  We study efficient solution methods for stochastic eigenvalue problems
arising from discretization of self-adjoint partial differential equations with
random data. With the stochastic Galerkin approach, the solutions are
represented as generalized polynomial chaos expansions. A low-rank variant of
the inverse subspace iteration algorithm is presented for computing one or
several minimal eigenvalues and corresponding eigenvectors of
parameter-dependent matrices. In the algorithm, the iterates are approximated
by low-rank matrices, which leads to significant cost savings. The algorithm is
tested on two benchmark problems, a stochastic diffusion problem with some
poorly separated eigenvalues, and an operator derived from a discrete
stochastic Stokes problem whose minimal eigenvalue is related to the inf-sup
stability constant. Numerical experiments show that the low-rank algorithm
produces accurate solutions compared to the Monte Carlo method, and it uses
much less computational time than the original algorithm without low-rank
approximation.
