Time-varying generalized tensor eigenanalysis via Zhang neural networks

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.