Local convergence of general Steffensen type methods

Abstract

We study the local convergence of a generalized Steffensen method. We show that this method substantially improves the convergence order of the classical Steffensen method. The convergence order of our method is greater or equal to the number of the controlled nodes used in the Lagrange-type inverse interpolation, which, in its turn, is substantially higher than the convergence orders of the Lagrange type inverse interpolation with uncontrolled nodes (since their convergence order is at most (2)).

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Keywords

nonlinear equations in R; Steffensen method.

References

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Cite this paper as:

I. Păvăloiu, Local convergence of general Steffensen type methods, Rev. Anal. Numér. Théor. Approx., 33 (2004) 1, pp. 79-86.

Print ISSN

1222-9024

Online ISSN

2457-8126

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