Abstract
A special class of recurrent neural networks (RNN) has recently been proposed by Zhang et al. for solving online time-varying matrix problems. Being different from conventional gradient-based neural networks (GNN), such RNN (termed specifically as Zhang neural networks, ZNN) are designed based on matrix-valued error functions, instead of scalar-valued norm-based energy functions. In this paper, we generalize and further investigate the ZNN model for time-varying matrix square root finding. For the purpose of possible hardware (e.g., digital circuit) realization, a discrete-time ZNN model is constructed and developed, which incorporates Newton iteration as a special case. Besides, to obtain an appropriate step-size value (in each iteration), a line-search algorithm is employed for the proposed discrete-time ZNN model. Computer-simulation results substantiate the effectiveness of the proposed ZNN model aided with a line-search algorithm, in addition to the connection and explanation to Newton iteration for matrix square root finding.
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Acknowledgments
This work is supported by the National Natural Science Foundation of China under Grants 60935001 and 60775050, by the Fundamental Research Funds for the Central Universities of China, and also by the opening Fund of Laboratory Sun Yat-sen University.
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Zhang, Y., Yang, Y., Cai, B. et al. Zhang neural network and its application to Newton iteration for matrix square root estimation. Neural Comput & Applic 21, 453–460 (2012). https://doi.org/10.1007/s00521-010-0445-x
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DOI: https://doi.org/10.1007/s00521-010-0445-x