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    Extending the mesh independence for solving nonlinear equations using restricted domains

    Autor: 
    Argyros, Ioannis K
    ;
    Sheth, Soham M.
    ;
    Younis, Rami M.
    ;
    Magreñán, Á. Alberto (1)
    ;
    George, Santhosh
    Fecha: 
    12/2017
    Palabra clave: 
    Newton’s method; Banach space; Operator equation; mesh independence; Scopus
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/8966
    DOI: 
    DOI https://doi.org/10.1007/s40819-017-0398-1
    Dirección web: 
    https://link.springer.com/article/10.1007%2Fs40819-017-0398-1#citeas
    Resumen:
    The mesh independence principle states that, if Newton’s method is used to solve an equation on Banach spaces as well as finite dimensional discretizations of that equation, then the behaviour of the discretized process is essentially the same as that of the initial method. This principle was inagurated in Allgower et al. (SIAM J Numer Anal 23(1):160–169, 1986). Using our new Newton–Kantorovich-like theorem and under the same information we show how to extend the applicability of this principle in cases not possible before. The results can be used to provide more efficient programming methods.
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