AbstractUsing a result from orbifold theory, McMullen showed that Newton’s method is generally convergent for solving x n − c = 0. In this paper, we extend McMullen’s result to the next two members of an infinite family of iteration functions called the Basic Family which starts with Newton’s method. With the aid of a visualization technique called polynomiography, we further conjecture the general convergence of all members of the Basic Family when extracting radicals. Using the computer algebra system Maple, we obtain some partial results toward the proof of our conjecture.
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