Letter to the Editor: On the global convergence of Chebyshev's iterative method

  • Authors:

  • S. Amat;S. Busquier;J. M. Gutiérrez;M. A. Hernández

  • Affiliations:

  • Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain;Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain;Departamento de Matemáticas y Computación, Universidad de La Rioja, Spain;Departamento de Matemáticas y Computación, Universidad de La Rioja, Spain

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2008

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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.