Quality of positive root bounds

HERMAN, AARON PAUL. Positive Root Bounds and Root Separation Bounds. (Under the direction of Hoon Hong.) In this thesis, we study two classes of bounds on the roots of a polynomial (or polynomial system). A positive root bound of a polynomial is an upper bound on the largest positive root. A root separation bound of a polynomial is a lower bound on the distance between the roots. Both classes of bounds are fundamental tools in computer algebra and computational real algebraic geometry, with numerous applications. In the first part of the thesis, we study the quality of positive root bounds. Higher quality means that the relative over-estimation (the ratio of the bound and the largest positive root) is smaller. We find that all known positive root bounds can be arbitrarily bad. We then show that a particular positive root bound is tight for certain important classes of polynomials. In the remainder of the thesis, we turn to root separation bounds. We observe that known root separation ...

• Type: Journal
• Year: 2016
• Where: JSC
• Authors: Aaron Herman, Hoon Hong
• Keywords: JSC 2016