On the speed of convergence of Newton’s method for complex polynomials
On the speed of convergence of Newton’s method for complex polynomials
We investigate Newtonâs 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 $\mathcal {S}_d$ of $3.33d\log ^2 d(1 + o(1))$ points with the following universal property: for every normalized polynomial of …