On the approximate solution of implicit functions using the Steffensen method

• Argyros, Ioannis K. ^[1] ; Catinas, Emil ^[2] ; Pavaloiu, Ion ^[2]
  1. [1] Cameron University

     Cameron University

     Estados Unidos

     
  2. [2] Institul de Calcul.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 19, Nº. 3, 2000, págs. 291-303
• Idioma: inglés
• DOI: 10.4067/S0716-09172000000300005
• Enlaces
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• Resumen

  • We use inexact Steffensen-Aitken-type methods to approximate implicit functions in a Banach space. Using a projection operator our equation reduces to solving a linear algebraic system of finite order. Semilocal convergence results as well as an error analysis are also provided.

• Referencias bibliográficas
  • Citas [1] Argyros, I.K. On the convergence of some projection methods with perturbations, J. Comp. Appl. Math. 36, (1991), 255–258.
  • [2] Argyros, I.K. On an application of the Zincenko method to the approximation of implicit functions, Z.A.A. 10, 3, (1991), 391–396.
  • [3] Argyros, I.K. and Szidarovszky, F. The Theory and Application of Iteration Methods, C.R.C. Press, Inc., Boca Raton, Florida, 1993.
  • [4] Catinas, E. On some iterative methods for solving nonlinear equations, Revue d’analyse Numerique et de theorie de l’approximation, 23,...
  • [5] Kantorovich, L.V. The method of successive approximation for functional equations, Acta Math. 71 (1939), 63–97.
  • [6] Pavaloiu, I. Sur une generalisation de la methode de Steffensen, Revue d’analyse Numerique et de theorie de l’approximation, 21, 1, (1992),...
  • [7] Pavaloiu, I. Bilateral approximations for the solutions of scalar equations, Revue d’analyse numerique et de theorie de l’approximation,...