A new inversion-free iterative algorithm for the discrete algebraic Riccati equation

In this paper, by the transformation form of the discrete algebraic Riccati equation (DARE), we propose a new inverse-free iterative algorithm to obtain the positive definite solution of the DARE. Furthermore, the monotone convergence is proved and convergence rate analysis is presented for the derived algorithm. Compared with some existing algorithms, numerical examples demonstrate the feasibility and effectiveness of our algorithm.

Automated summary

In this paper, a new inverse-free iterative algorithm is proposed to obtain the positive definite solution of the discrete algebraic Riccati equation (DARE). Monotone convergence is proved and convergence rate analysis is presented for the derived algorithm. Numerical examples demonstrate the feasibility and effectiveness of the proposed algorithm.