Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (5): 1923-1939.doi: 10.1007/s42967-024-00419-5

• ORIGINAL PAPERS • 上一篇    

Modified Alternately Linearized Implicit Iteration Methods for Nonsymmetric Coupled Algebraic Riccati Equation

Li Wang, Yi Xiao, Yu-Li Zhu, Yi-Bo Wang   

  1. School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China
  • 收稿日期:2023-12-30 修回日期:2024-04-26 接受日期:2024-04-27 出版日期:2024-08-08 发布日期:2024-08-08
  • 通讯作者: Li Wang,E-mail:wanglileigh@163.com E-mail:wanglileigh@163.com
  • 基金资助:
    The work was supported in part by the National Natural Science Foundation for Youths of China (11801164) and the Youth Project of Hunan Provincial Education Department of China (22B0498).

Modified Alternately Linearized Implicit Iteration Methods for Nonsymmetric Coupled Algebraic Riccati Equation

Li Wang, Yi Xiao, Yu-Li Zhu, Yi-Bo Wang   

  1. School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China
  • Received:2023-12-30 Revised:2024-04-26 Accepted:2024-04-27 Online:2024-08-08 Published:2024-08-08
  • Contact: Li Wang,E-mail:wanglileigh@163.com E-mail:wanglileigh@163.com
  • Supported by:
    The work was supported in part by the National Natural Science Foundation for Youths of China (11801164) and the Youth Project of Hunan Provincial Education Department of China (22B0498).

摘要: In this paper, according to the Shamanskii technology, an alternately linearized implicit (ALI) iteration method is proposed to compute the minimal nonnegative solution to the nonsymmetric coupled algebraic Riccati equation. Based on the ALI iteration method, we propose two modified alternately linearized implicit (MALI) iteration methods with double parameters. Further, we prove the monotone convergence of these iteration methods. Numerical examples demonstrate the effectiveness of the presented iteration methods.

关键词: Nonsymmetric coupled algebraic Riccati equation, Shamanskii technology, Alternately linearized iteration (ALI) method, Monotone convergence

Abstract: In this paper, according to the Shamanskii technology, an alternately linearized implicit (ALI) iteration method is proposed to compute the minimal nonnegative solution to the nonsymmetric coupled algebraic Riccati equation. Based on the ALI iteration method, we propose two modified alternately linearized implicit (MALI) iteration methods with double parameters. Further, we prove the monotone convergence of these iteration methods. Numerical examples demonstrate the effectiveness of the presented iteration methods.

Key words: Nonsymmetric coupled algebraic Riccati equation, Shamanskii technology, Alternately linearized iteration (ALI) method, Monotone convergence