Computation of Invariant Subspaces Corresponding to Stable Eigenvalues of Hamiltonian Matrices

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.