%0 Journal Article
%J SIAM Journal on Scientific Computing
%D 1999
%T The QLP Approximation to the Singular Value Decomposition
%A Stewart, G.W.
%K pivoted QR decomposition
%K QLP decomposition
%K rank determination
%K singular value decomposition
%X 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.
%B SIAM Journal on Scientific Computing
%V 20
%P 1336 - 1348
%8 1999///
%G eng
%U http://link.aip.org/link/?SCE/20/1336/1
%N 4
%R 10.1137/S1064827597319519