On the global convergence of Chebyshev's iterative method

  1. Amat, S. 1
  2. Busquier, S. 1
  3. Gutiérrez, J.M. 2
  4. Hernández, M.A. 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

Journal:
Journal of Computational and Applied Mathematics

ISSN: 0377-0427

Year of publication: 2008

Volume: 220

Issue: 1-2

Pages: 17-21

Type: Article

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DOI: 10.1016/J.CAM.2007.07.022 SCOPUS: 2-s2.0-47849132177 WoS: WOS:000258636800004 GOOGLE SCHOLAR

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Abstract

In [A. Melman, Geometry and convergence of Euler's and Halley's methods, SIAM Rev. 39(4) (1997) 728-735] the geometry and global convergence of Euler's and Halley's methods was studied. Now we complete Melman's paper by considering other classical third-order method: Chebyshev's method. By using the geometric interpretation of this method a global convergence theorem is performed. A comparison of the different hypothesis of convergence is also presented. © 2007 Elsevier B.V. All rights reserved.