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


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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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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  • Non-linear and noise-tolerant ZNN (NNT-ZNN)
  • Static and time-varying matrix square root finding
  • Constant noise
  • Random noise
  • Activation functions
  • Residual error