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What and Who

Improved Root Separation Bound: Bigger and Geometric

Hoon Hong
North Carolina State University
Talk
AG 1, AG 2, AG 3, AG 4, AG 5, SWS, RG1, MMCI  
Public Audience
English

Date, Time and Location

Tuesday, 6 March 2018
14:00
60 Minutes
E1 4
024
Saarbrücken

Abstract

Let f be a square-free polynomial. The root separation of f is the minimum of the pair-wise distance between the complex roots of f. A root separation bound is a lower bound on the root separation.

Finding a root separation bound is a fundamental problem, arising in numerous disciplines in mathematics, science and engineering. Due to its importance, there has been extensive research on this problem, resulting in various celebrated bounds.

However, the previous bounds are still very pessimistically small. Furthermore, surprisingly, they are not compatible with the geometry roots: for instance, when the roots are doubled, the bounds do not double. Worse yet, the bounds even become smaller.

In this talk, we present another bound, which is "nicer" than the previous bounds in that
(1) It is siginificanly bigger (hence better) than the previous bounds.
(2) It is compatible with the geometry of the roots.

If time allows, we will also describe a generalization to multivariate polynomials systems.

This is a joint work with Aaron Herman and Elias Tsigaridas.

Contact

Jennifer Müller
2900
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Uwe Brahm, 03/02/2018 12:22 PM
Jennifer Müller, 03/02/2018 10:07 AM -- Created document.