Numerical methods for the minimal non-negative solution of the non-symmetric coupled algebraic Riccati equation
Numerical methods for the minimal non-negative solution of the non-symmetric coupled algebraic Riccati equation
复制标题
非对称耦合代数Riccati方程最小非负解的数值方法
DOI：
10.1002/asjc.2205
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发表时间：
2021
影响因子：
2.4
通讯作者：
Tan Fangyuan
中科院分区：
文献类型：
--
作者：
Zhang Juan;Tan Fangyuan
本文在非对称代数Riccati方程和耦合Riccati方程理论的基础上，给出了非对称耦合代数Riccati方程（NCARE）的一般形式.为了有效求解NCARE的最小非负解，改进了两种数值迭代方法：不精确牛顿法（INewton）和交替线性隐式法（ALI）。进一步给出了这两种迭代法的收敛性定理。最后，我们提供了数值例子来证明所得到的方法的有效性。
In this paper, base on the theory of the non‐symmetric algebraic Riccati equation and the coupled Riccati equation, we give the general form of the non‐symmetric coupled algebraic Riccati equation (NCARE). In order to effectively solve the minimal non‐negative solution of the NCARE, two numerical iteration methods are improved: inexact Newton method (INewton) and alternate linear implicit method (ALI). Further, we give the convergence theory of the two iteration methods. Finally, we offer numerical examples to show the effectiveness of the derived methods.