Table of Contents
Journal of Nonlinear Dynamics
Volume 2015 (2015), Article ID 162818, 9 pages
http://dx.doi.org/10.1155/2015/162818
Research Article

On the Complex Dynamics of Continued and Discrete Cauchy’s Method

Department of Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria

Received 2 May 2015; Accepted 17 September 2015

Academic Editor: Ivo Petras

Copyright © 2015 Mohamed Lamine Sahari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a complex polynomial of fixed degree . In this paper we show that Cauchy’s method may fail to find all zeros of for any initial guess lying in the complex plane and we propose several ways to find all zeros of a given polynomial using scaled Cauchy’s methods.