Smoothed Analysis for the Condition Number of Structured Real Polynomial Systems

TL;DR

This paper investigates how small changes in coefficients affect the real zeros of structured polynomial systems, providing explicit condition number estimates and extending them within a smoothed analysis framework.

Contribution

It offers new explicit condition number estimates for structured polynomial systems and extends these results to smoothed analysis, enhancing understanding of system sensitivity.

Findings

Explicit condition number estimates for structured systems

Extension of estimates to smoothed analysis setting

Improved understanding of polynomial system sensitivity

Abstract

We consider the sensitivity of real zeros of structured polynomial systems to perturbations of their coefficients. In particular, we provide explicit estimates for condition numbers of structured random real polynomial systems, and extend these estimates to the smoothed analysis setting.