Review of some iterative root-finding methods from a dynamical point of view.

*(English)* Zbl 1137.37316
Summary: From a dynamical point of view applied to complex polynomials, we study a number of root-finding 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 Steffensen, among others. Since all of the iterative root-finding methods we study satisfy the Scaling Theorem, except for Stirling’s method and that of Steffensen, we obtain their conjugacy classes.

##### MSC:

37F10 | Polynomials; rational maps; entire and meromorphic functions |

30C15 | Zeros of polynomials, etc. (one complex variable) |