On the convergence of a higher order family of methods and its dynamics

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• 作者：Ioannis K. Argyros^a ; ^{iargyros@cameron.edu" class="auth_mail" title="E-mail the corresponding author} ; Alicia Cordero^b ; ^{acordero@mat.upv.es" class="auth_mail" title="E-mail the corresponding author} ; Á ; ngel Alberto Magreñ ; á ; n^c ; ^{alberto.magrenan@unir.net" class="auth_mail" title="E-mail the corresponding author} ; Juan Ram&oacute ; n Torregrosa^b ; ^{jrtorre@mat.upv.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Banach space ; Majorizing sequence ; Local/semilocal convergence ; Complex dynamics
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：542-562
• 全文大小：1523 K

文摘

In this paper, we present the study of the local convergence of a higher-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials is studied. Some anomalies are found in this family by means of studying the associated rational function. Parameter spaces are shown and the study of the stability of all the fixed points is presented.