  We study a multigrid method for solving large linear systems of equations
with tensor product structure. Such systems are obtained from stochastic finite
element discretization of stochastic partial differential equations such as the
steady-state diffusion problem with random coefficients. When the variance in
the problem is not too large, the solution can be well approximated by a
low-rank object. In the proposed multigrid algorithm, the matrix iterates are
truncated to low rank to reduce memory requirements and computational effort.
The method is proved convergent with an analytic error bound. Numerical
experiments show its effectiveness in solving the Galerkin systems compared to
the original multigrid solver, especially when the number of degrees of freedom
associated with the spatial discretization is large.
