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    Improved convergence analysis for Newton-like methods

    Autor: 
    Magreñán, Á. Alberto
    ;
    Argyros, Ioannis K
    Fecha: 
    04/2016
    Palabra clave: 
    secant-type method; banach space; majorizing sequence; divided difference; local convergence; semilocal convergence; JCR
    Revista / editorial: 
    Numerical Algorithms
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/5333
    DOI: 
    https://doi.org/10.1007/s11075-015-0025-3
    Dirección web: 
    https://link.springer.com/article/10.1007/s11075-015-0025-3
    Resumen:
    We present a new semilocal convergence analysis for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these methods in cases not covered in earlier studies. The advantages of our approach include a more precise convergence analysis under the same computational cost on the Lipschitz constants involved. Applications are also given in this study to show that our estimates on the distances involved are tighter than the older ones.
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