  We design a fast implicit real QZ algorithm for eigenvalue computation of
structured companion pencils arising from linearizations of polynomial
rootfinding problems. The modified QZ algorithm computes the generalized
eigenvalues of an $N\times N$ structured matrix pencil using $O(N)$ flops per
iteration and $O(N)$ memory storage. Numerical experiments and comparisons
confirm the effectiveness and the stability of the proposed method.
