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In this paper, applying the Newton method, we transform the complexcontinuous-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 ispresented to save computational amount effectively. Moreover, we analyze theconvergence of the Newton-GADI method. The convergence rate of the Newton-GADIand Newton-ADI methods is compared by analyzing their spectral radii.Furthermore, we give a way to select the quasi-optimal parameter. Correspondingnumerical tests are shown to illustrate the effectiveness of the proposedalgorithms.

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