Global exponential convergence and stability of gradient-based neural network for online matrix inversion

Applied Mathematics and Computation

Volumn 215, Issue 3, 2009, Pages 1301-1306

  Zhang, Yunong ^a   Shi, Yanyan ^a   Chen, Ke ^a   Wang, Chaoli ^b  

^a SUN YAT SEN UNIVERSITY   (China)

^b UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY   (China)

Author keywords

Asymptotical convergence; Global exponential convergence; Gradient based neural network; Lyapunov stability theory; Online matrix inversion

Indexed keywords

ASYMPTOTICAL CONVERGENCE; GLOBAL EXPONENTIAL CONVERGENCE; GRADIENT-BASED NEURAL NETWORK; LYAPUNOV STABILITY THEORY; ONLINE MATRIX INVERSION;

CONTROL THEORY; STABILITY;

NEURAL NETWORKS;

EID: 69249230743     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.06.048     Document Type: Article

References (25)

1. Zhang Y., and Leithead W.E. Exploiting Hessian matrix and trust-region algorithm in hyperparameters estimation of Gaussian process. Applied Mathematics and Computation 171 (2005) 1264-1281
2. Y. Zhang, Towards piecewise-linear primal neural networks for optimization and redundant robotics, in: Proceedings of IEEE International Conference on Networking, Sensing and Control, 2006, pp. 374-379.
3. Steriti R.J., and Fiddy M.A. Regularized image reconstruction using SVD and a neural network method for matrix inversion. IEEE Transactions on Signal Processing 41 (1993) 3074-3077
4. 2)-operation approximation of covariance matrix inverse in Gaussian process regression based on quasi-Newton BFGS method. Communications in Statistics - Simulation and Computation 36 (2007) 367-380
5. 2) operations and O (N)-level storage, in: Proceedings of the 44th IEEE Conference on Decision and Control, 2005, pp. 3711-3716.
6. Sarkar T., Siarkiewicz K., and Stratton R. Survey of numerical methods for solution of large systems of linear equations for electromagnetic field problems. IEEE Transactions on Antennas and Propagation 29 (1981) 847-856
7. Sturges Jr. R.H. Analog matrix inversion (robot kinematics). IEEE Journal of Robotics and Automation 4 (1988) 157-162
8. Y. Zhang, Revisit the analog computer and gradient-based neural system for matrix inversion, in: Proceedings of IEEE International Symposium on Intelligent Control, 2005, pp. 1411-1416.
9. Yeung K.S., and Kumbi F. Symbolic matrix inversion with application to electronic circuits. IEEE Transactions on Circuits and Systems 35 (1988) 235-238
10. El-Amawy A. A systolic architecture for fast dense matrix inversion. IEEE Transactions on Computers 38 (1989) 449-455
11. Neagoe V.E. Inversion of the Van der Monde matrix. IEEE Signal Processing Letters 3 (1996) 119-120
12. Wang Y.Q., and Gooi H.B. New ordering methods for sparse matrix inversion via diagonalization. IEEE Transactions on Power Systems 12 (1997) 1298-1305
13. Fathi Vajargah B. Different stochastic algorithms to obtain matrix inversion. Applied Mathematics and Computation 189 (2007) 1841-1846
14. Koc C.K., and Chen G. Inversion of all principal submatrices of a matrix. IEEE Transactions on Aerospace and Electronic Systems 30 (1994) 280-281
15. Manherz R.K., Jordan B.W., and Hakimi S.L. Analog methods for computation of the generalized inverse. IEEE Transactions on Automatic Control 13 (1968) 582-585
16. Jang J., Lee S., and Shin S. An optimization network for matrix inversion. Neural Information Processing Systems (1988), American Institute of Physics, New York
17. Wang J. A recurrent neural network for real-time matrix inversion. Applied Mathematics and Computation 55 (1993) 89-100
18. Zhang Y., Jiang D., and Wang J. A recurrent neural network for solving Sylvester equation with time-varying coefficients. IEEE Transactions on Neural Networks 13 (2002) 1053-1063
19. Y. Zhang, S.S. Ge, A general recurrent neural network model for time-varying matrix inversion, in: Proceedings of the 42nd IEEE Conference on Decision and Control, 2003, pp. 6169-6174.
20. Zhang Y., and Ge S.S. Design and analysis of a general recurrent neural network model for time-varying matrix inversion. IEEE Transactions on Neural Networks 16 (2005) 1477-1490
21. N.C.F. Carneiro, L.P. Caloba, A new algorithm for analog matrix inversion, in: Proceedings of the 38th Midwest Symposium on Circuits and Systems, 1995, pp. 401-404.
22. Mead C. Analog VLSI and Neural Systems (1989), Addison-Wesley, Reading, MA
23. Zhang Y., and Wang J. Global exponential stability of recurrent neural networks for synthesizing linear feedback control systems via pole assignment. IEEE Transactions on Neural Networks 13 (2002) 633-644
24. Zhang Y. A set of nonlinear equations and inequalities arsing in robotics and its online solution via a primal neural network. Neurocomputing 70 (2006) 513-524
25. The MathWorks, Inc.: Matlab 7.0, Natick, MA, 2004.