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 Num. Meth. Prog., 2009, Volume 10, Issue 4, Pages 402–407 (Mi vmp395)

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Convergence of a continuous analog of Newton's method for solving nonlinear equations

T. Zhanlav, O. Chuluunbaatar

Joint Institute for Nuclear Research, Dubna, Moscow region

Abstract: The influence of the parameter in the continuous analog of Newton's method (CANM) on the convergence and on the convergence rate is studied. A $\tau$-region of convergence of CANM for both scalar equations and equations in a Banach space is obtained. Some almost optimal choices of the parameter are proposed. It is also shown that the well-known higher order convergent iterative methods lead to the CANM with an almost optimal parameter. Several sufficient convergence conditions for these methods are obtained.

Keywords: iterative methods; rate of convergence; Newton-type methods; nonlinear equations.

Full text: PDF file (147 kB)
UDC: 519.6

Citation: T. Zhanlav, O. Chuluunbaatar, “Convergence of a continuous analog of Newton's method for solving nonlinear equations”, Num. Meth. Prog., 10:4 (2009), 402–407

Citation in format AMSBIB
\Bibitem{ZhaChu09} \by T.~Zhanlav, O.~Chuluunbaatar \paper Convergence of a continuous analog of Newton's method for solving nonlinear equations \jour Num. Meth. Prog. \yr 2009 \vol 10 \issue 4 \pages 402--407 \mathnet{http://mi.mathnet.ru/vmp395}