@article {17737,
title = {The QLP Approximation to the Singular Value Decomposition},
journal = {SIAM Journal on Scientific Computing},
volume = {20},
year = {1999},
month = {1999///},
pages = {1336 - 1348},
abstract = {In this paper we introduce a new decomposition called the pivoted QLP decomposition. It is computed by applying pivoted orthogonal triangularization to the columns of the matrix X in question to get an upper triangular factor R and then applying the same procedure to the rows of R to get a lower triangular matrix L. The diagonal elements of R are called the R-values of X; those of L are called the L-values. Numerical examples show that the L-values track the singular values of X with considerable fidelity---far better than the R-values. At a gap in the L-values the decomposition provides orthonormal bases of analogues of row, column, and null spaces provided of X. The decomposition requires no more than twice the work required for a pivoted QR decomposition. The computation of R and L can be interleaved, so that the computation can be terminated at any suitable point, which makes the decomposition especially suitable for low-rank determination problems. The interleaved algorithm also suggests a new, efficient 2-norm estimator.},
keywords = {pivoted QR decomposition, QLP decomposition, rank determination, singular value decomposition},
doi = {10.1137/S1064827597319519},
url = {http://link.aip.org/link/?SCE/20/1336/1},
author = {Stewart, G.W.}
}