Volume 48, Issue 1
On the Behavior of the Four Order Iteration in Euler's Family Near a Zero

Zhengda Huang

10.4208/jms.v48n1.15.06

J. Math. Study, 48 (2015), pp. 79-92.

Preview Full PDF BiBTex 332 702
  • Abstract

The aim of this paper is to study the local convergence of the four order iteration of Euler's family for solving nonlinear operator equations. We get the optimal radius of the local convergence ball of the method for operators satisfying the weak third order generalized Lipschitz condition with L-average. We also show that the local convergence of the method is determined by a period 2 orbit of the method itself applied to a real function.

  • History

Published online: 2015-03

  • AMS Subject Headings

65L20, 65N12, 39B42

  • Cited by