• 论文 •

### Krylov子空间法求解非对称代数Riccati方程

1. 中国海洋大学数学科学学院, 青岛 266100
• 收稿日期:2021-10-04 发布日期:2022-12-08
• 通讯作者: 郭晓霞, Email: guoxiaoxia@ouc.edu.cn.
• 基金资助:
国家自然科学基金(11871444)和中央高校基本科研业务费专项资金(201562012)资助.

Yang Yufeng, Guo Xiaoxia. A KRYLOV SUBSPACE METHOD FOR THE NONSYMMETRIC ALGEBRAIC RICCATI EQUATION[J]. Journal on Numerica Methods and Computer Applications, 2022, 43(4): 447-456.

### A KRYLOV SUBSPACE METHOD FOR THE NONSYMMETRIC ALGEBRAIC RICCATI EQUATION

Yang Yufeng, Guo Xiaoxia

1. School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
• Received:2021-10-04 Published:2022-12-08

The Krylov subspace iteration method for algebraic Riccati equation has been presented in [1]. In this paper, the Krylov invariant subspace iteration for solving the nonsymmetric algebraic Riccati equation is proposed. A very concise iterative formula is obtained by the Cayley transformation, which only involves matrix calculation. Furthermore, the proof of convergence becomes very simple and accessible. Finally, numerical experiments show that the proposed algorithm is feasible and effective.

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