# Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences

## Abstract

We study the conditions under which the well-known Aitken-Steffensen method for solving equations leads to monotonic sequences whose terms approximate (from the left and from the right) the root of an equation. The convergence order and efficiency index of this method are also studied in the general case and then in various particular cases.

## Keywords

nonlinear equations in R; Aitken-Steffensen method; monotone sequences; iterative methods; convergence order.

## References

[1] M. Balázs,A bilateral approximating method for finding the real roots of real equations, Rev. Anal. Numér. Théorie Approximation, (21),2 (1992), 111–117.
[2] V. Casulli, D. Trigiante,The convergence order for iterative multipoint procedures, Calcolo, (13),1 (1977), 25–44.
[3] A. M. Ostrowski,Solution of equations and systems of equations, (1960), Academic Press, New York and London.
[4] I. Păvăloiu,On the monotonicity of the sequences of approximations obtained by Steffensen’s method, Mathematica (Cluj), (35), (58),1 (1993), 71–76.
[5] I. Păvăloiu,Bilateral approximations for the solutions of scalar equations, Rev. Anal. Numér. Théorie Approximation, (23),1 (1994), 95–100.
[6] F. J. Traub,Iterative methods for the solution of equations, (1964), Prentice-Hall, Inc. Englewood Cliffs, N.J.

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##### Cite this paper as:

I. Păvăloiu, Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences, Calcolo, 32 (1995) nos. 1-2, pp. 69-82.

Springer

0008-0624

1126-5434