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Complex-valued Zhang neural network for online complex-valued time-varying matrix inversion. (English) Zbl 1220.65036

Summary: A new complex-valued recurrent neural network (CVRNN) called complex-valued Zhang neural network (CVZNN) is proposed and simulated to solve the complex-valued time-varying matrix-inversion problems. Such a CVZNN model is designed based on a matrix-valued error function in the complex domain, and utilizes the complex-valued first-order time-derivative information of the complex-valued time-varying matrix for online inversion. Superior to the conventional complex-valued gradient-based neural network (CVGNN) and its related methods, the state matrix of the resultant CVZNN model can globally exponentially converge to the theoretical inverse of the complex-valued time-varying matrix in an error-free manner. Moreover, by exploiting the design parameter \(\gamma >1\), superior convergence can be achieved for the CVZNN model to solve such complex-valued time-varying matrix inversion problems, as compared with the situation without design parameter \(\gamma \) involved (i.e., the situation with \(\gamma =1\)). Computer-simulation results substantiate the theoretical analysis and further demonstrate the efficacy of such a CVZNN model for online complex-valued time-varying matrix inversion.

MSC:

65F05 Direct numerical methods for linear systems and matrix inversion
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
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