We use perturbed Steffensen-Aitken methods to approximate a locally unique solution of an operator equation in a Banach space. Using projection operators, we reduce the problem to solving a finite linear system of algebraic equations. Since iterates can rarely be computed exactly, we control the residuals to guarantee the convergence of the method. Sufficient convergence conditions as well as an error analysis are given for our method.
nonlinear equations in Banach spaces; Steffensen-Aitken methods; projection operator; residuals.
Latex-pdf version of the paper.
I. Argyros, E. Cătinaş, I. Păvăloiu, Perturbed-Steffensen-Aitken projection methods for solving equations with nondifferentiable operators, Punjab Univ. J. Math. (Lahore), 33 (2000), pp. 105-113.
Punjab Univ. J. Math. (Lahore)