Optimization Strategies for the Floating-point Gcd

We describe algorithms for computing the greatest common divisor (GCD) of two univariate polynomials with inexactly-known coeecients. Assuming that an estimate for the GCD degree is available (e.g., using an SVD-based algorithm), we formulate and solve a nonlinear optimization problem in order to determine the coeecients of the \best" GCD. We discuss various issues related to the implementation of the algorithms and present some preliminary test results.

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