Semilocal convergence of a sixth order iterative method for quadratic equations.

  1. Amat, S. 1
  2. Hernández, M.A. 2
  3. Romero, N. 2
  1. 1 Universidad Politécnica de Cartagena
    info

    Universidad Politécnica de Cartagena

    Cartagena, España

    ROR https://ror.org/02k5kx966

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Applied Numerical Mathematics

ISSN: 0168-9274

Ano de publicación: 2012

Volume: 62

Número: 7

Páxinas: 833-841

Tipo: Artigo

DOI: 10.1016/J.APNUM.2012.03.001 SCOPUS: 2-s2.0-84859534296 WoS: WOS:000303642300002 GOOGLE SCHOLAR

Outras publicacións en: Applied Numerical Mathematics

Resumo

In this paper the modification of Chebyshev's iterative method constructed in Amat et al. (2008) [1] is revisited. The behavior of this method when considering quadratic nonlinear operators is analyzed. In this case, the iterative method has a competitive behavior due to its computational efficiency. Moreover, a new result of semilocal convergence assuming only a pointwise condition is obtained, improving the result given in Amat et al. (2008) [1]. The domain of uniqueness of the solution is also improved. The new technique used in the proof of these results allows us to achieve all these improvements. Finally, some theoretical and numerical applications for a quadratic system of equations are presented. © 2012 IMACS. Published by Elsevier B.V. All rights reserved.