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

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)).Fil: Cucker, Felipe. City University of Hong Kong; Hong KongFil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Malajovich, Gregorio. Universidade Federal do Rio de Janeiro; BrasilFil: Wschebor, Mario. Universidad de la República; Urugua