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

Zhengda Huang

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

Published online: 2015-03

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  • 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.

  • Keywords

Local convergence convergence ball period 2 orbit generalized Lipschitz condition

  • AMS Subject Headings

65L20 65N12 39B42

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zdhuang@zju.edu.cn (Zhengda Huang)

  • BibTex
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@Article{JMS-48-79, author = {Huang , Zhengda }, title = {On the Behavior of the Four Order Iteration in Euler's Family Near a Zero}, journal = {Journal of Mathematical Study}, year = {2015}, volume = {48}, number = {1}, pages = {79--92}, 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.}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v48n1.15.06}, url = {http://global-sci.org/intro/article_detail/jms/9911.html} }
TY - JOUR T1 - On the Behavior of the Four Order Iteration in Euler's Family Near a Zero AU - Huang , Zhengda JO - Journal of Mathematical Study VL - 1 SP - 79 EP - 92 PY - 2015 DA - 2015/03 SN - 48 DO - http://dor.org/10.4208/jms.v48n1.15.06 UR - https://global-sci.org/intro/article_detail/jms/9911.html KW - Local convergence KW - convergence ball KW - period 2 orbit KW - generalized Lipschitz condition AB - 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.
Zhengda Huang. (2019). On the Behavior of the Four Order Iteration in Euler's Family Near a Zero. Journal of Mathematical Study. 48 (1). 79-92. doi:10.4208/jms.v48n1.15.06
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