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 Computer Research and Modeling: Year: Volume: Issue: Page: Find

 Computer Research and Modeling, 2015, Volume 7, Issue 4, Pages 835–863 (Mi crm263)

NUMERICAL METHODS AND THE BASIS FOR THEIR APPLICATION

The correction to Newton's methods of optimization

A. B. Sviridenko

FSEI of HPE «Kuban State University» branch in Novorossiysk, Geroev-Desantnikov street 87, Russia

Abstract: An approach to the decrease of norm of the correction in Newton's methods of optimization, based on the Cholesky's factorization is presented, which is based on the integration with the technique of the choice of leading element of algorithm of linear programming as a method of solving the system of equations. We investigate the issues of increasing of the numerical stability of the Cholesky's decomposition and the Gauss' method of exception.

Keywords: correction, algorithm, Newton's methods of optimization, Cholesky's decomposition, Gauss' method of exception, linear programming, numerical stability, integration.

DOI: https://doi.org/10.20537/2076-7633-2015-7-4-835-863

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Full text: http://crm.ics.org.ru/.../2343
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UDC: 519.85
Revised: 23.03.2015

Citation: A. B. Sviridenko, “The correction to Newton's methods of optimization”, Computer Research and Modeling, 7:4 (2015), 835–863

Citation in format AMSBIB
\Bibitem{Svi15} \by A.~B.~Sviridenko \paper The correction to Newton's methods of optimization \jour Computer Research and Modeling \yr 2015 \vol 7 \issue 4 \pages 835--863 \mathnet{http://mi.mathnet.ru/crm263} \crossref{https://doi.org/10.20537/2076-7633-2015-7-4-835-863}