The QRGCD(f, g, x, eps) function returns univariate numeric polynomials u,v,d such that d is an approximate-GCD for the input polynomials (f, g). (See [1] for the definition of an approximate-GCD.)

With high probability, the output polynomials satisfy || u * f + v * g - d || < ||(f,g,u,v,d)|| * eps, || f - d * f1 || < ||f|| * eps, and || g - d * g1 || < ||g|| * eps, where the polynomials f1 and f2 are cofactors of f and g with respect to the divisor d.

The output polynomials u and v satisfy deg(u) < deg(g) - deg(d) and deg(v) < deg(f) - deg(d).

Corless, R. M.; Watt, S. M.; and Zhi, L. "QR Factoring to compute the GCD of Univariate Approximate Polynomials." IEEE Transactions on Signal Processing. Vol. 52(12), (2004): 3394-3402.