On the speed of convergence of Newton's method for complex polynomials
We investigate Newton's method for complex polynomials of arbitrary degree d, normalized so that all their roots are in the unit disk. For each degree d, we give an explicit set S-d of 3.33d log(2) d(1 + o(1)) points with the following universal property: for every normalized polynomial of degree d there are d starting points in S-d whose Newton iterations find all the roots with a low number of i
