ISSN 2079-6900 (Print) 
ISSN 2587-7496 (Online)

Middle Volga Mathematical Society Journal

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A continuous analogue of modified Newton method

I. P. Ryazantseva1, O. Yu. Bubnova2

AnnotationIn the iterative Newton method we invert derivative of operator of equation for every step. In the modified Newton method we findinverse of derivative of operator only at initial point of iterative process. Then amount of calculations decreases and convergence speed falls. Continuous analog of Newton method is known. We construct the continuous analog of the modified Newton method for equation with strongly monotone operator in this note. We obtain sufficient conditions of strong convergence in Hilbert space for propose method.
KeywordsHilbert space, strictly monotone operator, Frechet derivative, continuous method, operator of contraction, convergence

1Professor of Applid Mathematics Chair, Nizhny Novgorod State Tehnical University after R.E. Alekseev, Nizhny Novgorod;

2Associate Professor of Department of Mathematics, Computer Science and Information Technology, Nizhny Novgorod Academy of the Ministry of Internal Affairs of Russia, Nizhny Novgorod;

Citation: I. P. Ryazantseva, O. Yu. Bubnova, "[A continuous analogue of modified Newton method]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,18:2 (2016) 67–71 (In Russian)