On the convergence order of some Aitken-Steffensen type methods

  • Ion Păvăloiu Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy
Keywords: Steffensen, Aitken and Aitken-Steffensen iterations

Abstract

In this note we make a comparative study of the convergence orders for the Steffensen, Aitken and Aitken-Steffensen methods. We provide some conditions ensuring their local convergence. We study the case when the auxiliary operators used have convergence orders \(r_{1},r_{2}\in \mathbb{N}\) respectively. We show that the Steffensen, Aitken and Aitken-Steffensen methods have the convergence orders \(r_{1}+1\), \(r_{1}+r_{2}\) and \(r_{1}r_{2}+r_{1}\) respectively.
Published
2003-08-01
How to Cite
Păvăloiu, I. (2003). On the convergence order of some Aitken-Steffensen type methods. Rev. Anal. Numér. Théor. Approx., 32(2), 193-202. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2003-vol32-no2-art8
Section
Articles