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.

Authors

Keywords

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

References

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[4] I. Păvăloiu,On the monotonicity of the sequences of approximations obtained by Steffensen’s method, Mathematica (Cluj), (35), (58),1 (1993), 71–76.
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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.

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Publisher Name

Springer

Print ISSN

0008-0624

Online ISSN

1126-5434

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