Optimal Path Homotopy For Univariate Polynomials

Abstract

The goal of this paper is to study the path-following method for univariate polynomials. We propose to study the complexity and condition properties when the Newton method is applied as a correction operator. Then we study the geodesics and properties of the condition metric along those curves. Last, we compute approximations of geodesics and study how the condition number varies with the quality of the approximation.