A matrix pencil based numerical method for the computation of the GCD of polynomials

The paper presents a new numerical method for the computation of the greatest common divisor (GCD) of an m-set of polynomials of R[s], P _m,d, of maximal degree d. It is based on a previously proposed theoretical procedure (Karcanias, 1989) that characterizes the GCD of P_m,d as the output decoupling zero polynomial of a linear system S(Aˆ,Cˆ) that may be associated with P_m,d . The computation of the GCD is thus reduced to finding the finite zeros of the pencil sW-AW, where W is the unobservable subspace of S(Aˆ,Cˆ). If k=dim W, the GCD is determined as any nonzero entry of the kth compound C_k(sW-AˆW). The method defines the exact degree of GCD, works satisfactorily with any number of polynomials and evaluates successfully approximate solutions