An Algebraic Method for Separating Close-Root Clusters and the Minimum Root Separation
Tateaki Sasaki, Fujio Kako · Birkhäuser Basel eBooks · 2007
Given a univariate polynomial over C, we discuss two issues, an algebraic method for separating a factor of mutually close roots from the polynomial, and a reasonable formula for the minimum root separation, by assuming that the close roots form well-separated clusters. The technique we use is very simple and effective; we move the origin near to the center of a close-root cluster, and then we are able to treat the other roots collectively, reducing the problem to a very simple one. Following this idea, we present a very simple and stable algebraic method for separating the close-root cluster, derive two lower-bound formulas for the distance between two close roots, and obtain a fairly simple lower bound of the minimum root separation of polynomials over C.