MATLAB Simulation of Gradient-Based Neural Network for Online Matrix Inversion

This paper investigates the simulation of a gradient-based recurrent neural network for online solution of the matrix-inverse problem. Several important techniques are employed as follows to simulate such a neural system. 1) Kronecker product of matrices is introduced to transform a matrix-differential-equation (MDE) to a vector-differential-equation (VDE); i.e., finally, a standard ordinary-differential-equation (ODE) is obtained. 2) MATLAB routine "ode45" is introduced to solve the transformed initial-value ODE problem. 3) In addition to various implementation errors, different kinds of activation functions are simulated to show the characteristics of such a neural network. Simulation results substantiate the theoretical analysis and efficacy of the gradient-based neural network for online constant matrix inversion.

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

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

[3]  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.

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

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

[6]  Shuzhi Ge,et al.  A general recurrent neural network model for time-varying matrix inversion , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[7]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

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

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

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

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

[12]  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.

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

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

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

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

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

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

[19]  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..

[20]  Yunong Zhang,et al.  Revisit the Analog Computer and Gradient-Based Neural System for Matrix Inversion , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

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