期刊论文详细信息
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 卷:291
The majorant method in the theory of Newton-Kantorovich approximations and generalized Lipschitz conditions
Article
Argyros, Ioannis K.1  Hilout, Said2 
[1] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA
[2] Univ Poitiers, Lab Math & Applicat, F-86962 Futuroscope, France
关键词: Modified Newton's method;    Majorant method;    Banach space;    Rate of convergence;    Local/semilocal convergence;    Kantorovich's hypothesis;   
DOI  :  10.1016/j.cam.2014.12.013
来源: Elsevier
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【 摘 要 】

We provide a semilocal as well as a local convergence analysis for Newton's and modified Newton's methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. We use more precise majorizing sequences than in earlier studies such as Appell et al. (1997), Appell et al. (1991), Argyros (2004), Argyros and Hilout (2009), Kantorovich and Akilov (1982), Ortega and Rheinboldt (1970) and generalized Lipschitz continuity conditions. Our sufficient convergence conditions are weaker than before and our convergence analysis is tighter. Special cases and numerical examples are also given in this study. (C) 2014 Elsevier B.V. All rights reserved.

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