  Active subspaces are an emerging set of tools for identifying and exploiting
the most important directions in the space of a computer simulation's input
parameters; these directions depend on the simulation's quantity of interest,
which we treat as a function from inputs to outputs. To identify a function's
active subspace, one must compute the eigenpairs of a matrix derived from the
function's gradient, which presents challenges when the gradient is not
available as a subroutine. We numerically study two methods for estimating the
necessary eigenpairs using only linear measurements of the function's gradient.
In practice, these measurements can be estimated by finite differences using
only two function evaluations, regardless of the dimension of the function's
input space.
