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Zbl 1113.65047
Amat, S.; Busquier, Sonia; Plaza, S.
A construction of attracting periodic orbits for some classical third-order iterative methods. (English)
[J] J. Comput. Appl. Math. 189, No. 1-2, 22-33 (2006). ISSN 0377-0427

A family of root-finding iterative methods for finding roots of nonlinear equations is presented. The authors discuss a procedure for constructing polynomials so that superattracting periodic orbits of any prescribed period occur when these methods are applied. This family includes Chebyshev's method, Halley's method, the super-Halley method, an the c-method as particular cases. A detailed example is given and illustrated by a figure which shows the basins of attraction of the periodic orbit.
[René Lamour (Berlin)]

MSC 2000:: *65H05 Single nonlinear equations (numerical methods)
30C15 Zeros of polynomials, etc. (one complex variable)

Keywords: rational maps; numerical example; root-finding; Chebyshev's method, Halley's method; c-method; basins of attraction

Cited in: Zbl 1115.65052

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