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    Complexity of an Homotopy Method at the Neighbourhood of a Zero

    Autor: 
    Yakoubsohn, J. C.
    ;
    Gutierrez, J. M.
    ;
    Magreñán, Á. Alberto
    Fecha: 
    2016
    Palabra clave: 
    convergence; equations; newtons; Scopus(2); WOS(2)
    Tipo de Ítem: 
    bookPart
    URI: 
    https://reunir.unir.net/handle/123456789/10037
    DOI: 
    https://doi.org/10.1007/978-3-319-39228-8_7
    Dirección web: 
    https://link.springer.com/chapter/10.1007/978-3-319-39228-8_7
    Resumen:
    This paper deals with the enlargement of the region of convergence of Newton's method for solving nonlinear equations defined in Banach spaces. We have used an homotopy method to obtain approximate zeros of the considered function. The novelty in our approach is the establishment of new convergence results based on a Lipschitz condition with a L-average for the involved operator. In particular, semilocal convergence results (Kantorovich-type results), as well as local convergence results (gamma-theory) are obtained.
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