  We adapt Victor Y. Pan's root-based algorithm for finding approximate GCD to
the case where the polynomials are expressed in Bernstein bases. We use the
numerically stable companion pencil of Gudbj\"orn F. J\'onsson to compute the
roots, and the Hopcroft-Karp bipartite matching method to find the degree of
the approximate GCD. We offer some refinements to improve the process.
