On a Halley-Steffensen method for approximating the solutions of scalar equations - Păvăloiu, Ion (Rev. Anal. Numér. Théor. Approx., 2001)
In the present paper we show that the Steffensen method for solving the scalar equation \(f( x) =0\), applied to equation \[ h( x) =f( x) f^′( x) =0, \] 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.