Krylov子空间法求解非对称代数Riccati方程

doi:10.12288/szjs.s2021-0794

数值计算与计算机应用 ›› 2022, Vol. 43 ›› Issue (4): 447-456.DOI: 10.12288/szjs.s2021-0794

• 论文 • 上一篇

Krylov子空间法求解非对称代数Riccati方程

杨玉凤, 郭晓霞

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.

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杨玉凤, 郭晓霞. Krylov子空间法求解非对称代数Riccati方程[J]. 数值计算与计算机应用, 2022, 43(4): 447-456.

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

School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China

Received:2021-10-04 Published:2022-12-08

文献[1]给出了求解对称代数Riccati方程的Krylov子空间迭代法.本文利用该思想,提出了求解非对称代数Riccati方程的Krylov子空间迭代法.通过Cayley变换,我们得到了该方法的一个非常简洁的迭代公式,该公式只涉及矩阵计算.利用该公式,收敛性证明也变得非常简单易懂.最后数值算例验证了算法的可行性和有效性.

关键词： Riccati方程, M矩阵, 不变子空间, 最小非负解

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.

Key words: Riccati equation, M-Matrix, invariant subspace, minimal nonnegative linebreak solutions

MR(2010)主题分类:

15A06
65F05

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[1]	王淑娟, 郭晓霞. 关于非对称代数Riccati方程的ALI迭代算法收敛速率的讨论[J]. 数值计算与计算机应用, 2010, 31(1): 76-80.

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摘要

Krylov子空间法求解非对称代数Riccati方程

A KRYLOV SUBSPACE METHOD FOR THE NONSYMMETRIC ALGEBRAIC RICCATI EQUATION

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