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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 9, Pages 1486–1493 (Mi zvmmf243)  
This article is cited in 10 scientific papers (total in 10 papers)

The method of determining all real nonmultiple roots of systems of nonlinear equations

V. Yu. Semënov

NPO Delta, ul. Akademika Krymskogo 27, Kiev, 03142, Ukraine
Full-text PDF (1251 kB) Citations (10)
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Abstract: A method for determining all nonmultiple roots of the system of nonlinear equations in an $n$-dimensional parallelepiped is proposed. The main idea of the method is that the original set, in which the roots are sought, is divided into subsets where either the system of equations does not have solutions or its Jacobian matrix is nonsingular. A partition algorithm is presented and its convergence is proved. The application of the method is demonstrated using several examples.
Key words: system of nonlinear equations, root localization, Jacobian matrix, Newton method.
Received: 19.06.2006
English version:
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Issue 9, Pages 1428–1434
DOI: https://doi.org/10.1134/S0965542507090047
Bibliographic databases:
Document Type: Article
UDC: 519.615.2
Language: Russian
Citation: V. Yu. Semënov, “The method of determining all real nonmultiple roots of systems of nonlinear equations”, Zh. Vychisl. Mat. Mat. Fiz., 47:9 (2007), 1486–1493; Comput. Math. Math. Phys., 47:9 (2007), 1428–1434
Citation in format AMSBIB
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\by V.~Yu.~Sem\"enov
\paper The method of determining all real nonmultiple roots of systems of nonlinear equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 9
\pages 1486--1493
\mathnet{http://mi.mathnet.ru/zvmmf243}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2387657}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 9
\pages 1428--1434
\crossref{https://doi.org/10.1134/S0965542507090047}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34848886328}
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    Full-text PDF :313
    References:49
    First page:3
     
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