Local convergence for multi-point-parametric Chebyshev–Halley-type methods of high convergence order

• Ioannis K. Argyros ^[2] ; Santhosh George ^[3] ; Á. Alberto Magreñán ^[1]
  1. [1] Universidad Internacional de La Rioja

     Universidad Internacional de La Rioja

     Logroño, España

     
  2. [2] Cameron University

     Cameron University

     Estados Unidos

     
  3. [3] National Institute of Technology Karnataka, India

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• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 282, Nº 1 (July 2015), 2015, págs. 215-224
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.12.023
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• Resumen

  • We present a local convergence analysis for general multi-point-Chebyshev–Halley-type methods (MMCHTM) of high convergence order in order to approximate a solution of an equation in a Banach space setting. MMCHTM includes earlier methods given by others as special cases. The convergence ball for a class of MMCHTM methods is obtained under weaker hypotheses than before. Numerical examples are also presented in this study.