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    Third-degree anomalies of Traub's method

    Autor: 
    Argyros, Ioannis K
    ;
    Cordero, Alicia
    ;
    Magreñán, Á. Alberto
    ;
    Torregrosa, Juan Ramón
    Fecha: 
    01/2017
    Palabra clave: 
    nonlinear equations; traub’s iterative method; basin of attraction; parameter plane; stability; matrix equations; JCR; Scopus
    Revista / editorial: 
    Journal of Computational and Applied Mathematics
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/5338
    DOI: 
    https://doi.org/10.1016/j.cam.2016.01.060
    Dirección web: 
    http://www.sciencedirect.com/science/article/pii/S0377042716300425?via%3Dihub
    Resumen:
    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.
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