Journal
NEUROCOMPUTING
Volume 407, Issue -, Pages 465-479Publisher
ELSEVIER
DOI: 10.1016/j.neucom.2020.04.115
Keywords
Time-varying tensor; Eigenvalue and eigenvector; Z-eigenvalue; H-eigenvalue; Time-varying matrix; Generalized eigenvalues; Zhang neural network; Zhang dynamics model
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Funding
- Promotion Program of Excellent Doctoral Research, Fudan University [SSH6281011/001]
- National Natural Science Foundations of China [11771099]
- National Natural Science Foundation of China [11771099]
- Natural Science Foundation of Gansu Province
- Innovative Ability Promotion Project in Colleges and Universities of Gansu Province [2019B-146]
- Innovation Program of Shanghai Municipal Education Commission
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Eigenanalysis of matrices with parameters has a long history. When the parameter is time, or the matrix is time-dependent, the Zhang neural networks for the time-varying matrix problem have been developed in recent years. Motivated by tensor generalized eigenvalues and the Zhang dynamics method, we inves-tigate the time-varying eigenpair of symmetric tensors. A continuous Zhang dynamics model is given to compute the tensor eigenpairs, such as the H-and Z-eigenpairs. In order to accelerate the convergence, a modified Zhang dynamics model is also presented. Moreover, the generalized tensor/matrix eigenpairs could also be computed by the two proposed models. Theoretical analysis of the convergence and robust-ness are provided. We also test some numerical examples which illustrate that the two proposed models are effective. (C) 2020 Elsevier B.V. All rights reserved.
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