HAMILTONIAN AND SYMPLECTIC ALGORITHMS FOR THE ALGEBRAIC RICCATI EQUATION.

摘要

The algebraic Riccati equation is a matrix quadratic equation that arises in the theory of optimal and stochastic control. The relationship with symplectic linear algebra is reviewed. An investigation of the perturbation theory leads to a condition number for the problem. A new numerical method, the Hamiltonian QR algorithm, preserves special structure and is numerically stable and efficient.