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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2004, Volume 7, Number 3, Pages 249–260
(Mi sjvm161)
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This article is cited in 1 scientific paper (total in 1 paper)
Refinement of convergence conditions of the Chebyshev method
M. I. Nechepurenko Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences
Abstract:
The iterative Chebyshev method of an approximate solution of equations of the form $F(x)=0$ in Banach
spaces is studied, assuming that $F''$ satisfies the Lipschitz condition. Accurate (attainable) estimates of the
domains of existence and uniqueness of solution, non-refinable conditions of existence and convergence of the
Chebyshev method as well as asymptotic estimates of the rate of convergence have been obtained.
Key words:
equations in Banach spaces, iterative Chebyshev method, accurate estimates, domains of existence and uniqueness.
Received: 31.03.2003 Revised: 25.12.2003
Citation:
M. I. Nechepurenko, “Refinement of convergence conditions of the Chebyshev method”, Sib. Zh. Vychisl. Mat., 7:3 (2004), 249–260
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https://www.mathnet.ru/eng/sjvm161 https://www.mathnet.ru/eng/sjvm/v7/i3/p249
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Abstract page: | 555 | Full-text PDF : | 287 | References: | 40 |
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