Affiliation:
1. University of Tennessee, Knoxville, Knoxville, TN
2. University of Maryland, College Park, College Park, MD
Abstract
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 (
XR
11
−1
)(
R
11
R
12
), where
X
consists of columns of A. The second, the SCR approximation, is of the form the form
A
≅
XTY
T
, 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.
Publisher
Association for Computing Machinery (ACM)
Subject
Applied Mathematics,Software
Cited by
43 articles.
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