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    New Improvement of the Domain of Parameters for Newton’s Method

    Autor: 
    Amorós, Cristina (1)
    ;
    Argyros, Ioannis K
    ;
    González, Daniel
    ;
    Magreñán, Á. Alberto
    ;
    Regmi, Samundra
    ;
    Sarría, Íñigo (1)
    Fecha: 
    01/2020
    Palabra clave: 
    domain; Newton’s method; improvement; JCR; Scopus
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/10096
    DOI: 
    https://doi.org/10.3390/math8010103
    Dirección web: 
    https://www.mdpi.com/2227-7390/8/1/103
    Open Access
    Resumen:
    There is a need to extend the convergence domain of iterative methods for computing a locally unique solution of Banach space valued operator equations. This is because the domain is small in general, limiting the applicability of the methods. The new idea involves the construction of a tighter set than the ones used before also containing the iterates leading to at least as tight Lipschitz parameters and consequently a finer local as well as a semi-local convergence analysis. We used Newton's method to demonstrate our technique. However, our technique can be used to extend the applicability of other methods too in an analogous manner. In particular, the new information related to the location of the solution improves the one in previous studies. This work also includes numerical examples that validate the proven results.
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