Reducing Chaos and Bifurcations in Newton-Type Methods
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/726701 |
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| Summary: | 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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| ISSN: | 1085-3375 1687-0409 |