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2013 Reducing Chaos and Bifurcations in Newton-Type Methods
S. Amat, S. Busquier, Á. A. Magreñán
Abstr. Appl. Anal. 2013(SI36): 1-10 (2013). DOI: 10.1155/2013/726701

Abstract

We study the dynamics of some Newton-type iterative methods when they are applied of polynomials degrees two and three. The methods are free of high-order derivatives which are the main limitation of the classical high-order iterative schemes. The iterative schemes consist of several steps of damped Newton's method with the same derivative. We introduce a damping factor in order to reduce the bad zones of convergence. The conclusion is that the damped schemes become real alternative to the classical Newton-type method since both chaos and bifurcations of the original schemes are reduced. Therefore, the new schemes can be utilized to obtain good starting points for the original schemes.

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S. Amat. S. Busquier. Á. A. Magreñán. "Reducing Chaos and Bifurcations in Newton-Type Methods." Abstr. Appl. Anal. 2013 (SI36) 1 - 10, 2013. https://doi.org/10.1155/2013/726701

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 07095287
MathSciNet: MR3081605
Digital Object Identifier: 10.1155/2013/726701

Rights: Copyright © 2013 Hindawi

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