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 CMFD, 2016, Volume 62, Pages 152–165 (Mi cmfd315)

On the convergence rate of continuous Newton method

A. Gibalia, D. Shoikheta, N. Tarkhanovb

a Department of Mathematics, Ort Braude College, Karmiel 2161002, Israel
b Institute of Mathematics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany

Abstract: 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.

 Funding Agency Grant Number Deutsche Forschungsgemeinschaft TA 289/12-1

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Citation: A. Gibali, D. Shoikhet, N. Tarkhanov, “On the convergence rate of continuous Newton method”, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), CMFD, 62, PFUR, M., 2016, 152–165

Citation in format AMSBIB
\Bibitem{GibShoTar16} \by A.~Gibali, D.~Shoikhet, N.~Tarkhanov \paper On the convergence rate of continuous Newton method \inbook Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A.~L.~Skubachevskii (Peoples' Friendship University of Russia) \serial CMFD \yr 2016 \vol 62 \pages 152--165 \publ PFUR \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd315}