Iterative solution of the random eigenvalue problem

Abstract

Algebraic eigenvalue problems play an important role in a variety of fields. In structural mechanics, eigenvalue problems commonly appear in the context of, e.g., vibrations and buckling. In the case that the considered structure as well as the considered loading conditions are exactly known, i.e. deterministic, efficient and robust methods for the computation of eigenvalues and corresponding eigenvectors exist. In the more realistic case that the structure and the loading conditions are uncertain (described by random fields), eigenvalues and eigenvectors will also be uncertain. These random eigenvalues and random eigenvectors can then be determined by solving the random eigenvalue problem, for which the availability of efficient and robust methods is limited.