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.

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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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