Abstract
Nonlinear matrix equation \(X-\sum \limits _{i = 1}^m {A_i^*{X^{-1}}{A_i} = Q} \) has wide applications in control theory, dynamic planning, interpolation theory and random filtering. In this paper, a fixed-point accelerated iteration method is proposed, and based on the basic characteristics of the Thompson distance, the convergence and error estimation of the proposed algorithm are proved. Numerical comparison experiments show that the proposed algorithm is feasible and effective.
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The authors thank the anonymous referee for valuable suggestions which can be helped us to improve this article.
Funding
Dr Peng Jingjing, Special Research Project for Guangxi Young Innovative Talents(AD20297063) Dr. Zhenyun Peng, National Natural Science Foundation of China(11961012) Master Tong Li, Innovation Project of GUET Graduate Education (2022YCXS140).
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TL and JP wrote the main manuscript text; ZT and YZ prepared the figures and tables; ZP and ZT modified the full manuscript.
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Research supported by National Natural Science Foundation of China (11961012), Special Research Project for Guangxi Young Innovative Talents (AD20297063) and Innovation Project of GUET Graduate Education (2022YCXS140).
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Li, T., Peng, J., Peng, Z. et al. Fixed-point accelerated iterative method to solve nonlinear matrix equation \(X - \sum \limits _{i = 1}^m {A_i^*{X^{ - 1}}{A_i} = Q^*}\). Comp. Appl. Math. 41, 415 (2022). https://doi.org/10.1007/s40314-022-02119-3
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DOI: https://doi.org/10.1007/s40314-022-02119-3