A construction of attracting periodic orbits for some classical third-order iterative methods

摘要

We use a family of root-finding iterative methods for finding roots of nonlinear equations. We present 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, and the c-methods, as particular cases.