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    Stability study of eighth-order iterative methods for solving nonlinear equations

    Autor: 
    Cordero, Alicia
    ;
    Magreñán, Á. Alberto
    ;
    Quemada, Carlos
    ;
    Torregrosa, Juan Ramón
    Fecha: 
    01/2016
    Palabra clave: 
    nonlinear equations; iterative methods; stability; parameter space; basin of attraction; JCR; Scopus
    Revista / editorial: 
    Journal of Computational and Applied Mathematics
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/5337
    DOI: 
    https://doi.org/10.1016/j.cam.2015.01.006
    Dirección web: 
    http://www.sciencedirect.com/science/article/pii/S0377042715000187?via%3Dihub
    Resumen:
    In this paper, we study the stability of the rational function associated to a known family of eighth-order iterative schemes on quadratic polynomials. The asymptotic behavior of the fixed points corresponding to the rational function is analyzed and the parameter space is shown, in which we find choices of the parameter for which there exists convergence to cycles or even chaotical behavior showing the complexity of the family. Moreover, some elements of the family with good stability properties are obtained.
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