On the Convergence Rate of Continuous Newton Method


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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.

About the authors

Aviv Gibali

Ort Braude College

Email: avivg@braude.ac.il
Karmiel, Israel

David Shoikhet

Ort Braude College

Email: davs@braude.ac.il
Karmiel, Israel

Nikolai Tarkhanov

University of Potsdam

Email: tarkhanov@math.uni-potsdam.de
Potsdam, Germany

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