Reducing Chaos and Bifurcations in Newton-Type Methods

S. Amat, S. Busquier and Á. A. Magreñán

Abstract and Applied Analysis, 2013, vol. 2013, 1-10

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:726701

DOI: 10.1155/2013/726701

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