We study the conditions under which the well-known Aitken-Steffensen method for solving equations leads to monotonic sequences whose terms approximate (from the left and from the right) the root of an equation. The convergence order and efficiency index of this method are also studied in the general case and then in various particular cases.
(Tiberiu Popoviciu Institute of Numerical Analysis)
nonlinear equations in R; Aitken-Steffensen method; monotone sequences; iterative methods; convergence order.
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Latex version of the paper (soon).
I. Păvăloiu, Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences, Calcolo, 32 (1995) nos. 1-2, pp. 69-82.