We discuss a parallel library of efficient algorithms for the solution of linear-quadratic optimal control problems involving largescale systems with state-space dimension up to $O(10^4)$. We survey the numerical algorithms underlying the implementation of the chosen optimal control methods. The approaches considered here are based on invariant and deflating subspace techniques, and avoid the explicit solution of the associated algebraic Riccati equations in case of possible ill-conditioning. Still, our algorithms can also optionally compute the Riccati solution. The major computational task of finding spectral projectors onto the required invariant or deflating subspaces is implemented using iterative schemes for the sign and disk functions. Experimental results report the numerical accuracy and the parallel performance of our approach on a cluster of Intel Itanium-2 processors.

We study canonical forms for Hamiltonian and symplectic matrices or pencils under equivalence transformations which keep the class invariant. In contrast to other canonical forms our forms are as close as possible to a triangular structure in the same class. We give necessary and sufficient conditions for the existence of Hamiltonian and symplectic triangular Jordan, Kronecker and Schur forms. The presented results generalize results of Lin and Ho [17] and simplify the proofs presented there.

We study canonical forms for Hamiltonian and symplectic matrices or pencils under equivalence transformations which keep the class invariant. In contrast to other canonical forms our forms are as close as possible to a triangular structure in the same class. We give necessary and sufficient conditions for the existence of Hamiltonian and symplectic triangular Jordan, Kronecker and Schur forms. The presented results generalize results of Lin and Ho [17] and simplify the proofs presented there.