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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 11, Pages 1827–1834
DOI: https://doi.org/10.7868/S0044466915110022 (Mi zvmmf10294) 		 
This article is cited in 7 scientific papers (total in 7 papers)

A numerical method for solving systems of nonlinear equations

A. A. Abramovab, L. F. Yukhnocd

a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia
b Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
c Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia
d National Research Nuclear University, Kashirskoe sh. 31, Moscow, 115409, Russia
Full-text PDF (98 kB) Citations (7)
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DOI: https://doi.org/10.7868/S0044466915110022
Abstract: Under certain conditions on nonlinear equations in a real finite-dimensional space, a numerical method for solving such equations is proposed. The method is based on the use of an auxiliary differential equation. A fairly rough approximate solution to this equation can be refined by applying Newton's method to the original problem. The result produced by the auxiliary equation is automatically a good initial approximation for Newton’s method. This combination ensures that the original problem can be solved to the required accuracy starting from any initial approximation.
Key words: system of nonlinear equations, Newton's method, Hadamard existence theorem.
Received: 21.04.2015
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 11, Pages 1794–1801
DOI: https://doi.org/10.1134/S0965542515110020
Bibliographic databases:
Document Type: Article
UDC: 519.624
MSC: 65H10
Language: Russian
Citation: A. A. Abramov, L. F. Yukhno, “A numerical method for solving systems of nonlinear equations”, Zh. Vychisl. Mat. Mat. Fiz., 55:11 (2015), 1827–1834; Comput. Math. Math. Phys., 55:11 (2015), 1794–1801
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:127
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