Third-degree anomalies of Traub’s method

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• 作者：Ioannis K. Argyros^a ; ^{ioannisa@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 ; . Alberto Magreñ ; á ; n^c ; ^{alberto.magrenan@unir.net" class="auth_mail" title="E-mail the corresponding author} ; Juan R. Torregrosa^b ; ^{jrtorre@mat.upv.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Nonlinear equations ; Traub&rsquo ; s iterative method ; Basin of attraction ; Parameter plane ; Stability ; Matrix equations
• 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：511-521
• 全文大小：2597 K

文摘

Traub’s method is a tough competitor of Newton’s scheme for solving nonlinear equations as well as nonlinear systems. Due to its third-order convergence and its low computational cost, it is a good procedure to be applied on complicated multidimensional problems. In order to better understand its behavior, the stability of the method is analyzed on cubic polynomials, showing the existence of very small regions with unstable behavior. Finally, the performance of the method on cubic matrix equations arising in control theory is presented, showing a good performance.