论文标题
一种通用交替方向隐式牛顿方法，用于求解复杂的连续时间代数riccati矩阵方程
A general alternating-direction implicit Newton method for solving complex continuous-time algebraic Riccati matrix equation
论文作者
论文摘要
在本文中，应用牛顿方法，我们将复杂的连续时间代数riccati矩阵方程转换为lyapunov方程。然后，我们引入了一种有效的一般交替方向隐式（GADI）方法来求解Lyapunov方程。提出了不精确的牛顿 - 加迪方法，以有效地节省计算量。此外，我们分析了牛顿 - 加迪法的收敛性。通过分析其光谱半径，比较了牛顿 - 加迪和牛顿 - 亚种方法的收敛速率。此外，我们提供了一种选择准最佳参数的方法。显示相应的数值测试以说明所提出算法的有效性。
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.
