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On the dynamics of a family of third-order iterative functions

Published online by Cambridge University Press:  17 February 2009

Sergio Amat ,
Sonia Busquier  and
Sergio Plaza
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Abstract

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We study the dynamics of a family of third-order iterative methods that are used to find roots of nonlinear equations applied to complex polynomials of degrees three and four. This family includes, as particular cases, the Chebyshev, the Halley and the super-Halleyroot-finding algorithms, as well as the so-called c-methods. The conjugacy classes of theseiterative methods are found explicitly.

Keywords

iteration functionsdynamicsrational mapsconjugacy classes.
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 3 , January 2007 , pp. 343 - 359
Copyright
Copyright © Australian Mathematical Society 2007

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