# Algorithm 844

Algorithm 844: Computing sparse reduced-rank approximations to sparse matrices 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. {it G. W. Stewart} [Numer. Math. 83, No. 2, 313--323 (1999; Zbl 0957.65031)] 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 SCR approximation, is of the form the form $Acong XTYT$, 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. (Source: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.

## References in zbMATH (referenced in 17 articles , 1 standard article )

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