Euclidean algorithm for numerical polynomial GCD. JSC 1998

In this paper we provide a taet, numerically stable algorithm to determine when two given polynomials a arid b are relatively prime and remain relatively prime even after small perturbations of their coefficients. Such a problem is important in ninny applications where input data are only available up to a certain precision.Our method—an extension of the Cabay-Meleshko algorithm for Pade approximation—is typically ли order of magnitude faster than previously known stable methods. As such it may lie used an an inexpensive t.-sl which may lie applied before attempt ing to compute a ''numerical GCIJ'', in general a much more difficult task. We prove that the algorithm is numerically stable and give experiments verifying the numerical behaviour. Finally, we discuss possible extensions of our approach that can be applied to tin- problem of actually computing a numerical GCD.