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05557305 Zhang, Yunong Yang, Yiwen Tan, Ning Time-varying matrix square roots solving via Zhang neural network and gradient neural network: Modeling, verification and comparison. Yu, Wen (ed.) et al., Advances in neural networks -- ISNN 2009. 6th international symposium on neural networks, ISNN 2009, Wuhan, China, May 26--29, 2009. Proceedings, Part I. Berlin: Springer (ISBN 978-3-642-01506-9/pbk). Lecture Notes in Computer Science 5551, 11-20 (2009). 2009 Berlin: Springer EN Time-varying matrix square roots Recurrent neural networks Zhang neural networks Gradient neural networks

doi:10.1007/978-3-642-01507-6_2

Summary: A special kind of recurrent neural networks (RNN) with implicit dynamics has recently been proposed by Zhang et al, which could be generalized to solve online various time-varying problems. In comparison with conventional gradient neural networks (GNN), such RNN (or termed specifically as Zhang neural networks, ZNN) models are elegantly designed by defining matrix-valued indefinite error functions. In this paper, we generalize and investigate the ZNN and GNN models for online solution of time-varying matrix square roots. In addition, software modeling techniques are investigated to model and simulate both neural-network systems. Computer-modeling results verify that superior convergence and efficacy could be achieved by such ZNN models in this time-varying problem solving, as compared to the GNN models.