Institute of Systems Analysis, Russian Academy of Sciences
b Mari State University
Full-text PDF (719 kB) Citations (1)
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Abstract: We propose and study a class of methods for approximation of solutions to nonlinear equations with smooth operators in a Banach space, when the operators are approximately given and their derivatives are not regular. The construction of the presented methods is connected with the operator differential equation obtained by linearization of the original equation using the Newton–Kantorovich scheme and various ways of its regularization. When the initial discrepancy possesses a sourcewise representation, we establish estimates for the approximation errors.
Key words: nonlinear equation, irregular equation, Banach space, operator differential equation, regularization, stopping rule.
Received: 25.02.2003
Revised: 01.04.2003
Bibliographic databases:
UDC: 517.988.68
Language: Russian
Citation: A. B. Bakushinskii, M. Yu. Kokurin, “Continuous methods for stable approximation of solutions to nonlinear equations in the Banach space based on the regularized Newton–Kantarovich scheme”, Sib. Zh. Vychisl. Mat., 7:1 (2004), 1–12
Citation in format AMSBIB
\Bibitem{BakKok04}
\by A.~B.~Bakushinskii, M.~Yu.~Kokurin
\paper Continuous methods for stable approximation of solutions to nonlinear equations in the Banach space based on the regularized Newton--Kantarovich scheme
\jour Sib. Zh. Vychisl. Mat.
\yr 2004
\vol 7
\issue 1
\pages 1--12
\mathnet{http://mi.mathnet.ru/sjvm140}
\zmath{https://zbmath.org/?q=an:1052.65053}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Sibirskii Zhurnal Vychislitel'noi Matematiki
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