A new convergence analysis for the two-step Newton Method for order three

• Argyros, Ioannis K. ^[1] ; Khattri, S. K. ^[2]
  1. [1] Cameron University

     Cameron University

     Estados Unidos

     
  2. [2] Stord Haugesund University College.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 32, Nº. 1, 2013, págs. 73-90
• Idioma: inglés
• DOI: 10.4067/S0716-09172013000100006
• Enlaces
  • Texto completo
• Resumen

  • We present a tighter than before semilocal convergence analysis for the two-step Newton method of order three using recurrent functions.Numerical examples are also provided to show that our convergence criteria are satisfied but earlier studies such as in nine, thirteen, fifteen are not satisfied.

• Referencias bibliográficas
  • Citas [1] Amat, S., Busquier, S., and Gutiérrez, J.M., On the local convergence of secant-type methods, Int. J. Comput. Math. 81, 9, pp....
  • [2] Appell, J., De Pascale, E., Evkhuta, N.A. and Zabrejko, P. P., On the Two-step Newton Method for the Solution of Nonlinear Operator Equations,...
  • [3] Argyros, I. K., On a multistep Newton method in Banach spaces and the Ptak error estimates, Adv. Nonlinear Var. Inequal. 6, 2, pp. 121—135,...
  • [4] Argyros, I. K., A unifying local—semilocal convergence analysis and applications for two-point Newton-like methods in Banach space, J....
  • [5] Argyros, I. K., Cho, J. Y. and Hilout, S., Numerical Methods for Equations and its Applications, CRC Press Taylor & Francis Group...
  • [6] Brent, R. P., Algorithms for Minimization without Derivatives, Prentice Hall, Englewood Cliffs, New Jersey, (1973).
  • [7] Catinas, E., On some iterative methods for solving nonlinear equations, Rev. Anal. Numér. Théor. Approx., 23, 1, pp. 47—53, (1994).
  • [8] Ezquerro, J. A. and Hernández, M. A., Multipoint Super-Halley Type Approximation Algorithms in Banach Spaces, Numer. Funct. Anal. Optim....
  • [9] Ezquerro, J. A., Hernández, M. A. and Salanova, M. A., A Newton-like method for solving some boundary value problems, Numer. Funct. Anal....
  • [10] Ezquerro, J. A., Hernández, M. A. and Salanova, M. A., A discretization scheme for some conservative problems, J. Comput. Appl. Math....
  • [11] Hernández, M. A., Rubio, M. J., and Ezquerro, J. A., Secant-like methods for solving nonlinear integral equations of the Hammerstein...
  • [12] Hernández, M. A. and Rubio, M. J., Semilocal convergence of the secant method under mild convergence conditions of differentiability,...
  • [13] Kantorovich, L. V. and Akilov, G. P., Functional Analysis, Pergamon Press, Oxford, (1982.
  • [14] Ostrowski, A. M., Solutions of Equations in Euclidean and Banach Spaces, A Series of Monographs and Textbooks, Academic Press, New York,...
  • [15] Ortega, J. M. and Rheinboldt, W. C., Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York (1970).
  • [16] Pavaloiu I., A convergence theorem concerning the method of Chord, Rev. Anal. Numér. Théor. Approx., 21 1, pp. 59—65, (1972).
  • [17] Potra, F. A., An iterative algorithm of order 1.839... for solving nonlinear operator equations, Numer. Funct. Anal. Optim. 7, 1, pp....