A small probabilistic universal set of starting points for finding roots of complex polynomials by Newton's method

Béla Bollobás, Malte Lackmann, Dierk Schleicher

We specify a small set, consisting of $O(d(\log \log d{)}^2)$ points, that intersects the basins under Newton's method of \emph{all} roots of \emph{all} (suitably normalized) complex…