Absolute real root separation

TL;DR

This paper investigates the minimal nonzero distance between the absolute values of real roots of polynomials, providing the first comprehensive bounds for this absolute root separation problem.

Contribution

The paper introduces the concept of absolute root separation and establishes tight bounds specifically for real roots, filling a gap in classical polynomial root analysis.

Findings

Derived tight bounds for absolute root separation of real roots

Extended classical root separation concepts to absolute values

Provided theoretical framework for future research in polynomial root analysis

Abstract

While the separation (the minimal nonzero distance) between roots of a polynomial is a classical topic, its absolute counterpart (the minimal nonzero distance between their absolute values) does not seem to have been studied much. We present the general context and give tight bounds for the case of real roots.