Smoothed Analysis for the Condition Number of Structured Real Polynomial Systems

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.

Title changed due to an interesting journal policy, to appear in Mathematics of Computation

References in corpus (2)

• A Numerical Algorithm for Zero Counting. I: Complexity and Accuracy
• A Numerical Algorithm for Zero Counting. II: Distance to Ill-posedness and Smoothed Analysis