MATLAB SIMULATION OF THE HYBRID OF RECURSIVE NEURAL DYNAMICS FOR ONLINE MATRIX INVERSION

Ivan S. Živković, Predrag S. Stanimirović

DOI Number
-
First page
799
Last page
809

Abstract


A novel kind of a hybrid recursive neural implicit dynamics for real-time matrix inversion has been recently proposed and investigated. Our goal is to compare the hybrid recursive neural implicit dynamics on the one hand, and conventional explicit neural dynamics on the other hand. Simulation results show that the hybrid model can coincide better with systems in practice and has higher abilities in representing dynamic systems. More importantly, hybrid model can achieve superior convergence performance in comparison with the existing dynamic systems, specifically recently-proposed Zhang dynamics. This paper presents the Simulink model of a hybrid recursive neural implicit dynamics and gives a simulation and comparison to the existing Zhang dynamics for real-time matrix inversion. Simulation results confirm a superior convergence of the hybrid model compared to Zhang model.

Keywords

Zhang neural network; gradient neural network; matrix inverse; convergence.

Keywords


Zhang neural network; gradient neural network; matrix inverse; conver-

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References


K. Chen, Recurrent implicit dynamics for online matrix inversion, Appl. Math. Comput. 219(20) (2013), 10218–10224.

K. Chen, C. Yi, Robustness analysis of a hybrid of recursive neural dynamics for online matrix inversion. Appl. Math. Comput. 273 (2016), 969–975.

A. Cichocki, T. Kaczorek, A. Stajniak, Computation of the Drazin inverse of a singular matrix making use of neural networks, Bulletin of the Polish Academy of Sciences Technical Sciences, 40 (1992).

J.S. Jang, S.Y. Lee, S. Y. Shin, J. S. Jang, and S. Y. Shin, An optimization network for matrix inversion, Neural Inf. Process. Ser. (1987), 397–401.

S. Li, S. Chen, B. Liu, Accelerating a recurrent neural network to finite-time convergence for solving time-varying Sylvester Equation by using a sign-bi-power activation function, Neural Process. Lett. 37 (2013), 189–205.

Z. Li, Y. Zhang, Improved Zhang neural network model and its solution of time-varying generalized linear matrix equations, Expert Syst. Appl. 37 (2010), 7213–7218.

B. Liao, Y. Zhang, Different complex ZFs leading to different complex ZNN models for time-varying complex generalized inverse matrices, IEEE Trans. Neural Netw. Learn. Syst., 25 (2014), 1621–1631.

F.L. Luo, Z. Bao, Neural network approach to computing matrix inversion, Appl. Math. Comput. 47 (1992), 109–120.

S. Qiao, X.-Z. Wang, Y. Wei, Two finite-time convergent Zhang neural network models for time-varying complex matrix Drazin inverse, Linear Algebra Appl. http://dx.doi.org/10.1016/j.laa.2017.03.014.

P.S. Stanimirović, I. Živković, Y. Wei, Recurrent neural network approach based on the integral representation of the Drazin inverse, Neural Comput. 27(10) (2015), 2107–2131.

P.S. Stanimirović, I. S. Živković, Y. Wei, Recurrent neural network for computing the Drazin inverse, IEEE Trans. Neural Netw. Learn. Syst. 26 (2015), 2830–2843.

I. Stojanović, P.S. Stanimirović, I. Živković, D. Gerontitis, X.-Z. Wang, ZNN models for computing matrix inverse based on hyperpower iterative methods, Filomat 31:10 (2017), 2999–3014.

J. Wang, A recurrent neural network for real-time matrix inversion, Appl. Math. Comput. 55 (1993), 89–100.

J. Wang, Recurrent neural networks for solving linear matrix equations, Comput. Math. Appl. 26 (1993), 23–34.

J. Wang, Recurrent neural networks for computing pseudoinverses of rank-deficient matrices, SIAM J. Sci. Comput. 18 (1997), 1479–1493.

Y. Wei, Recurrent neural networks for computing weighted Moore-Penrose inverse, Appl. Math. Comput. 116 (2000), 279–287.

Y. Zhang, Y. Yang, N. Tan, B. Cai, Zhang neural network solving for time-varying full-rank matrix Moore-Penrose inverse, Computing 92 (2011), 97–121.

Y. Zhang, Y. Shi, K. Chen, C. Wang, Global exponential convergence and stability of gradient-based neural network for online matrix inversion, Appl. Math. Comput. 215 (2009), 1301–1306.

Y. Zhang, Design and analysis of a general recurrent neural network model for time-varying matrix inversion, IEEE Trans. Neural Netw. 16(6) (2005), 1477–1490.

Y. Zhang, Y. Shi, K. Chen, C. Wang, Global exponential convergence and stability of gradient-based neural network for online matrix inversion, Appl. Math. Comput. 215 (2009), 1301–1306.


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