Geodesic
Regularized continuous analog of the Newton method for monotone equations in the Hilbert space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2016), pp. 53-67

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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
Mots-clés : convergence. 
@article{IVM_2016_11_a4,
     author = {I. P. Ryazantseva},
     title = {Regularized continuous analog of the {Newton} method for monotone equations in the {Hilbert} space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {53--67},
     publisher = {mathdoc},
     number = {11},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_11_a4/}
}
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I. P. Ryazantseva. Regularized continuous analog of the Newton method for monotone equations in the Hilbert space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2016), pp. 53-67. http://geodesic.mathdoc.fr/item/IVM_2016_11_a4/