In many applications\,---\,latent semantic indexing, for
example\,---\,it is required to obtain a reduced rank approximation to
a sparse matrix $A$.  Unfortunately, the approximations based on   
traditional decompositions, like the singular value and QR
decompositions, are not in general sparse.  Stewart [{\it Numer.\
Math.}\ 83 (1999) 313--323] has shown how to use a variant of the
classical Gram--Schmidt algorithm, called the
quasi--Gram-Schmidt--algorithm, to obtain two kinds of low-rank
approximations.  The first, the SPQR, approximation, is a pivoted,
Q-less QR approximation of the form
$(XR_{11}\inv)\brv{cc}R_{11}&R_{12} \erv$, where $X$ consists of
columns of A.  The second is of the form the form $A \cong XTY\trp$,  
where $X$ and $Y$ consist of columns and rows $A$ and $T$ is small.
In this paper we treat the computational details of the algorithm and
describe a Matlab implementation.
(UMIACS-TR-2004-35)