# Numerically stable algorithms for computing remainder of polynomials

Let $f, g \in \mathbb{R}[x]$ and $\deg f > \deg g$. I am looking for asymptotically fast and numerically stable algorithms for computing $f \bmod g$. In the applications intended, both $f, g$ are dense polynomials with double precision floating-point coefficients. But, for now, I'm more interested in the algorithms rather than the implementation. References for algorithms for computing GCD of numerical polynomials are also appreciated.