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Local convergence analysis of inexact Newton-like methods under majorant condition. (English) Zbl 1279.90195
The aim of this paper is to present a new local convergence analysis of inexact Newton-like methods for solving nonlinear equations under majorant conditions. In this analysis, the classical Lipschitz condition is relaxed using a majorant function. This condition is equivalent to Wang’s condition introduced in [X. Wang, IMA J. Numer. Anal. 20, No. 1, 123–134 (2000; Zbl 0942.65057)] and used by J. Chen and W. Li in [J. Comput. Appl. Math. 191, No. 1, 143–164 (2006; Zbl 1092.65043)] to study the inexact Newton-like methods. The presented convergence analysis is linear in an arbitrary norm. It provides a new estimate for the convergence radius and a clear relationship between the majorant function and the nonlinear operator under consideration. The results also allow to obtain some special cases that can be evaluated as an application.

MSC:
90C53 Methods of quasi-Newton type
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