Aitken-Steffensen-type methods for nonsmooth functions (II)

Ion Păvăloiu
(original), paper

Abstract

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.

Author

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)

Keywords

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

PDF

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. https://doi.org/10.33993/jnaat312-724

About this paper

Journal

Revue d’Analyse Numérique et de Théorie de l’Approximation

Publisher Name

Editions de l’Academie Roumaine

DOI

https://doi.org/10.33993/jnaat312-724

Print ISSN

1222-9024

Online ISSN

2457-8126

References

[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.
2002

Related Posts