On the approximate solution of implicit functions using the Steffensen method
DOI:
https://doi.org/10.4067/S0716-09172000000300005Keywords:
Steffensen-Aitken method, implicit function, projection operator, método Steffensen-Aitken, función implícita, operador de proyección.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.References
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[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.
[7] Pavaloiu, I. Bilateral approximations for the solutions of scalar equations, Revue d’analyse numerique et de theorie de l’approximation, 23, 1, (1994), 95–100.
[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.
[7] Pavaloiu, I. Bilateral approximations for the solutions of scalar equations, Revue d’analyse numerique et de theorie de l’approximation, 23, 1, (1994), 95–100.
Published
2017-06-14
How to Cite
[1]
I. K. Argyros, E. Catinas, and I. Pavaloiu, “On the approximate solution of implicit functions using the Steffensen method”, Proyecciones (Antofagasta, On line), vol. 19, no. 3, pp. 291-303, Jun. 2017.
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