Posts by Ion Păvăloiu


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.


Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)


nonlinear equations in R; Aitken-Steffensen method; monotone iterations; bilateral approximations.


PDF-LaTeX file (on the journal website).

Cite this paper as:

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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[1] Balazs, M., A bilateral approximating method for finding the real roots of real equations , Rev. Anal. Num ́er. Th ́eor. Approx., 21, no. 2, pp. 111–117, 1992.
[2] Casulli, V. and Trigiante, D., The convergence order for iterative multipoint procedures, Calcolo, 13, no. 1, pp. 25–44, 1977.
[3] Cobzas ̧, S., Mathematical Analysis, Presa Universitar a Clujean a, Cluj-Napoca, 1997 (in Romanian).
[4] Ostrowski, A. M., Solution of Equations and Systems of Equations, Academic Press, New York, 1960.
[5] Pavaloiu, I., On the monotonicity of the sequences of approximations obtained by Steffensens’s method, Mathematica (Cluj), 35 (58), no. 1, pp. 71–76, 1993.
[6] Pavaloiu, I., Bilateral approximations for the solutions of scalar equations, Rev. Anal. Numer. Theor. Approx., 23 , no. 1, pp. 95–100, 1994.
[7] Pavaloiu, I., Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences, Calcolo, 32, no. 1–2, pp. 69–82, 1995.
[8] Pavaloiu, I., Aitken-Steffensen-type methods for nonsmooth functions (I), Rev. Anal.Numer. Theor. Approx., 31, no. 1, pp. 111–116, 2002.
[9] Traub, F. J., Iterative Methods for the Solution of Equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964.

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