  We compute a \emph{sparse} solution to the classical least-squares problem
$\min_x||A x -b||,$ where $A$ is an arbitrary matrix. We describe a novel
algorithm for this sparse least-squares problem. The algorithm operates as
follows: first, it selects columns from $A$, and then solves a least-squares
problem only with the selected columns. The column selection algorithm that we
use is known to perform well for the well studied column subset selection
problem. The contribution of this article is to show that it gives favorable
results for sparse least-squares as well. Specifically, we prove that the
solution vector obtained by our algorithm is close to the solution vector
obtained via what is known as the "SVD-truncated regularization approach".
