Parameter-based algorithms for approximating local solution of nonlinear complex equations

• Argyros, Ioannis K. ^[1] ; Chen, Dong ^[2]
  1. [1] Cameron University

     Cameron University

     Estados Unidos

     
  2. [2] University of Arkansas, Arkansas.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 13, Nº. 1, 1994, págs. 53-61
• Idioma: inglés
• DOI: 10.22199/S07160917.1994.0001.00007
• Enlaces
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• Resumen

  • We study the Ostrowski-Kantorovich convergence for a family of Halley- Werner type iteration methods in the complex plane. We provide an upper error bound for all parameter ⍺ ∊ [1 , 2). We show that the error bound is a decreasing function of ⍺. We prove also that the Halley method has the largest error bound.

• Referencias bibliográficas
  • Citas [1] E. Halley, A New Exact and Easy Method of Finding the Roots of equations Generally and that Without any Previous Reduction, Phil....
  • [2] W. B. Gragg and R.A. Tapia, Optimal Error Bounds for the Newton-Kantorovich Theorem, SIAM J. Numer.Anal., 11(1974), 10-13.
  • [3] L.V. Kantorovich and G.P. Akilov, Functional Analysis in Normed Spaces, Pergamon Press, New York, 1977.
  • [4] A.M. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, Third Edition, New York, 1973.
  • [5] W. Werner, Some Improvements of Classical Iterative Methods for the Solutions of Nonlinear Equations, Lecture Notes in Mathematics, Numerical...