  In this paper, applying the Newton method, we transform the complex
continuous-time algebraic Riccati matrix equation into a Lyapunov equation.
Then, we introduce an efficient general alternating-direction implicit (GADI)
method to solve the Lyapunov equation. The inexact Newton-GADI method is
presented to save computational amount effectively. Moreover, we analyze the
convergence of the Newton-GADI method. The convergence rate of the Newton-GADI
and Newton-ADI methods is compared by analyzing their spectral radii.
Furthermore, we give a way to select the quasi-optimal parameter. Corresponding
numerical tests are shown to illustrate the effectiveness of the proposed
algorithms.
