Aitken-Steffensen type methods for nondifferentiable functions (I)

Authors

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

Keywords:

Aitken-Steffensen method, bilateral approximations

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

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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.

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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

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. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2002-vol31-no1-art12

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