Structure-preserving Schur methods for computing square roots of real   skew-Hamiltonian matrices
  Our contribution is two-folded. First, starting from the known fact that every real skew-Hamiltonian matrix has a real Hamiltonian square root, we give a complete characterization of the square roots of a real skew-Hamiltonian matrix W. Second, we propose a structure exploiting method for computing square roots of W. Compared to the standard real Schur method, which ignores the structure, our method requires significantly less arithmetic. 
Zhongyun Liu, Yulin Zhang, Carla Ferreira and Rui Ralha
math.NA