We study the local convergence of some Aitken–Steffensen–Hermite type methods of order three. We obtain that under some reasonable conditions on the monotony and convexity of the nonlinear function, the iterations offer bilateral approximations for the solution, which can be efficiently used as a posteriori estimations.
I. Păvăloiu, E. Cătinaş, Bilateral approximations for some Aitken-Steffensen-Hermite type methods of order three, Appl. Math. Comput., 217 (2011) 12, pp. 5838-5846
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