Improved local convergence analysis of the Gauss-Newton method under a majorant condition
Argyros, Ioannis K
Magreñán, Á. Alberto (UNIR)
Tipo de Ítem:Articulo Revista Indexada
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.
Este ítem aparece en la(s) siguiente(s) colección(es)
Mostrando ítems relacionados por Título, autor o materia.
Argyros, Ioannis K; Magreñán, Á. Alberto (UNIR); Orcos, Lara (UNIR); Sicilia, Juan Antonio (UNIR) (Journal of Mathematical Chemistry, 08/2017)We present a local convergence analysis for a relaxed two-step Newton-like method. We use this method to approximate a solution of a nonlinear equation in a Banach space setting. Hypotheses on the first Fr,chet derivative ...
Magreñán, Á. Alberto (UNIR); Argyros, Ioannis K; Sicilia, Juan Antonio (UNIR) (Journal of Mathematical Chemistry, 08/2017)We present a new semilocal convergence analysis for Newton-like methods using restricted convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these methods in cases ...
Local convergence and a chemical application of derivative free root finding methods with one parameter based on interpolation Argyros, Ioannis K; Magreñán, Á. Alberto (UNIR); Orcos, Lara (UNIR) (Journal of Mathematical Chemistry, 08/2016)We present a local convergence analysis of a derivative free fourth order method with one parameter based on rational interpolation in order to approximate a locally unique root of a function. The method is optimal in the ...