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On the semilocal convergence of a fast two-step Newton method
Convergencia semilocal de un método de Newton de dos pasos
Schlagworte:
Two-step Newton method, Newton method, Banach space, Majorizing sequence, Newton-Kantorovich hypothesis, Semilocal convergence, Fréchet-derivative, 2000 Mathematics Subject Classification. 65H10, 65G99, 47H17, 49M15 (en)Método de Newton de dos pasos, Método de Newton, Espacio de Banach, Secuencia mayorante, Hipótesis de Newton-Kantorovich, Convergencia semilocal, Derivada de Fréchet (es)
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Abstract. We provide a semilocal convergence analysis for a cubically convergent two-step Newton method (2) recently introduced by H. Homeier [8], [9], and also studied by A. Ӧzban [13]. In contrast to the above works we examine the semilocal convergence of the method in a Banach space setting, instead of the local in the real or complex number case. A comparison is given with a two step Newton-like method using the same information.
Proporcionamos un análisis de convergencia semilocal para un método de Newton de dos pasos, cúbicamente convergente, recientemente introducido por H. Homeier [8], [9], también estudiado por A. Ӧzban [13]. En contraste con esto, examinamos la convergencia local del método en espacios de Banach en lugar del local, en el caso real y complejo. Damos una comparación con el método de Newton de dos pasos usando la misma información.
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