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    New semilocal and local convergence analysis for the Secant method

    Autor: 
    Magreñán, Á. Alberto
    ;
    Argyros, Ioannis K
    Fecha: 
    06/2015
    Palabra clave: 
    secant method; Bartsch space; majorizing sequence; divided difference; Frechet derivative; JCR; Scopus
    Revista / editorial: 
    Applied Mathematics and Computation
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/5678
    DOI: 
    http://dx.doi.org/10.1016/j.amc.2015.04.026
    Dirección web: 
    http://www.sciencedirect.com/science/article/pii/S0096300315004774?via%3Dihub
    Resumen:
    We present a new convergence analysis, for the Secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center-Lipschitz instead of just Lipschitz conditions in the convergence analysis. The new convergence analysis leads to more precise error bounds and to a better information on the location of the solution than the corresponding ones in earlier studies such as [2,6,9,11,14,15,17,20,22-26]. Numerical examples validating the theoretical results are also provided in this study. (C) 2015 Elsevier Inc. All rights reserved.
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