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    Extending the convergence domain of Newton's method for twice Frechet differentiable operators

    Autor: 
    Argyros, Ioannis K
    ;
    Magreñán, Á. Alberto (1)
    Fecha: 
    03/2016
    Palabra clave: 
    fixed point; Newton’s method; banach space; semilocal convergence; Lipschitz/center-Lipschitz condition; Frechet derivative; JCR; Scopus
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/5335
    DOI: 
    https://doi.org/10.1142/S0219530515500013
    Dirección web: 
    http://www.worldscientific.com/doi/abs/10.1142/S0219530515500013
    Resumen:
    We present a semi-local convergence analysis of Newton's method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Using center-Lipschitz condition on the first and the second Frechet derivatives, we provide under the same computational cost a new and more precise convergence analysis than in earlier studies by Huang [A note of Kantorovich theorem for Newton iteration, J. Comput. Appl. Math. 47 (1993) 211-217] and Gutierrez [A new semilocal convergence theorem for Newton's method, J. Comput. Appl. Math. 79 (1997) 131-145]. Numerical examples where the old convergence criteria cannot apply to solve nonlinear equations but the new convergence criteria are satisfied are also presented at the concluding section of this paper.
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