Unified convergence domains of Newton-like methods for solving operator equations

Ioannis K. Argyros and Santhosh George

Applied Mathematics and Computation, 2016, vol. 286, issue C, 106-114

Abstract: We present a unified semilocal convergence analysis in order to approximate a locally unique zero of an operator equation in a Banach space setting. Using our new idea of restricted convergence domains we generate smaller Lipschitz constants than in earlier studies leading to the following advantages: weaker sufficient convergence criteria, tighter error estimates on the distances involved and an at least as precise information on the location of the zero. Hence, the applicability of these methods is extended. These advantages are obtained under the same cost on the parameters involved. Numerical examples where the old sufficient convergence criteria cannot apply to solve equations but the new criteria can apply are also provided in this study.

Keywords: Banach space; Newton-like methods; Semilocal convergence; Twice Fréchet differentiable operator; Lipschitz constant (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:286:y:2016:i:c:p:106-114

DOI: 10.1016/j.amc.2016.04.010

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