A functional neural network for computing the largest modulus eigenvalues and their corresponding eigenvectors of an anti-symmetric matrix

Abstract

Efficient computation of the largest modulus eigenvalues of a real anti-symmetric matrix is a very important problem in engineering. Using a neural network to complete these operations is in an asynchronous manner and can achieve high performance. This paper proposes a functional neural network (FNN) that can be transformed into a complex differential equation to do this work. Firstly, the mathematical analytic solution of the equation is received, and then the convergence properties of this FNN are analyzed. The simulation result indicates that with general initial complex values, the network will converge to the complex eigenvector corresponding to the eigenvalue whose imaginary part is positive, and modulus is the largest of all eigenvalues. Comparing with other neural networks used for computing eigenvalues and eigenvectors, this network is adaptive to real anti-symmetric matrices for completing these operations.