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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 5, Pages 784–795 (Mi zvmmf288)  
This article is cited in 7 scientific papers (total in 7 papers)

The Gauss–Newton method for finding singular solutions to systems of nonlinear equations

M. Yu. Erinaa, A. F. Izmailovb

a Dorodnitsyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
Full-text PDF (1379 kB) Citations (7)
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Abstract: An approach to the computation of singular solutions to systems of nonlinear equations is proposed. It consists in the construction of an (overdetermined) defining system to which the Gauss–Newton method is applied. This approach leads to completely implementable local algorithms without nondeterministic elements. Under fairly weak conditions, these algorithms have locally superlinear convergence.
Key words: nonlinear equation, singular solution, defining system, regularity, nondegeneracy, Gauss–Newton method.
Received: 25.10.2006
English version:
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Issue 5, Pages 748–759
DOI: https://doi.org/10.1134/S096554250705003X
Bibliographic databases:
Document Type: Article
UDC: 519.615.5
Language: Russian
Citation: M. Yu. Erina, A. F. Izmailov, “The Gauss–Newton method for finding singular solutions to systems of nonlinear equations”, Zh. Vychisl. Mat. Mat. Fiz., 47:5 (2007), 784–795; Comput. Math. Math. Phys., 47:5 (2007), 748–759
Citation in format AMSBIB
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\by M.~Yu.~Erina, A.~F.~Izmailov
\paper The Gauss--Newton method for finding singular solutions to systems of nonlinear equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 5
\pages 784--795
\mathnet{http://mi.mathnet.ru/zvmmf288}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2378658}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 5
\pages 748--759
\crossref{https://doi.org/10.1134/S096554250705003X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34249686457}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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