Fast Doubling Algorithm for the Solution of the Riccati Equation Using Cyclic Reduction Method

A new iterative doubling algorithm for the solution of the discrete time Riccati equation is proposed. The algorithm is based on the Cyclic Reduction Method (CRM). The proposed doubling algorithm does not require non-singularity of the transition matrix and is faster than the classical doubling algorithm. The method can be applied to infinite measurement noise case, where the Riccati equation takes the form of the Lyapunov equation. In this case, the classical doubling algorithm is faster.