Perturbed-Steffensen-Aitken projection methods for solving equations with nondifferentiable operators

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.

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)

nonlinear equations in Banach spaces; Steffensen-Aitken methods; projection operator; residuals.

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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.

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