On the convergence of the accelerated riccati iteration method

Abstract

In this paper, we establish results fully addressing two open problems proposed recently by I. Ivanov, see Nonlinear Analysis 69 (2008) 4012–4024, with respect to the convergence of the accelerated Riccati itera tion methodfor solving the continuous coupled algebraic Riccati equation, or CCAREfor short. These results confirm several desirable features of that method, including the monotonicity and boundedness of the sequences it produces, its capability of determining whether the CCARE has a solution, the extremal solu tions it computes under certain circumstances, and its faster convergence than the regular Riccati iteration method.