Recurrence relations for semilocal convergence of a Newton-like method in Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:345

Article

Parida, P. K.¹  Gupta, D. K.¹ 

[1] Indian Inst Technol, Dept Math, Kharagpur 721302, W Bengal, India

关键词: Newton-like method;    Lipschitz continuous;    Holder continuous;    cubic convergence;    recurrence relations;   

DOI  :  10.1016/j.jmaa.2008.03.064

来源: Elsevier

【 摘 要 】

The aim of this paper is to establish the semilocal convergence of a multipoint third order Newton-like method for solving F(x) = 0 in Banach spaces by using recurrence relations. The convergence of this method is studied under the assumption that the second Frechet derivative of F satisfies Holder continuity condition. This continuity condition is milder than the usual Lipschitz continuity condition. A new family of recurrence relations are defined based on the two new constants which depend on the operator F. These recurrence relations give a priori error bounds for the method. Two numerical examples are worked out to demonstrate the applicability of the method in cases where the Lipschitz continuity condition over second derivative of F fails but Holder continuity condition holds. (C) 2008 Elsevier Inc. All rights reserved.

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