Geometry of polynomials and root-finding via path-lifting
Geometry of polynomials and root-finding via path-lifting
Using the interplay between topological, combinatorial, and geometric properties of polynomials and analytic results (primarily the covering structure and distortion estimates), we analyze a path-lifting method for finding approximate zeros, similar to those studied by Smale, Shub, Kim, and others. Given any polynomial, this simple algorithm always converges to a …