Extending the applicability of the local and semilocal convergence of Newton’s method

Ioannis K. Argyros and Á. Alberto Magreñán

Applied Mathematics and Computation, 2017, vol. 292, issue C, 349-355

Abstract: We present a local as well a semilocal convergence analysis for Newton’s method in a Banach space setting. Using the same Lipschitz constants as in earlier studies, we extend the applicability of Newton’s method as follows: local case: a larger radius is given as well as more precise error estimates on the distances involved. Semilocal case: the convergence domain is extended; the error estimates are tighter and the information on the location of the solution is at least as precise as before. Numerical examples further justify the theoretical results.

Keywords: Newton’s method; Banach space; Local-semilocal convergence; Kantorovich hypothesis (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:292:y:2017:i:c:p:349-355

DOI: 10.1016/j.amc.2016.07.012

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