Another neural network based approach for computing eigenvalues and eigenvectors of real skew-symmetric matrices

This paper introduces a novel neural network based approach for extracting the eigenvalues with the largest or smallest modulus of real skew-symmetric matrices, as well as the corresponding eigenvectors. To this end, unlike the previous neural network based methods that can be summarized by some 2n-dimensional ordinary differential equations (ODEs), where n is the order of the given skew-symmetric matrix, our proposed approach corresponds to an ODE of order n, instead of 2n. Hence, the scale of networks can be reduced a lot. Simulations verify the computational capability of such approach.