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/sub m,d/, of maximal degree d. It is based on a procedure that characterizes the GCD of P/sub m,d/ as the output decoupling zero polynomial of a linear system that may be associated with P/sub 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.<
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