On the convergence of inexact two-point Newton-like methods on Banach spaces

Ioannis Konstantinos Argyros and Ángel Alberto Magreñán

Applied Mathematics and Computation, 2015, vol. 265, issue C, 893-902

Abstract: We present a unified convergence analysis of Inexact Newton-like methods in order to approximate a locally unique solution of a nonlinear operator equation containing a nondifferentiable term in a Banach space setting. The convergence conditions are more general and the error analysis more precise than in earlier studies such as (Argyros, 2007; Cătinaş, 2005; Cătinaş, 1994; Chen and Yamamoto, 1989; Dennis, 1968; Hernández and Romero, 2005; Potra and Pták, 1984; Rheinboldt, 1977). Special cases of our results can be used to find zeros of derivatives. Numerical examples are also provided in this study.

Keywords: Inexact Newton-like methods; Banach space; Local convergence; Semilocal convergence; Divided difference of order one; Univariate unconstrained optimization (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:265:y:2015:i:c:p:893-902

DOI: 10.1016/j.amc.2015.05.127

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