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    Unified local convergence for newton's method and uniqueness of the solution of equations under generalized conditions in a Banach space

    Autor: 
    Argyros, Ioannis K
    ;
    Magreñán, Á. Alberto
    ;
    Orcos, Lara (1)
    ;
    Sarría, Íñigo (1)
    Fecha: 
    05/2019
    Palabra clave: 
    Newton's method; local convergence; Newton-Mysovskii conditions; Banach space; JCR; Scopus
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/8788
    DOI: 
    https://doi.org/10.3390/math7050463
    Dirección web: 
    https://www.mdpi.com/2227-7390/7/5/463
    Open Access
    Resumen:
    Under the hypotheses that a function and its Frechet derivative satisfy some generalized Newton-Mysovskii conditions, precise estimates on the radii of the convergence balls of Newton's method, and of the uniqueness ball for the solution of the equations, are given for Banach space-valued operators. Some of the existing results are improved with the advantages of larger convergence region, tighter error estimates on the distances involved, and at-least-as-precise information on the location of the solution. These advantages are obtained using the same functions and Lipschitz constants as in earlier studies. Numerical examples are used to test the theoretical results.
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