An implicit iterative algorithm for generalized algebraic Riccati matrix equations

In this paper, an implicit iterative algorithm is developed to obtain the unique positive definite solution of the generalized algebraic Riccati matrix equation. For this proposed algorithm, there exisits a tuning parameter which can be chosen such that this algorithm achieves better convergence performance. Some convergence results are given for the proposed algorithm. Moreover, an approach is also provided to choose an appropriate initial condition for this algorithm. Finally, a numerical example is presented to verify the effectiveness of this algorithm.