This paper addresses some numerical issues that arise in computing a basis for the stable invariant subspace of a Hamiltonian matrix. Such a basis is required in solving the algebraic Riccati equation using the well-known method due to Laub. Two algorithms based on certain properties of Hamiltonian matrices are proposed as viable alternatives to the conventional approach.
Patel, R. V.,
& Misra, P.
(1994). Computation of Stable Invariant Subspaces of Hamiltonian Matrices. SIAM Journal on Matrix Analysis and Applications, 15 (1), 284-298.