A numerical algorithm for zero counting. III: Randomization and condition

Abstract

In a recent paper [7] we analyzed a numerical algorithm for computing the number of real zeros of a polynomial system. The analysis relied on a condition number κ(f) for the input system f. In this paper we look at κ(f) as a random variable derived from imposing a probability measure on the space of polynomial systems and give bounds for both the tail P{κ(f) > a} and the expected value E(log κ(f)).