We study the monotone convergence of two general methods of Aitken-Steffenssen type. These methods are obtained from the Lagrange inverse interpolation polynomial of degree two, having controlled nodes. The obtained results provide information on controlling the errors at each iteration step.
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)
Aitken-Steffenssen methods; Lagrange inverse interpolation
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I. Păvăloiu, Bilateral approximations of the roots of scalar equations by Lagrange-Aitken-Steffensen method of order three, Rev. Anal. Numér. Théor. Approx., 35 (2006) no. 2, pp. 173-182.