Expanding the applicability of some high order Househölder-like methods

  1. Amat, S. 1
  2. Argyros, I.K. 3
  3. Hernández-Verón, M.A. 2
  4. 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

  3. 3 Cameron University
    info

    Cameron University

    Lawton, Estados Unidos

    ROR https://ror.org/00rgv0036

Journal:
Algorithms

ISSN: 1999-4893

Year of publication: 2017

Volume: 10

Issue: 2

Type: Article

DOI: 10.3390/A10020064 SCOPUS: 2-s2.0-85020380376 WoS: WOS:000404542100029 GOOGLE SCHOLAR

More publications in: Algorithms

Abstract

This paper is devoted to the semilocal convergence of a Househölder-like method for nonlinear equations. The method includes many of the studied third order iterative methods. In the present study, we use our new idea of restricted convergence domains leading to smaller γ-parameters, which in turn lead to the following advantages over earlier works (and under the same computational cost): larger convergence domain; tighter error bounds on the distances involved, and at least as precise information on the location of the solution. © 2017 by the authors.