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

  • Ion Păvăloiu Tiberiu Popoviciu Institute of Numerical Analysis

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.

Published
2001-02-01
How to Cite
Păvăloiu, I. (2001). On a Halley-Steffensen method for approximating the solutions of scalar equations. Rev. Anal. Numér. Théor. Approx., 30(1), 69-74. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2001-vol30-no1-art9
Section
Articles