A simple functional neural network for computing the largest and smallest eigenvalues and corresponding eigenvectors of a real symmetric matrix

Efficient computation of the largest eigenvalue and the smallest eigenvalue of a real symmetric matrix is a very important problem in engineering. Using neural networks to complete these operations is in an asynchronous manner and can achieve high performance. This paper proposes a concise functional neural network (FNN) expressed as a differential equation and designs steps to do this work. Firstly, the mathematical analytic solution of the equation is received, and then the convergence properties of this FNN are fully gained. Finally, the computing steps are designed in detail. The proposed method can compute the smallest eigenvalue and the largest eigenvalue whether the matrix is non-definite, positive definite or negative definite. Compared with other methods based on neural networks, this FNN is very simple and concise, so it is very easy to realize.