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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 11, Pages 53–67 (Mi ivm9175)  

Regularized continuous analog of the Newton method for monotone equations in the Hilbert space

I. P. Ryazantseva

R. E. Alekseev Nizhny Novgorod Technical University, 24 Minina str., Nizhny Novgorod, 603155 Russia

Abstract: We construct regularized continuous analog of the Newton method in the Hilbert space for nonlinear equation with Frechét differentiable and monotone operator. We obtain sufficient conditions of its strong convergence to normal solution of the given equation under approximate assignment of an operator and right-hand of an equation.

Keywords: Hilbert space, monotone operator, Newton method, continuous method, convergence.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:11, 45–57

Bibliographic databases:

UDC: 519.642
Received: 19.03.2015

Citation: I. P. Ryazantseva, “Regularized continuous analog of the Newton method for monotone equations in the Hilbert space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 11, 53–67; Russian Math. (Iz. VUZ), 60:11 (2016), 45–57

Citation in format AMSBIB
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\by I.~P.~Ryazantseva
\paper Regularized continuous analog of the Newton method for monotone equations in the Hilbert space
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 11
\pages 53--67
\mathnet{http://mi.mathnet.ru/ivm9175}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 11
\pages 45--57
\crossref{https://doi.org/10.3103/S1066369X16110050}
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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