AN IMPLICITLY RESTARTED SYMPLECTIC LANCZOS METHOD FOR THE HAMILTONIANEIGENVALUE PROBLEM

An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem is presented. The Lanczos vectors are constructed t o form a symplectic basis. The inherent numerical difficulties of the symplectic Lanczos method are addressed by inexpensive implicit restar ts. The method is used to compute eigenvalues, eigenvectors, and invar iant subspaces of large and sparse Hamiltonian matrices and low-rank a pproximations to the solution of continuous-time algebraic Riccati equ ations with large and sparse coefficient matrices. (C) 1997 Elsevier S cience Inc.