On some Aitken-Steffensen-Halley-type method for approximating the roots of scalar equations

Abstract

We extend the Aitken-Steffensen method to the Halley transformation. Under some rather simple assumptions we obtain error bounds for each iteration step; moreover, the convergence order of the iterates is 3, i.e. higher than for the Aitken-Steffensen case.

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Keywords

nonlinear equations in R; Aitken-Steffensen-Halley method.

References

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Cite this paper as:

I. Păvăloiu, On some Aitken-Steffensen-Halley-type method for approximating the roots of scalar equations, Rev. Anal. Numér. Théor. Approx., 30 (2001) no. 2, pp. 207-212.

Print ISSN

1222-9024

Online ISSN

2457-8126

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