Abstract
In this paper, a modified alternately linear implicit (MALI) iteration method is derived for solving the non-symmetric coupled algebraic Riccati equation (NCARE). In the MALI iteration algorithm, the coefficient matrices of the linear matrix equations are fixed at each iteration step. In addition, the MALI iteration method utilizes a weighted average of the estimates in both the last step and current step to update the estimates in the next iteration step. Further, we give the convergence theory of the modified algorithm. Last, numerical examples demonstrate the effectiveness and feasibility of the derived algorithm.
Funding Statement
The work was supported in part by National Natural Science Foundation for Youths of China (11801164) and the Youth Project of Hunan Provincial Education Department of China (22B0498), National Natural Science Foundation of China (11571292) and the Key Project of National Natural Science Foundation of China (91430213).
Acknowledgments
The authors would like to thank Yuli Zhu for providing an example of data and improving the English expression in this paper.
Citation
Li Wang. Yibo Wang. "A Modified Iterative Method for Solving the Non-symmetric Coupled Algebraic Riccati Equation." Taiwanese J. Math. 28 (2) 377 - 396, April, 2024. https://doi.org/10.11650/tjm/231101
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