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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2004, Volume 7, Number 1, Pages 1–12
(Mi sjvm140)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/sjvm140 https://www.mathnet.ru/eng/sjvm/v7/i1/p1
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Abstract page: | 262 | Full-text PDF : | 101 | References: | 49 |
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