A JACOBI-LIKE METHOD FOR SOLVING ALGEBRAIC RICCATI-EQUATIONS ON PARALLEL COMPUTERS

An algorithm to solve continuous-time algebraic Riccati equations thro ugh the Hamiltonian Schur form is developed. It is an adaption for Ham iltonian matrices of an unsymmetric Jacobi method of Eberlein [15]. It uses unitary symplectic similarity transformations and preserves the Hamiltonian structure of the matrix, Each iteration step needs only lo cal information about the current matrix, thus admitting efficient par allel implementations on certain parallel architectures, Convergence p erformance of the algorithm is compared with the Hamiltonian-Jacobi al gorithm of Byers [12], The numerical experiments suggest that the meth od presented here converges considerably faster for non-Hermitian Hami ltonian matrices than Byers' Hamiltonian-Jacobi algorithm, Besides tha t, numerical experiments suggest that for the method presented here, t he number of iterations needed for convergence can be predicted by a s imple function of the matrix size.