Aitken-Steffensen type methods for nondifferentiable functions (I)

Authors

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

DOI:

https://doi.org/10.33993/jnaat311-713

Keywords:

Aitken-Steffensen method, bilateral approximations
Abstract views: 276

Abstract

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.

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References

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, http://ictp.acad.ro/jnaat/journal/article/view/1992-vol21-no2-art3

Casulli, V. and Trigiante, D., The convergence order for iterative multipoint procedures, Calcolo, 13, no. 1, pp. 25-44, 1977, https://doi.org/10.1007/BF02576646 DOI: https://doi.org/10.1007/BF02576646

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, http://ictp.acad.ro/jnaat/journal/article/view/1994-vol23-no1-art10

Păvăloiu, I., Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences, Calcolo, 32, no. 1-2, pp. 69-82, 1995, https://doi.org/10.1007/BF02576543 DOI: https://doi.org/10.1007/BF02576543

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

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Published

2002-02-01

How to Cite

Păvăloiu, I. (2002). Aitken-Steffensen type methods for nondifferentiable functions (I). Rev. Anal. Numér. Théor. Approx., 31(1), 109–114. https://doi.org/10.33993/jnaat311-713

Issue

Vol. 31 No. 1 (2002)

Section

Articles

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