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Open AccessArticle

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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Academic Editor: Alicia Cordero
Algorithms 2015, 8(3), 514-528; https://doi.org/10.3390/a8030514
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)
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
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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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