Spectral Power Iterations for the Random Eigenvalue Problem

摘要

Two computationally efficient algorithms are developed for solving the stochastic eigenvalue problem. An algorithm based on the power iteration technique is proposed for the calculation of the dominant eigenpairs. This algorithm is then extended to find other subdominant random eigenpairs. The uncertainty in the operator is represented by a polynomial chaos expansion, and a similar representation is considered for the random eigenvalues and eigenvectors. The algorithms are distinguished due to their speed in converging to the true random eigenpairs and their ability to estimate a prescribed number of subdominant eigenpairs. The algorithms are demonstrated on two examples with close agreement observed with the exact solution and a solution synthesized through Monte Carlo sampling.