A class of Hamiltonian-symplectic methods for solving the algebraic Riccati equation

AbstractThe algebraic Riccati equation can be solved by finding a certain invariant subspace of a related Hamiltonian matrix. G. Ammar and V. Mehrmann devised a method for calculating this invariant subspace that exploits the Hamiltonian structure of the matrix by using unitary, symplectic similarity transformations. This paper discusses a class of methods that find the invariant subspace by using symplectic similarity transformations that are not necessarily unitary. The method of Ammar and Mehrmann is a special case