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

  • Xiaoxiao Li
  • Jiguo YuEmail author
  • Shuai Li
  • Zehui Shao
  • Lina Ni


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.


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



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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Information Science and EngineeringQufu Normal UniversityRizhaoChina
  2. 2.Qilu University of Technology (Shandong Academy of Sciences), Shandong Computer Science Center (National Supercomputer Center in Jinan)JinanChina
  3. 3.Department of ComputingThe Hong Kong Polytechnic UniversityHung Hom, KowloonChina
  4. 4.Research Institute of Intelligence SoftwareGuangzhou UniversityGuangzhouChina
  5. 5.College of Computer Science and EngineeringShandong University of Science and TechnologyQingdaoChina

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