Abstract
In this paper we study the convergence of the continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on recent progress in the geometric theory of spiral-like functions. We prove convergence theorems and illustrate them by numerical simulations.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 62, Differential and Functional Differential Equations, 2016.
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Gibali, A., Shoikhet, D. & Tarkhanov, N. On the Convergence Rate of the Continuous Newton Method. J Math Sci 239, 867–879 (2019). https://doi.org/10.1007/s10958-019-04331-9
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DOI: https://doi.org/10.1007/s10958-019-04331-9