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
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.
nonlinear equation, singular solution, defining system, regularity, nondegeneracy, Gauss–Newton method.
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Computational Mathematics and Mathematical Physics, 2007, 47:5, 748–759
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
\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.
\jour Comput. Math. Math. Phys.
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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
Boik R.J., “Model-Based Principal Components of Correlation Matrices”, J. Multivar. Anal., 116 (2013), 310–331
A. F. Izmailov, “New implementations of the 2-factor method”, Comput. Math. Math. Phys., 55:6 (2015), 922–934
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