A general alternating-direction implicit Newton method for solving continuous-time algebraic Riccati equation

Abstract

The complex continuous-time algebraic Riccati equation (CCARE) is quadratic, which is closely related to the analysis of the optimal control problem. In this paper, we apply Newton method as the outer iteration and an efficient general alternating-direction implicit (GADI) method as the inner iteration to solve CCARE. Meanwhile, we propose the inexact Newton-GADI method to further improve the efficiency of the algorithm. We give the convergence analysis of our proposed method and prove that its convergence rate is faster than the classical Newton-ADI method. Finally, some numerical examples are given to illustrate the effectiveness of our algorithms and the correctness of the theoretical analysis.