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    Improved local convergence analysis of the Gauss-Newton method under a majorant condition

    Autor: 
    Argyros, Ioannis K
    Magreñán, Á. Alberto (1)
    Fecha: 
    03/2015
    Palabra clave: 
    least squares problems; Newton-Gauss methods; banach space; majorant condition; local convergence; JCR
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/5651
    DOI: 
    http://dx.doi.org/10.1007/s10589-014-9704-6
    Dirección web: 
    https://link.springer.com/article/10.1007%2Fs10589-014-9704-6
    Resumen:
    We present a local convergence analysis of Gauss-Newton method for solving nonlinear least square problems. Using more precise majorant conditions than in earlier studies such as Chen (Comput Optim Appl 40:97-118, 2008), Chen and Li (Appl Math Comput 170:686-705, 2005), Chen and Li (Appl Math Comput 324:13811394, 2006), Ferreira (J Comput Appl Math 235:1515-1522, 2011), Ferreira and Goncalves (Comput Optim Appl 48:1-21, 2011), Ferreira and Goncalves (J Complex 27(1):111-125, 2011), Li et al. (J Complex 26:268-295, 2010), Li et al. (Comput Optim Appl 47:1057-1067, 2004), Proinov (J Complex 25:38-62, 2009), Ewing, Gross, Martin (eds.) (The merging of disciplines:new directions in pure, applied and computational mathematics 185-196, 1986), Traup (Iterative methods for the solution of equations, 1964), Wang (J Numer Anal 20:123-134, 2000), we provide a larger radius of convergence; tighter error estimates on the distances involved and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost.
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