Neural networks based approach for computing eigenvectors and eigenvalues of symmetric matrix

Abstract

Efficient computation of eigenvectors and eigenvalues of a matrix is an important problem in engineering, especially for computing eigenvectors corresponding to largest or smallest eigenvalues of a matrix. This paper proposes a neural network based approach to compute eigenvectors corresponding to the largest or smallest eigenvalues of any real symmetric matrix. The proposed network model is described by differential equations, which is a class of continuous time recurrent neural network model. It has parallel processing ability in an asynchronous manner and can achieve high computing performance. This paper provides a clear mathematical understanding of the network dynamic behaviors relating to the computation of eigenvectors and eigenvalues. Computer simulation results show the computational capability of the network model.