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Neural networks for total least squares solution of the time-varying linear systems

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Abstract

In this paper, we consider the total least squares solution of time-varying linear systems with time-varying right-hand side vectors. The neural network model termed as the neural network model for solving time-varying total least squares problems (NNTVTLS) and its discrete form of the neural network model for solving time-varying total least squares problems (DNNTVTLS) are provided to solve this problem. The analyses of convergence and robustness demonstrate that the proposed DNNTVTLS model exhibits global convergence and superior noise immunity. Numerical experiments further verify the superiority and effectiveness of the DNNTVTLS model in solving time-varying linear equations, taking into account the presence of noise.

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Acknowledgements

The authors would like to thank the handling editor and two anonymous reviewers for their detailed and valuable comments.

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Authors and Affiliations

  1. School of Mathematics, Hexi University, Zhangye, 734000, People’s Republic of China

    Xuezhong Wang

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Jiali Shan

  3. School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Yimin Wei

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  1. Xuezhong Wang
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  2. Jiali Shan
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Correspondence to Yimin Wei.

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Xuezhong Wang is supported by the National Natural Science Foundation of China under grant 12461055; The Natural Science Foundation of Gansu Province under grant 23JRRG0008. Jiali Shan is supported by the National Natural Science Foundation of China (Youth Student Basic Research Program) under grant 123B1008. Yimin Wei is supported by the Ministry of Science and Technology of China under grant H20240841 and the Joint Research Project between China and Serbia under grant 2024-6-7.

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Wang, X., Shan, J. & Wei, Y. Neural networks for total least squares solution of the time-varying linear systems. Comp. Appl. Math. 44, 106 (2025). https://doi.org/10.1007/s40314-024-03070-1

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  • DOI: https://doi.org/10.1007/s40314-024-03070-1

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