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Convergence analysis of the weighted state space search algorithm for recurrent neural networks
1.  Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong 
2.  Department of Mathematics, Cleveland State University, Cleveland, OH 44115 
References:
[1] 
A. F. Atiya and A. G. Parlos, New results on recurrent network training: Unifying the algorithms and accelerating convergence, IEEE Transcations on Neural Networks, 11 (2000), 697709. 
[2] 
R. A. Conn, K. Scheinberg and N. L. Vicente, Introduction to Derivativefree Optimization, SIAM, Philadelphia, 2009. doi: 10.1137/1.9780898718768. 
[3] 
L. Jin, N. Nikifork and M. M. Gupta, Absolute stability conditions for discretetime neural networks, IEEE Tranc. Neural Networks, 5 (1994), 954964. 
[4] 
L. K. Li, Learning sunspot series dynamics by recurrent neural networks, Advances in Data Mining and Modeling (eds. W. K. Ching and K. P. Ng), World Science (2003), 107115. 
[5] 
L. K. Li and S. Shao, Dynamic properties of recurrent neural networks and its approximations, International Journal of Pure and Applied Mathematics, 39 (2007), 545562. 
[6] 
L. K. Li, S. Shao and T. Zheleva, A state space search algorithm and its application to learn the shortterm foreign exchange rates, Applied Mathematical Sciences, 2 (2008), 17051728. 
[7] 
L. K. Li, Sally Shao and K. F. Cedric Yiu, Nonlinear dynamical system modeling via recurrent neural networks and a weighted wtate space search algorithm, Journal of Industrial and Management Optimization, 7 (2011), 385400. doi: 10.3934/jimo.2011.7.385. 
[8] 
Q. Liu and J. Wang, Finitetime convergent recurrent neural network with a hardliming activation function for constrained optimization with piecewiselinear objective functions, IEEE Transactions on Neural Networks, 22 (2011), 601613. 
[9] 
D. T. Mirikitani and N. Nikolaev, Recursive Bayesian recurrent neural networks for timeseries modeling, IEEE Transactions on Neural Networks, 2 (2010), 262274. 
[10] 
Q. Song, On the weight convergence of Elman networks, IEEE Transactions on Neural Networks, 21 (2010), 463480. 
[11] 
X. Wang and E. K. Blum, Discretetime versus continuoustime models of neural networks, Journal of Computer and System Sciences, 45 (1992), 119. doi: 10.1016/00220000(92)90038K. 
[12] 
X. Wang and H. Huang, Convergence Study in Extended Kalman Filterbased Training of Recurrent Neural Networks, IEEE Trans. on Neural Networks, 22 (2011), 588600. 
[13] 
L. Xu and W. Liu, A new recurrent neural network adaptive approach for hostgate way rate control protocol within intranets using ATM ABR service, Journal of Industrial and Management Optimization, 1 (2005), 389404. doi: 10.3934/jimo.2005.1.337. 
[14] 
F. Xu and Z. Yi, Convergence Analysis of a class of simplified background netural networks with subnetworks, Neurocomputing, 74 (2011), 38773883. 
[15] 
J. Yao and C. L. Tan, A case study on using neural networks to perform technical forecasting of forex, Neural Computation, 34 (2000), 7998. 
[16] 
K. F. C. Yiu, S. Wang, K. L. Teo and A. C. Tsoi, Nonlinear System modeling via knotoptimizing Bsplines networks, IEEE Transactions on Neural Networks, 12 (2001), 10131022. 
[17] 
Y. Zhang and K. K. Tan, Convergence Analysis of Recurrent Neural Networks. Kluwer, Norwell, MA, (2004). doi: 10.1007/9781475738193. 
[18] 
L. Zhang and Z. Yi., Selectable and unselectable sets of neurons in recurrent neural networks with saturated piecewise linear transfer function, IEEE Transactions on Neural Networks, 22 (2011), 10211031. 
show all references
References:
[1] 
A. F. Atiya and A. G. Parlos, New results on recurrent network training: Unifying the algorithms and accelerating convergence, IEEE Transcations on Neural Networks, 11 (2000), 697709. 
[2] 
R. A. Conn, K. Scheinberg and N. L. Vicente, Introduction to Derivativefree Optimization, SIAM, Philadelphia, 2009. doi: 10.1137/1.9780898718768. 
[3] 
L. Jin, N. Nikifork and M. M. Gupta, Absolute stability conditions for discretetime neural networks, IEEE Tranc. Neural Networks, 5 (1994), 954964. 
[4] 
L. K. Li, Learning sunspot series dynamics by recurrent neural networks, Advances in Data Mining and Modeling (eds. W. K. Ching and K. P. Ng), World Science (2003), 107115. 
[5] 
L. K. Li and S. Shao, Dynamic properties of recurrent neural networks and its approximations, International Journal of Pure and Applied Mathematics, 39 (2007), 545562. 
[6] 
L. K. Li, S. Shao and T. Zheleva, A state space search algorithm and its application to learn the shortterm foreign exchange rates, Applied Mathematical Sciences, 2 (2008), 17051728. 
[7] 
L. K. Li, Sally Shao and K. F. Cedric Yiu, Nonlinear dynamical system modeling via recurrent neural networks and a weighted wtate space search algorithm, Journal of Industrial and Management Optimization, 7 (2011), 385400. doi: 10.3934/jimo.2011.7.385. 
[8] 
Q. Liu and J. Wang, Finitetime convergent recurrent neural network with a hardliming activation function for constrained optimization with piecewiselinear objective functions, IEEE Transactions on Neural Networks, 22 (2011), 601613. 
[9] 
D. T. Mirikitani and N. Nikolaev, Recursive Bayesian recurrent neural networks for timeseries modeling, IEEE Transactions on Neural Networks, 2 (2010), 262274. 
[10] 
Q. Song, On the weight convergence of Elman networks, IEEE Transactions on Neural Networks, 21 (2010), 463480. 
[11] 
X. Wang and E. K. Blum, Discretetime versus continuoustime models of neural networks, Journal of Computer and System Sciences, 45 (1992), 119. doi: 10.1016/00220000(92)90038K. 
[12] 
X. Wang and H. Huang, Convergence Study in Extended Kalman Filterbased Training of Recurrent Neural Networks, IEEE Trans. on Neural Networks, 22 (2011), 588600. 
[13] 
L. Xu and W. Liu, A new recurrent neural network adaptive approach for hostgate way rate control protocol within intranets using ATM ABR service, Journal of Industrial and Management Optimization, 1 (2005), 389404. doi: 10.3934/jimo.2005.1.337. 
[14] 
F. Xu and Z. Yi, Convergence Analysis of a class of simplified background netural networks with subnetworks, Neurocomputing, 74 (2011), 38773883. 
[15] 
J. Yao and C. L. Tan, A case study on using neural networks to perform technical forecasting of forex, Neural Computation, 34 (2000), 7998. 
[16] 
K. F. C. Yiu, S. Wang, K. L. Teo and A. C. Tsoi, Nonlinear System modeling via knotoptimizing Bsplines networks, IEEE Transactions on Neural Networks, 12 (2001), 10131022. 
[17] 
Y. Zhang and K. K. Tan, Convergence Analysis of Recurrent Neural Networks. Kluwer, Norwell, MA, (2004). doi: 10.1007/9781475738193. 
[18] 
L. Zhang and Z. Yi., Selectable and unselectable sets of neurons in recurrent neural networks with saturated piecewise linear transfer function, IEEE Transactions on Neural Networks, 22 (2011), 10211031. 
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