Computing eigenvectors and corresponding eigenvalues with largest or smallest modulus of real antisymmetric matrix based on neural network with less scale

Abstract

In this paper, we extend the neural network based approaches, which can asymptotically compute the largest or smallest eigenvalues and the corresponding eigenvectors of real symmetric matrix, to the real antisymmetric matrix case. Given any n-by-n real antisymmetric matrix, unlike the previous neural network based methods that were summarized by some ordinary differential equations (ODEs) with 2n dimension, our proposed method can be represented by some n dimensional ODEs, which can much reduce the scale of networks and achieve higher computing performance. Simulations verify the computational capability of our proposed method.