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A class of fixed point iteration for the coupled algebraic Riccati equation

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Abstract

In this paper, we consider the positive solution of the coupled algebraic Riccati equation. If this equation has a positive solution, the existence and convergence rate for the solution is discussed. Additionally, we show special properties for the positive solution of this equation. Further, a fixed point iteration method for the minimal positive solution of the coupled algebraic Riccati equation is proposed. Finally, we offer corresponding numerical examples to show the effectiveness of the derived results.

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Acknowledgements

The work was supported in part by the National Natural Science Foundation of China (11771368, 11771370), Natural Science Foundation for Distinguished Young Scholars of Hunan Province (2021JJ10037), Hunan Youth Science and Technology Innovation Talents Project (2021RC3110), the Key Project of Education Department of Hunan Province (19A500, 21A0116).

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  1. Juan Zhang and Jianzhou Liu have contributed equally to this work.

Authors and Affiliations

  1. Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Department of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, China

    Juan Zhang, Jianzhou Liu & Fangfang Luo

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  1. Juan Zhang
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  2. Jianzhou Liu
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  3. Fangfang Luo
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Correspondence to Juan Zhang.

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Zhang, J., Liu, J. & Luo, F. A class of fixed point iteration for the coupled algebraic Riccati equation. J. Appl. Math. Comput. 68, 4119–4133 (2022). https://doi.org/10.1007/s12190-021-01697-5

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  • DOI: https://doi.org/10.1007/s12190-021-01697-5

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