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Algorithms 2015, 8(3), 514-528; doi:10.3390/a8030514

On the Accessibility of Newton’s Method under a Hölder Condition on the First Derivative

Department of Mathematics and Computation, University of La Rioja, Calle Luis de Ulloa s/n, 26004 Logroño, Spain
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Author to whom correspondence should be addressed.
Academic Editor: Alicia Cordero
Received: 22 June 2015 / Revised: 15 July 2015 / Accepted: 17 July 2015 / Published: 23 July 2015
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
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Abstract

We see how we can improve the accessibility of Newton’s method for approximating a solution of a nonlinear equation in Banach spaces when a center Hölder condition on the first derivative is used to prove its semi-local convergence. View Full-Text
Keywords: Newton’s method; semi-local convergence; recurrence relations; domain of parameters; nonlinear system Newton’s method; semi-local convergence; recurrence relations; domain of parameters; nonlinear system
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Ezquerro, J.A.; Hernández-Verón, M.Á. On the Accessibility of Newton’s Method under a Hölder Condition on the First Derivative. Algorithms 2015, 8, 514-528.

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