Third-degree anomalies of Traub's method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:309

Article; Proceedings Paper

Argyros, Ioannis K.¹  Cordero, Alicia²  Alberto Magrenan, A.³  Torregrosa, Juan R.² 

[1] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA

[2] Univ Politecn Valencia, Inst Univ Matemat Multidisciplinar, Valencia, Spain

[3] Univ Int La Rioja, C Gran Via 41, Logrono 26005, La Rioja, Spain

关键词: Nonlinear equations;    Traub's iterative method;    Basin of attraction;    Parameter plane;    Stability;    Matrix equations;   

DOI  :  10.1016/j.cam.2016.01.060

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free