We present some new conditions which assure that the Aitken-Steffensen method yields bilateral approximation for the solution of a nonlinear scalar equation. The auxiliary functions appearing in the method are constructed under the hypothesis that the nonlinear application is not differentiable on an interval containing the solution.
(Tiberiu Popoviciu Institute of Numerical Analysis)
nonlinear equations in R; Aitken-Steffensen method; monotone iterations; bilateral approximations.
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I. Păvăloiu, Aitken-Steffensen-type methods for nonsmooth functions (II), Rev. Anal. Numér. Théor. Approx., 31 (2002) no. 2, pp. 191-196.
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