  In this paper, we consider low-rank approximations for the solutions to the
stochastic Helmholtz equation with random coefficients. A Stochastic Galerkin
finite element method is used for the discretization of the Helmholtz problem.
Existence theory for the low-rank approximation is established when the system
matrix is indefinite. The low-rank algorithm does not require the construction
of a large system matrix which results in an advantage in terms of CPU time and
storage. Numerical results show that, when the operations in a low-rank method
are performed efficiently, it is possible to obtain an advantage in terms of
storage and CPU time compared to computations in full rank. We also propose a
general approach to implement a preconditioner using the low-rank format
efficiently.
