Geodesic
On the convergence rate of continuous Newton method
Contemporary Mathematics. Fundamental Directions, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), Tome 62 (2016), pp. 152-165 
A. Gibali; D. Shoikhet; N. Tarkhanov. On the convergence rate of continuous Newton method. Contemporary Mathematics. Fundamental Directions, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), Tome 62 (2016), pp. 152-165. http://geodesic.mathdoc.fr/item/CMFD_2016_62_a9/
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     title = {On the convergence rate of continuous {Newton} method},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2016_62_a9/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In this paper, we study the convergence of continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on a recent progress in the geometric theory of spirallike functions. We prove convergence theorems and illustrate them by numerical simulations.

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