A concise functional neural network computing the largest modulus eigenvalues and their corresponding eigenvectors of a real skew matrix

Abstract

Quick extraction of the largest modulus eigenvalues of a real antisymmetric matrix is important for some engineering applications. As neural network runs in concurrent and asynchronous manner in essence, using it to complete this calculation can achieve high speed. This paper introduces a concise functional neural network (FNN), which can be equivalently transformed into a complex differential equation, to do this work. After obtaining the analytic solution of the equation, the convergence behaviors of this FNN are discussed. Simulation result indicates that with general initial complex values, the network will converge to the complex eigenvector which corresponds to the eigenvalue whose imaginary part is positive, and modulus is the largest of all eigenvalues. Comparing with other neural networks designed for the like aim, this network is applicable to real skew matrices.