Counting roots of a polynomial in a convex compact region by means of winding number calculation via sampling (Q2175597)

The authors propose an algorithm for counting the roots of a given polynomial in a fixed convex region on the complex plane by expressing their number as the winding number computed along the boundary of the region, provided that the boundary is sufficiently isolated from the roots of the polynomial. The correctness of the proposed algorithm is tested by means of some experiments. For the entire collection see [Zbl 1428.68016].