New and Generalized Convergence Conditions for the Newton-Kantorovich Method
نویسندگان
چکیده
منابع مشابه
New and Generalized Convergence Conditions for the Newton-kantorovich Method
We present new semilocal convergence theorems for Newton methods in a Banach space. Using earlier general conditions we find more precise error estimates on the distances involved using the majorant principle. Moreover we provide a better information on the location of the solution. In the special case of Newton’s method under Lipschitz conditions we show that the famous Newton–Kantorovich hypo...
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Hongmin Ren College of Information and Engineering, Hangzhou Polytechnic, Hangzhou 311402, Zhejiang, PR China Email:[email protected] Abstract.We present new sufficient semilocal convergence conditions for the Newton-Kantorovich method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Examples are given to show that our results apply but earlier on...
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We present results on extended convergence domains and their applications for the Newton-Kantorovich method (NKM), using the same information as in previous papers. Numerical examples are provided to emphasize that our results can be applied to solve nonlinear equations using (NKM), in contrast with earlier results which are not applicable in these cases. MSC 2010. 65J15, 65G99, 47H99, 49M15.
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The goal of this paper is to present a local convergence analysis of Newton’s method for approximating a locally unique solution of an equation in a Banach space setting. Using the gauge function theory and our new idea of restricted convergence regions we present an extended and unified convergence theory. Key–Words: Newton’s method, Banach space, semilocal convergence, gauge function, converg...
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ژورنال
عنوان ژورنال: Journal of Applied Analysis
سال: 2003
ISSN: 1425-6908,1869-6082
DOI: 10.1515/jaa.2003.287