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    Extending the Applicability of Stirling's Method

    Autor: 
    Amorós, Cristina (1)
    ;
    Argyros, Ioannis K
    ;
    Magreñán, Á. Alberto
    ;
    Regmi, Samundra
    ;
    González-Crespo, Rubén (1)
    ;
    Sicilia, Juan Antonio (1)
    Fecha: 
    01/2020
    Palabra clave: 
    Stirling’s method; Newton’s method; convergence; Fréchet derivative; banach space; JCR; Scopus
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/10097
    DOI: 
    https://doi.org/10.3390/math8010035
    Dirección web: 
    https://www.mdpi.com/2227-7390/8/1/35
    Open Access
    Resumen:
    Stirling's method is considered as an alternative to Newton's method when the latter fails to converge to a solution of a nonlinear equation. Both methods converge quadratically under similar convergence criteria and require the same computational effort. However, Stirling's method has shortcomings too. In particular, contractive conditions are assumed to show convergence. However, these conditions limit its applicability. The novelty of our paper lies in the fact that our convergence criteria do not require contractive conditions. Hence, we extend its applicability of Stirling's method. Numerical examples illustrate our new findings.
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