A new method for computing the stable invariant subspace of a real Hamiltonian matrix

A new backward stable, structure preserving method of complexity O(n3) is presented for computing the stable invariant subspace of a real Hamiltonian matrix and the stabilizing solution of the continuous-time algebraic Riccati equation. The new method is based on the relationship between the invariant subspaces of the Hamiltonian matrix H and the extended matrix 0HH0 and makes use of the symplectic URV-like decomposition that was recently introduced by the authors.