Reducing chaos and bifurcations in newton-type methods

Journal ar
Abstract and Applied Analysis
  • Volumen: 2013
  • Fecha: 20 August 2013
  • ISSN: 10853375 16870409
  • Source Type: Journal
  • DOI: 10.1155/2013/726701
  • Document Type: Article
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. © 2013 S. Amat et al.

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