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

Ion Păvăloiu

Authors

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

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Abstract

In this note 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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