Neural network for solving generalized eigenvalues of matrix pair

Abstract

Neural networks for solving a class of generalized eigenvalue problems of matrix pair are proposed, in which a universal function satisfying several conditions is introduced by replacing some ones. For its simplicity in structure and excellence in performance, it can be widely used in many areas including array signal processing, blind equalization and identification. Both the theoretical analysis and the experimental results show that the proposed network can gives the extreme eigenvalue and its corresponding eigenvector of the matrix pair (A, B) in real time.