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A Non-linear and Noise-Tolerant ZNN Model and Its Application to Static and Time-Varying Matrix Square Root Finding

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Abstract

Based on the indefinite error-monitoring function, we propose a novel Zhang neural network (ZNN) model called NNT-ZNN with two properties of nonlinear and noise-tolerant for the time-varying and static matrix square root finding in this paper. Compared to the existing models associated with the square matrix root finding, the NNT-ZNN model proposed in this study fully takes error caused by possible noise on ZNN hardware implementation into account. Under the background that the large model-implementation error, the model still has the ability to converge to the theoretical square root of the given matrix with simulative results illustrated in the paper. For the purpose of comparison, the ZNN model proposed by Zhang et al. is also introduced. Beyond that, the corresponding convergence results of the NNT-ZNN model corresponding to various activation functions, are also shown via time-varying and static positive definite matrix. In the end, the experiments are simulated with MATLAB, which further verifies the availability, effectiveness of the proposed NNT-ZNN model, and robustness against unknown noise.

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Authors and Affiliations

  1. School of Information Science and Engineering, Qufu Normal University, Rizhao, 276826, Shandong, China

    Xiaoxiao Li & Jiguo Yu

  2. Qilu University of Technology (Shandong Academy of Sciences), Shandong Computer Science Center (National Supercomputer Center in Jinan), Jinan, 250014, Shandong, China

    Jiguo Yu

  3. Department of Computing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

    Shuai Li

  4. Research Institute of Intelligence Software, Guangzhou University, Guangzhou, 510006, China

    Zehui Shao

  5. College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao, China

    Lina Ni

Authors
  1. Xiaoxiao Li
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  2. Jiguo Yu
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  3. Shuai Li
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  4. Zehui Shao
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  5. Lina Ni
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Correspondence to Jiguo Yu.

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This work is supported by NSF of China under Grants 61672321, 61832012, 61771289 and 61373027.

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Li, X., Yu, J., Li, S. et al. A Non-linear and Noise-Tolerant ZNN Model and Its Application to Static and Time-Varying Matrix Square Root Finding. Neural Process Lett 50, 1687–1703 (2019). https://doi.org/10.1007/s11063-018-9953-y

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  • DOI: https://doi.org/10.1007/s11063-018-9953-y

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