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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 [(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 (XR11-1)(R11 R12), where X consists of columns of A. The second, the SOB approximation, is of the form the form A ... XTYT, where X and Y consist of columns and rows A and T, is small. In this article we treat the computational details of these algorithms and describe a MATLAB implementation. [ABSTRACT FROM AUTHOR]