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    Extending the applicability of the local and semilocal convergence of Newton's method

    Autor: 
    Argyros, Ioannis K
    ;
    Magreñán, Á. Alberto (1)
    Fecha: 
    01/2017
    Palabra clave: 
    Newton’s method; banach space; local/semilocal convergence; Kantorovich hypothesis; JCR; Scopus
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/5331
    DOI: 
    https://doi.org/10.1016/j.amc.2016.07.012
    Dirección web: 
    http://www.sciencedirect.com/science/article/pii/S0096300316304428?via%3Dihub
    Resumen:
    We present a local as well a semilocal convergence analysis for Newton's method in a Banach space setting. Using the same Lipschitz constants as in earlier studies, we extend the applicability of Newton's method as follows: local case: a larger radius is given as well as more precise error estimates on the distances involved. Semilocal case: the convergence domain is extended; the error estimates are tighter and the information on the location of the solution is at least as precise as before. Numerical examples further justify the theoretical results.
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