Neural Network Based Algorithm for Generalized Eigenvalue Problem

Abstract

The present paper introduces a neural network based on approach for solving the generalized eigenvalue problem Ax = λBx, where n-by-n matrices A and B are realvalued, B is non-singular, and 1 B A - is an orthogonal matrix whose determinant is equal to 1. The approach can extract the modulus largest and the modulus smallest eigenvalues, and the corresponding n-dimensional complex eigenvectors can be extracted by using the proposed algorithm that is essentially based on an ordinary differential equation of order n. Experimental results demonstrated the effectiveness of the proposed algorithm.