A new linearized implicit iteration method for nonsymmetric algebraic Riccati equations

For the nonsymmetric algebraic Riccati equation, we establish a new linearized implicit iteration method (LI) for computing its minimal nonnegative solution. And a modified linearized implicit iteration method (MLI) is obtained through Shamanskii technique. Under suitable conditions, we prove the monotone convergence of the LI and MLI iteration methods. Numerical experiments show that the LI and MLI iteration methods are feasible and effective. Moreover, the MLI iteration method outperforms the alternately linearized implicit iteration method (in: Bai et al., Numer. Linear Algebr. Appl. 13:655–674, 2006). © 2015, Korean Society for Computational and Applied Mathematics.