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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 5, Pages 784–795 (Mi zvmmf288)  

This article is cited in 4 scientific papers (total in 4 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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:5, 748–759

Bibliographic databases:

Document Type: Article
UDC: 519.615.5
Received: 25.10.2006

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{http://www.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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34249686457}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Yu. Erina, A. F. Izmailov, “Defining systems and Newton-like methods for finding singular solutions to nonlinear boundary value problems”, Comput. Math. Math. Phys., 47:9 (2007), 1409–1427  mathnet  crossref  mathscinet
    2. A. F. Izmailov, E. I. Uskov, “On the application of Newton-type methods to Fritz John optimality conditions”, Comput. Math. Math. Phys., 51:7 (2011), 1114–1127  mathnet  crossref  mathscinet  isi
    3. Boik R.J., “Model-Based Principal Components of Correlation Matrices”, J. Multivar. Anal., 116 (2013), 310–331  crossref  mathscinet  zmath  isi  elib  scopus
    4. A. F. Izmailov, “New implementations of the 2-factor method”, Comput. Math. Math. Phys., 55:6 (2015), 922–934  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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