On a Halley-Steffensen method for approximating the solutions of scalar equations

Ion Păvăloiu

doi:10.33993/jnaat301-683

Authors

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

DOI:

https://doi.org/10.33993/jnaat301-683

Abstract views: 244

Abstract

In the present paper we show that the Steffensen method for solving the scalar equation \(f\left( x\right) =0\), applied to equation
\[
h\left( x\right) =\tfrac{f\left( x\right) }{\sqrt{f^{\prime}\left( x\right) }}=0,
\]
leads to bilateral approximations for the solution. Moreover, the convergence order is at least 3, i.e. as in the case of the Halley method.

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