Review of some iterative root¯finding methods from adynamical point of view

Resumen

From a dynamical point of view applied to complex polynomials, we
study a number of root{¯nding iterative methods. We consider Newton's method, Newton's method for multiple roots, Jarratt's method, the super{Halley method, the convex as well as the double convex acceleration of Whittaker's method, the methods of Chebyshev, Stirling, and Ste®ensen, among others. Since all of the iterative root{¯nding methods we study satisfy the Scaling Theorem, except for Stirling's method and that of Ste®ensen, we obtain their conjugacy classes.