Journal
NEURAL COMPUTING & APPLICATIONS
Volume 21, Issue 3, Pages 453-460Publisher
SPRINGER LONDON LTD
DOI: 10.1007/s00521-010-0445-x
Keywords
Recurrent neural networks; Matrix square root; Discrete-time model; Newton iteration; Line-search algorithm
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Funding
- National Natural Science Foundation of China [60935001, 60775050]
- Fundamental Research Funds for the Central Universities of China
- Laboratory Sun Yat-sen University
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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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