Semilocal convergence of a k-step iterative process and its application for solving a special kind of conservative problems

  1. Hernández-Verón, M.A. 1
  2. Martínez, E. 2
  3. Teruel, C. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad Politécnica de Valencia
    info

    Universidad Politécnica de Valencia

    Valencia, España

    ROR https://ror.org/01460j859

Revista:
Numerical Algorithms

ISSN: 1017-1398

Año de publicación: 2017

Volumen: 76

Número: 2

Páginas: 309-331

Tipo: Artículo

DOI: 10.1007/S11075-016-0255-Z SCOPUS: 2-s2.0-85006835896 WoS: WOS:000411622000001 GOOGLE SCHOLAR

Otras publicaciones en: Numerical Algorithms

Proyectos relacionados

Ecuaciones no lineales y métodos iterativos. Aplicaciones a problemas de optimización y ecuaciones matriciales. Nonlinear equations and iterative methods. Applications to optimization problems and matrix equations.

2015/00069/001

Resumen

In this paper, we analyze the semilocal convergence of k-steps Newton’s method with frozen first derivative in Banach spaces. The method reaches order of convergence k + 1. By imposing only the assumption that the Fréchet derivative satisfies the Lipschitz continuity, we define appropriate recurrence relations for obtaining the domains of convergence and uniqueness. We also define the accessibility regions for this iterative process in order to guarantee the semilocal convergence and perform a complete study of their efficiency. Our final aim is to apply these theoretical results to solve a special kind of conservative systems. © 2016 Springer Science+Business Media New York