turkmath.org

The condition number of a polynomial system measures the sensitivity of its roots to perturbations in the coefficients. We study the condition number of random polynomial systems for a broad family of distributions. Our work is motivated by Smale's 17th problem on the complexity of polynomial system solving. We present a brief overview of current state in Smale's 17th problem then proceed with our recent results on average conditioning. This is joint work with J.Maurice Rojas and Grigoris Paouris.