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

Algorithms

José Antonio Ezquerro¹  Miguel Ángel Hernández-Verón² 

[1] Department of Mathematics and Computation, University of La Rioja, Calle Luis de Ulloa s/n, 26004 Logroño, Spain; E-Mail

关键词: Newton’s method;    semi-local convergence;    recurrence relations;    domain of parameters;    nonlinear system;   

DOI  :  10.3390/a8030514

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.