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    On the election of the damped parameter of a two-step relaxed Newton-type method

    Autor: 
    Amat, Sergio
    ;
    Busquier, Sonia
    ;
    Bermúdez, Concepción
    ;
    Magreñán, Á. Alberto (1)
    Fecha: 
    04/2016
    Palabra clave: 
    complex dynamics; nonlinear problems; parameter space; iterative methods; basins of attraction; newton-type methods; JCR; Scopus
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/5334
    DOI: 
    https://doi.org/10.1007/s11071-015-2179-x
    Dirección web: 
    https://link.springer.com/article/10.1007%2Fs11071-015-2179-x
    Resumen:
    In this paper, we are interested to justified two typical hypotheses that appear in the convergence analysis, |λ|≤2|λ|≤2 and z0z0 sufficient close to z∗z∗ . In order to proof these ideas, the dynamics of a damped two-step Newton-type method for solving nonlinear equations and systems is presented. We present the parameter space for values of the damping factor in the complex plane, focusing our attention in such values for which the fixed points related to the roots are attracting. Moreover, we study the stability of the strange fixed points, showing that there exists attracting cycles and chaotical behavior for some choices of the damping factor.
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