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    Extended convergence results for the Newton–Kantorovich iteration

    Autor: 
    Argyros, Ioannis K
    ;
    Magreñán, Á. Alberto
    Fecha: 
    10/2015
    Palabra clave: 
    Newton–Kantorovich method; convergence domain; analytic operator; JCR; Scopus
    Revista / editorial: 
    Journal of Computational and Applied Mathematics
    Citación: 
    Argyros, I. .K. & Magreñán, A. .A. (2015). Extended convergence results for the Newton–Kantorovich iteration. Journal of computational and Applied Mathematics, 286(1), 54-67
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/4748
    DOI: 
    https://doi.org/10.1016/j.cam.2015.02.059
    Dirección web: 
    http://www.sciencedirect.com/science/article/pii/S037704271500148X
    Resumen:
    We present new semilocal and local convergence results for the Newton–Kantorovich method. These new results extend the applicability of the Newton–Kantorovich method on approximate zeros by improving the convergence domain and ratio given in earlier studies by Argyros (2003), Cianciaruso (2007), Smale (1986) and Wang (1999). These advantages are also obtained under the same computational cost. Numerical examples where the old sufficient convergence criteria are not satisfied but the new convergence criteria are satisfied are also presented in this study.
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