reducing chaos and bifurcations in newton-type methods
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ID: 193911
2013
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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.
| Reference Key |
amat2013abstractreducing
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|---|---|
| Authors | ;S. Amat;S. Busquier;Á. A. Magreñán |
| Journal | science and technology of advanced materials |
| Year | 2013 |
| DOI |
10.1155/2013/726701
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| URL | |
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