Faster Numerical Univariate Polynomial Root-Finding by Means of Subdivision Iterations.

Root-finding for a univariate polynomial is four millennia old and still highly important for Computer Algebra and various other fields. Subdivision root-finders for a complex univariate polynomial are known to be highly efficient and practically promising. The recent one by Becker et al. [2] competes for user’s choice and is nearly optimal for dense polynomials represented in monomial basis, but [18] proposes and analyzes further significant acceleration, which becomes dramatic for polynomials admitting their fast evaluation (e.g., sparse ones). Here and in the companion paper [19], we present some of these results and algorithms.