Recurrent implicit dynamics for online matrix inversion

A novel kind of recurrent implicit dynamics together with its electronic realization is proposed and exploited for real-time matrix inversion. Compared to conventional explicit neural dynamics, our proposed model in the form of implicit dynamics has the following advantages: (a) can coincide better with systems in practice; and (b) has higher abilities in representing dynamic systems. More importantly, our model can achieve superior convergence performance in comparison with the existing dynamic systems, specifically Gradient-based dynamics (GD) and recently-proposed Zhang dynamics (ZD). Theoretical analysis and computer simulation results substantiate the effectiveness and superior efficiency of our model for online matrix inversion.

[1]  Yunong Zhang,et al.  O(N 2)-Operation Approximation of Covariance Matrix Inverse in Gaussian Process Regression Based on Quasi-Newton BFGS Method , 2007, Commun. Stat. Simul. Comput..

[2]  Yunong Zhang,et al.  Time-series Gaussian Process Regression Based on Toeplitz Computation of O(N2) Operations and O(N)-level Storage , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[3]  Ke Chen,et al.  Global exponential convergence and stability of gradient-based neural network for online matrix inversion , 2009, Appl. Math. Comput..

[4]  Çetin Kaya Koç,et al.  Inversion of all principal submatrices of a matrix , 1994 .

[5]  Shuzhi Sam Ge,et al.  Design and analysis of a general recurrent neural network model for time-varying matrix inversion , 2005, IEEE Transactions on Neural Networks.

[6]  Hoay Beng Gooi,et al.  New ordering methods for sparse matrix inversion via diagonalization , 1997 .

[7]  Carver Mead,et al.  Analog VLSI and neural systems , 1989 .

[8]  K. S. Yeung,et al.  Symbolic matrix inversion with application to electronic circuits , 1988 .

[9]  Yunong Zhang.  Towards Piecewise-Linear Primal Neural Networks for Optimization and Redundant Robotics , 2006, 2006 IEEE International Conference on Networking, Sensing and Control.

[10]  Soo-Young Lee,et al.  An Optimization Network for Matrix Inversion , 1987, NIPS.

[11]  Jun Wang,et al.  A recurrent neural network for solving Sylvester equation with time-varying coefficients , 2002, IEEE Trans. Neural Networks.

[12]  Yunong Zhang,et al.  Analogue recurrent neural network for linear algebraic equation solving , 2008 .

[13]  T. Sarkar,et al.  Survey of numerical methods for solution of large systems of linear equations for electromagnetic field problems , 1981 .

[14]  Ke Chen,et al.  Performance Analysis of Gradient Neural Network Exploited for Online Time-Varying Matrix Inversion , 2009, IEEE Transactions on Automatic Control.

[15]  L.P. Caloba,et al.  A new algorithm for analog matrix inversion , 1995, 38th Midwest Symposium on Circuits and Systems. Proceedings.

[16]  S. Hakimi,et al.  Analog methods for computation of the generalized inverse , 1968 .

[17]  Robert H. Sturges,et al.  Analog matrix inversion [robot kinematics] , 1988, IEEE J. Robotics Autom..

[18]  Michael A. Fiddy,et al.  Regularized image reconstruction using SVD and a neural network method for matrix inversion , 1993, IEEE Trans. Signal Process..

[19]  Ahmed El-Amawy.  A Systolic Architecture for Fast Dense Matrix Inversion , 1989, IEEE Trans. Computers.

[20]  Shaogang Gong,et al.  Feature Mining for Localised Crowd Counting , 2012, BMVC.

[21]  Victor-Emil Neagoe,et al.  Inversion of the Van der Monde matrix , 1996, IEEE Signal Processing Letters.

[22]  Yunong Zhang,et al.  Complex-valued Zhang neural network for online complex-valued time-varying matrix inversion , 2011, Appl. Math. Comput..

[23]  Jun Wang,et al.  A recurrent neural network for real-time matrix inversion , 1993 .