Communications on Applied Mathematics and Computation >

2025 , Vol. 7 >Issue 5: 1923 - 1939

DOI: https://doi.org/10.1007/s42967-024-00419-5

ORIGINAL PAPERS

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

  • Li Wang ,
  • Yi Xiao ,
  • Yu-Li Zhu ,
  • Yi-Bo Wang
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  • School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China

Received date: 2023-12-30

  Revised date: 2024-04-26

  Accepted date: 2024-04-27

  Online published: 2024-08-08

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).

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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

Cite this article

Li Wang , Yi Xiao , Yu-Li Zhu , Yi-Bo Wang . Modified Alternately Linearized Implicit Iteration Methods for Nonsymmetric Coupled Algebraic Riccati Equation[J]. Communications on Applied Mathematics and Computation, 2025 , 7(5) : 1923 -1939 . DOI: 10.1007/s42967-024-00419-5

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