Bilateral approximations for some Aitken-Steffensen-Hermite type methods of order three


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.


Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

Emil Cătinaş
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)


Nonlinear equations in R; Aitken–Steffensen type methods; Hermite inverse interpolatory polynomials; divided differences.

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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
doi: 10.1016/j.amc.2010.12.067


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