On the approximate solutions of implicit functions using the Steffensen method

Abstract

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.

Authors

Ioannis K. Argyros
(Cameron University)

Emil Cătinaş
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

Keywords

nonlinear equations in Banach spaces; Steffensen-Aitken method; implicit function; projection operator.

References

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About this paper

Cite this paper as:

I. Argyros, E. Cătinaş, I. Păvăloiu On the approximate solutions of implicit functions using the Steffensen method, Proyecciones, 19 (2000) no. 3, pp. 291-303

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Proyecciones

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Section 1

[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, 1, (1994), 47–53.

[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), 59–65.

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