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A construction of attracting periodic orbits for some classical third-order iterative methods. (English) Zbl 1113.65047
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.

MSC:
65H05Single nonlinear equations (numerical methods)
30C15Zeros of polynomials, etc. (one complex variable)