(joint work with Agnes Szanto)
We present a symbolic-numeric technique to find the closest multivariate
polynomial system to a given one which has roots with prescribed multiplicity
structure. We prove that the distance of the given system from the set of
systems with given root multiplicity structure is equal to the least square
value of the generalized Weierstrass map, defined by Ruatta to compute the
exact roots of a polynomial system. We give explicitly an iteration function
which computes this minimum. Our results extend previous results in the
univariate case and in the multivariate case.