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    Expanding the aplicability of secant method with applications

    Autor: 
    Magreñán, Á. Alberto
    ;
    Argyros, Ioannis K
    Fecha: 
    05/2015
    Palabra clave: 
    secant method; banach space; majorizing sequence; divided difference; Frechet derivative; JCR; Scopus
    Revista / editorial: 
    Bulletin of the Korean Mathematical Society
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/5673
    DOI: 
    http://dx.doi.org/10.4134/BKMS.2015.52.3.865
    Dirección web: 
    http://koreascience.or.kr/article/ArticleFullRecord.jsp?cn=E1BMAX_2015_v52n3_865
    Open Access
    Resumen:
    We present new sufficient convergence criteria for the convergence of the secant-method to 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 criteria can always be weaker than the corresponding ones in earlier studies. Numerical examples are also provided in this study to solve equations in cases not possible before.
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