ANZIAM J.
48 (2007), 343-359
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On the dynamics of a family of third-order iterative functions
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Sergio Amat
Departamento de Matemática Aplicada
y Estadística
Universidad Politécnica de Cartagena
Spain
sergio.amat@upct.es
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Sonia Busquier
Departamento de Matemática Aplicada
y Estadística
Universidad Politécnica de Cartagena
Spain;
sonia.busquier@upct.es
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Sergio Plaza
Depto. de Matemáticas
Facultad de Ciencias
Universidad de Santiago de Chile
Casilla 307, Correo 2
Santiago
Chile
splaza@lauca.usach.cl
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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-Halley
root-finding algorithms, as well as the so-called
c-methods. The conjugacy classes of these
iterative methods are found explicitly.
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Australian Mathematical Publishing Association Inc.
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©
Australian MS
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