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On the convergence of continuous Newton method

  • 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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Metadaten
Author details:Aviv Gibali, David Shoikhet, Nikolai Nikolaevich TarkhanovORCiDGND
URN:urn:nbn:de:kobv:517-opus4-81537
ISSN:2193-6943
Publication series (Volume number):Preprints des Instituts für Mathematik der Universität Potsdam (4 (2015)10)
Publisher:Universitätsverlag Potsdam
Place of publishing:Potsdam
Publication type:Preprint
Language:English
Year of first publication:2015
Publication year:2015
Publishing institution:Universität Potsdam
Publishing institution:Universitätsverlag Potsdam
Release date:2015/10/02
Tag:Newton method; spirallike function
Volume:4
Issue:10
Number of pages:15
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M15 Newton-type methods
58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Cxx Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx] / 58C15 Implicit function theorems; global Newton methods
Collection(s):Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2015
Publishing method:Universitätsverlag Potsdam
License (German):License LogoKeine öffentliche Lizenz: Unter Urheberrechtsschutz
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