The convergence of a Halley-Chebysheff-type method under Newton-Kantorovich hypotheses
نویسندگان
چکیده
منابع مشابه
On Extended Convergence Domains for the Newton-kantorovich Method
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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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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Article history: Received 2 September 2008 Received in revised form 23 October 2008 Accepted 4 November 2008 Available online 13 November 2008 MSC: 65H10 65J15 47H30
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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: Applied Mathematics Letters
سال: 1993
ISSN: 0893-9659
DOI: 10.1016/0893-9659(93)90104-u