  We study random eigenvalue problems in the context of spectral stochastic
finite elements. In particular, given a parameter-dependent, symmetric
positive-definite matrix operator, we explore the performance of algorithms for
computing its eigenvalues and eigenvectors represented using polynomial chaos
expansions. We formulate a version of stochastic inverse subspace iteration,
which is based on the stochastic Galerkin finite element method, and we compare
its accuracy with that of Monte Carlo and stochastic collocation methods. The
coefficients of the eigenvalue expansions are computed from a stochastic
Rayleigh quotient. Our approach allows the computation of interior eigenvalues
by deflation methods, and we can also compute the coefficients of multiple
eigenvectors using a stochastic variant of the modified Gram-Schmidt process.
The effectiveness of the methods is illustrated by numerical experiments on
benchmark problems arising from vibration analysis.
