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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 263893, 8 pages
http://dx.doi.org/10.1155/2012/263893
Research Article

Attracting Periodic Cycles for an Optimal Fourth-Order Nonlinear Solver

Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea

Received 28 November 2011; Accepted 14 February 2012

Academic Editor: Khalida Inayat Noor

Copyright © 2012 Mi Young Lee and Changbum Chun. 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

We consider an optimal fourth-order method for solving nonlinear equations and construct polynomials such that the rational map arising from the method applied to these polynomials has an attracting periodic orbit of any prescribed period.