离散耦合Riccati矩阵方程的无反演牛顿迭代法
Newton Iteration Method without Inversion for Discrete Coupled Riccati Matrix Equations
摘要: 本文研究了离散耦合Riccati矩阵方程的求解问题。我们利用矩阵反演等式得到离散耦合Riccati矩阵方程的等价形式，并通过牛顿求根方法构造无反演的迭代算法求解离散耦合Riccati矩阵方程。此外我们证明了无反演牛顿迭代算法的收敛性。最后，利用数值例子来验证提出的理论结果。
Abstract: In this paper, the discrete coupled Riccati matrix equation is considered. We obtain the equivalent form of the discrete coupled Riccati matrix equation by using the matrix inversion equation. And an iterative algorithm without inversion is constructed to solve the discrete coupled Riccati matrix equation by Newton’s method of finding roots. In addition, we prove the convergence of Newtonian iterative algorithm without inversion. Finally, a numerical example demonstrates the theoretical results.
文章引用：庄柔柔. 离散耦合Riccati矩阵方程的无反演牛顿迭代法[J]. 应用数学进展, 2025, 14(4): 342-354. https://doi.org/10.12677/aam.2025.144167

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