Neural network based on approach for computing eigen-pairs of special orthogonal matrices

Efficient computation of eigenvectors and eigenvalues of a matrix is an important problem in engineering. For the eigen-pairs problem of special orthogonal matrix whose determinant equal to 1 and the modulus of all eigenvalues are identical to 1, this article proposed a subtle neural network algorithm for direct computing all eigenvectors and the corresponding eigenvalues of special orthogonal matrix without any time-consuming preprocessing and postprocessing. The proposed approach extended the applied range of the classical neural model that only could be used to compute the largest or smallest eigenvalue and the corresponding eigenvectors of real symmetric matrix to the case of special orthogonal matrix. Numerical result verify the efficient of the proposed approach.