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