On the semilocal convergence of Newton-type methods, when the derivative is not continuously invertible

• Ioannis K Argyros ^[1] ; Saïd Hilout ^[2]
  1. [1] Cameron University

     Cameron University

     Estados Unidos

     
  2. [2] Poitiers University Laboratoire de Mathematiques et Applications
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 13, Nº. 3, 2011, págs. 1-15
• Idioma: inglés
• DOI: 10.4067/S0719-06462011000300001
• Enlaces
  • Texto completo
• Resumen
  • español

    Ofrecemos un análisis de convergencia semilocal de los metodos de Newton type para aproximar una solución local unica de una ecuación no lineal en un entorno de un espacio de Banach. L derivada de Frechet del operador en cuestion no es necesariamente invertible continua. De esta manera ampliamos la aplicabilidad de los metodos del tipo Newton [1]-[12]. Tambien proporcionamos condiciones suficientes mas debiles de convergencia, y una cota de error más fina de las distancias involucradas que [1]-[12] (en el mismo coste computacional), en algunos casos interesantes. tambien presentamos ejemplos numericos.

  • English

    We provide a semilocal convergence analysis for Newton-type methods to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The Frechet-derivative of the operator involved is not necessarily continuous invertible. This way we extend the applicability of Newton-type methods Ώ]-[12]. We also provide weaker sufficient convergence conditions, and finer error bound on the distances involved (under the same computational cost) than [1]-[12], in some intersting cases. Numerical examples are also provided in this study.

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