We provide sufficient conditions for the convergence of the Steffensen method for solving the scalar equation \(f(x)=0\), without assuming differentiability of \(f\) at other points than the solution \(x^\ast\). We analyze the cases when the Steffensen method generates two sequences which approximate bilaterally the solution.
nonlinear equations in R; Aitken-Steffensen method; monotone iterations; bilateral approximations.
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I. Păvăloiu, Aitken-Steffensen-type methods for nonsmooth functions (III), Rev. Anal. Numér. Théor. Approx., 32 (2003) no. 1, pp. 73-77.