Implicit QR for Companion-like Pencils
  A fast implicit QR algorithm for eigenvalue computation of low rank corrections of unitary matrices is adjusted to work with matrix pencils arising from polynomial zerofinding problems . The modified QZ algorithm computes the generalized eigenvalues of certain NxN rank structured matrix pencils using O(N^2) ops and O(N) memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method. 
Paola Boito, Yuli Eidelman, Luca Gemignani
math.NA