  This paper presents a regularization theory for numerical computation of
polynomial greatest common divisors and a convergence analysis, along with a
detailed description of a blackbox-type algorithm. The root of the
ill-posedness in conventional GCD computation is identified by its geometry
where polynomials form differentiable manifolds entangled in a stratification
structure. With a proper regularization, the numerical GCD is proved to be
strongly well-posed. Most importantly, the numerical GCD solves the problem of
finding the GCD accurately using floating point arithmetic even if the data are
perturbed. A sensitivity measurement, error bounds at each computing stage, and
the overall convergence are established rigorously. The computing results of
selected test examples show that the algorithm and software appear to be robust
and accurate.
