SR Algorithms for Structured Hamiltonian and Symplectic Eigenproblems

摘要

In this work, structure-preserving algorithms based on the SR algorithm are presented for three classes of structured Hamiltonian and symplectic eigenproblems, which occur in control theory. Compared with the standard QR algorithm for computing all the eigenvalues of these structured Hamiltonian and symplectic matrices, our algorithms cut work requirement and calculate a symplectic orthogonal basis for all the invariant subspaces.