Pseudozero Set of Real Multivariate Polynomials

The pseudozero set of a system P of polynomials in n variables is the subset of C consisting of the union of the zeros of all polynomial systems Q that are near to P in a suitable sense. This concept arises naturally in Scientific Computing where data often have a limited accuracy. When the polynomials of the system are polynomials with complex coefficients, the pseudozero set has already been studied. In this paper, we focus on the case where the polynomials of the system have real coefficients and such that all the polynomials in all the perturbed polynomial systems have real coefficients as well. We provide an explicit definition to compute this pseudozero set. At last, we analyze different methods to visualize this set. Mathematics Subject Classification (2000). 12D10, 30C10, 30C15, 26C10.