Iterative solution of the random eigenvalue problem with application to spectral stochastic finite element systems

A new algorithm for the computation of the spectral expansion of the eigenvalues and eigenvectors of a random non-symmetric matrix is proposed. The algorithm extends the deterministic inverse power method using a spectral discretization approach. The convergence and accuracy of the algorithm is studied for both symmetric and non-symmetric matrices. The method turns out to be efficient and robust compared to existing methods for the computation of the spectral expansion of random eigenvalues and eigenvectors.