Aitken-Steffensen type methods for nondifferentiable functions (I)


  • Ion Păvăloiu Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy


Aitken-Steffensen method, bilateral approximations


We study the convergence of the Aitken-Steffensen method for solving a scalar equation \(f(x)=0\). Under reasonable conditions (without assuming the differentiability of \(f\)) we construct some auxilliary functions used in these iterations, which generate bilateral sequences approximating the solution of the considered equation.


Download data is not yet available.


Balázs, M., A bilateral approximating method for finding the real roots of real equations, Rev. Anal. Numér. Théor. Approx., 21, no. 2, pp. 111-117, 1992,

Casulli, V. and Trigiante, D., The convergence order for iterative multipoint procedures, Calcolo, 13, no. 1, pp. 25-44, 1977,

Cobzaş, S., Mathematical Analysis, Presa Universitară Clujeană, Cluj-Napoca, 1997 (in Romanian).

Ostrowski, A. M., Solution of Equations and Systems of Equations, Academic Press, New York, 1960.

Păvăloiu, I., On the monotonicity of the sequences of approximations obtained by Steffensens's method, Mathematica (Cluj), 35 (58), no. 1, pp. 71-76, 1993.

Păvăloiu, I., Bilateral approximations for the solutions of scalar equations, Rev. Anal. Numér. Théor. Approx., 23, no. 1, pp. 95-100, 1994,

Păvăloiu, I., Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences, Calcolo, 32, no. 1-2, pp. 69-82, 1995,

Traub, F. J., Iterative Methods for the Solution of Equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964.




How to Cite

Păvăloiu, I. (2002). Aitken-Steffensen type methods for nondifferentiable functions (I). Rev. Anal. Numér. Théor. Approx., 31(1), 109–114. Retrieved from