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

The authors present a novel 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 procedure that characterizes the GCD of P_m,d as the output decoupling zero polynomial of a linear system that may be associated with P_m,d. The computation of the GCD is thus reduced to finding the finite zeros of a certain pencil. An error analysis proving the stability of the described procedures is given. Three numerical results that demonstrate the effectiveness of the method are presented