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

• ORIGINAL PAPERS • Previous Articles    

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).

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