  Polynomial chaos methods have been extensively used to analyze systems in
uncertainty quantification. Furthermore, several approaches exist to determine
a low-dimensional approximation (or sparse approximation) for some quantity of
interest in a model, where just a few orthogonal basis polynomials are
required. We consider linear dynamical systems consisting of ordinary
differential equations with random variables. The aim of this paper is to
explore methods for producing low-dimensional approximations of the quantity of
interest further. We investigate two numerical techniques to compute a
low-dimensional representation, which both fit the approximation to a set of
samples in the time domain. On the one hand, a frequency domain analysis of a
stochastic Galerkin system yields the selection of the basis polynomials. It
follows a linear least squares problem. On the other hand, a sparse
minimization yields the choice of the basis polynomials by information from the
time domain only. An orthogonal matching pursuit produces an approximate
solution of the minimization problem. We compare the two approaches using a
test example from a mechanical application.
