Letter: A simple functional neural network for computing the largest and smallest eigenvalues and corresponding eigenvectors of a real symmetric matrix

Authors:
Yiguang Liu;Zhisheng You;Liping Cao
Affiliations:
Center for Nonlinear and Complex Systems, University of Electronic Science and Technology, Chengdu 610054, P.R. China and Institute of Image & Graphics, College of Computer, Sichuan University, Ch ...;Institute of Image & Graphics, College of Computer, Sichuan University, Chengdu 610064, P.R. China;Department of Information Management, Sichuan University, Chengdu 610064, P.R. China
Venue:
Neurocomputing
Year:
2005

Citing 3
Cited 7

Training spatially homogeneous fully recurrent neural networks in eigenvalue space

Neural Networks
Eigenspace separation of autocorrelation memory matrices for capacity expansion

Neural Networks
Complex recurrent neural network for computing the inverse and pseudo-inverse of the complex matrix

Applied Mathematics and Computation

A functional neural network computing some eigenvalues and eigenvectors of a special real matrix

Neural Networks
Fundamental study: A concise functional neural network computing the largest modulus eigenvalues and their corresponding eigenvectors of a real skew matrix

Theoretical Computer Science
A recurrent neural network computing the largest imaginary or real part of eigenvalues of real matrices

Computers & Mathematics with Applications
Design of AI neural network based controller for controlling dissolved oxygen concentration in a sequencing batch reactor

International Journal of Knowledge-based and Intelligent Engineering Systems
Letters: Recurrent neural network model for computing largest and smallest generalized eigenvalue

Neurocomputing
Notes on "Recurrent neural network model for computing largest and smallest generalized eigenvalue"

Neurocomputing
A concise functional neural network for computing the extremum eigenpairs of real symmetric matrices

ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I

Quantified Score

Hi-index	0.01

Visualization

Abstract

Efficient computation of the largest eigenvalue and the smallest eigenvalue of a real symmetric matrix is a very important problem in engineering. Using neural networks to complete these operations is in an asynchronous manner and can achieve high performance. This paper proposes a concise functional neural network (FNN) expressed as a differential equation and designs steps to do this work. Firstly, the mathematical analytic solution of the equation is received, and then the convergence properties of this FNN are fully gained. Finally, the computing steps are designed in detail. The proposed method can compute the smallest eigenvalue and the largest eigenvalue whether the matrix is non-definite, positive definite or negative definite. Compared with other methods based on neural networks, this FNN is very simple and concise, so it is very easy to realize.