Recurrent implicit dynamics for online matrix inversion

Applied Mathematics and Computation

Volumn 219, Issue 20, 2013, Pages 10218-10224

  Chen, Ke ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Explicit dynamics; Global exponential convergence; Implicit dynamics; Lyapunov stability theory; Online matrix inversion

Indexed keywords

COMPUTATIONAL METHODS; MATHEMATICAL TECHNIQUES;

EXPLICIT DYNAMICS; GLOBAL EXPONENTIAL CONVERGENCE; IMPLICIT DYNAMICS; LYAPUNOV STABILITY THEORY; ONLINE MATRIX;

DYNAMICS;

EID: 84893682117     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2013.03.117     Document Type: Article

References (23)

1. 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. (Pubitemid 46900516)
2. R.J. Steriti, MA Fiddy, Regularized image reconstruction using SVD and a neural network method for matrix inversion, IEEE Transactions on Signal Processing 41 (1993) 3074-3077.
3. T. Sarkar, K. Siarkiewicz, R. Stratton, 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.
4. RH. Sturges Jr, Analog matrix inversion (robot kinematics), IEEE Journal of Robotics and Automation 4 (1988) 157-162.
5. K. Chen, C.C. Loy, S. Gong, T. Xiang, Feature mining for localised crowd counting, in: Proceedings of British Machine Vision Conference, 2012, pp. 21.1-21.11.
6. K.S. Yeung, F. Kumbi, Symbolic matrix inversion with application to electronic circuits, IEEE Transactions on Circuits and Systems 35 (1988) 235-238. (Pubitemid 18596701)
7. A. El-Amawy, A systolic architecture for fast dense matrix inversion, IEEE Transactions on Computers 38 (1989) 449-455.
8. V.E. Neagoe, Inversion of the Van der Monde matrix, IEEE Signal Processing Letters 3 (1996) 119-120.
9. Y.Q. Wang, H.B. Gooi, New ordering methods for space matrix inversion via diagonaliztion, IEEE Transactions on Power Systems 12 (1997) 1298-1305. (Pubitemid 127771507)
10. CK. Koe, G. Chen, Inversion of all principal submatrices of a matrix, IEEE Transactions on Aerospace and Electronic Systems 30 (1994) 280-281.
11. 2) operations and 0 (N)-level storage, in: Proceedings of the 44th IEEE Conference on Decision and, Control, 2005, pp. 3711-3716. (Pubitemid 46297547)
12. 2)-operation approximation of covariance matrix inverse in Gaussian process regression based on quasi-Newton BFGS methods, Communications in Statistics - Simulation and Computation 36 (2007) 367-380. (Pubitemid 46394200)
13. R.K. Manherz, B.W. Jordan, S.L. Hakimi, Analog methods for computation of the generalized inverse, IEEE Transactions on Automatic Control 13 (1968) 582-585.
14. J. Jang, S. Lee, S. Shin, An Optimization Network for Matrix Inversion, Neural Information Processing Systems, American Institute of Physics, New York, 1988. pp. 397-401.
15. J. Wang, A recurrent neural network for real-time matrix inversion, Applied Mathematics and Computation 55 (1993) 89-100.
16. Y. Zhang, Y. Shi, K. Chen, C. Wang, Global exponential convergence and stability of gradient-based neural network for online matrix inversion, Applied Mathematics and Computation 215 (2009) 1301-1306.
17. Y. Zhang, D. Jiang, J. Wang, A recurrent neural network for solving Sylvester equation with time-varying coefficients, IEEE Transactions on Neural Networks 13 (2002) 1053-1063.
18. Y. Zhang, S.S. Ge, Design and analysis of a general recurrent neural network model for time-varying matrix inversion, IEEE Transactions on Neural Networks 16 (2005) 1477-1490. (Pubitemid 41709645)
19. Y. Zhang, Z. Li, K. Li, Complex-valued Zhang neural network for online complex-valued time-varying matrix inversion, Applied Mathematics and Computation 217 (2011) 10066-10073.
20. 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.
21. C. Mead, Analog VLSI and Neural Systems, Addison-Wesley, Reading, MA, 1989.
22. C. Yi, Y. Zhang, Analogue recurrent neural network for linear algebraic equation solving, Electronics Letters 44 (2008) 1078-1079.
23. Y. Zhang, K. Chen, H.-Z. Tan, Performance analysis of gradient neural network exploited for online time-varying matrix inversion, IEEE Transactions on Automatic Control 54 (2009) 1940-1945.