TY - JOUR
T1 - The QLP Approximation to the Singular Value Decomposition
JF - SIAM Journal on Scientific Computing
Y1 - 1999
A1 - Stewart, G.W.
KW - pivoted QR decomposition
KW - QLP decomposition
KW - rank determination
KW - singular value decomposition
AB - 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.
VL - 20
UR - http://link.aip.org/link/?SCE/20/1336/1
CP - 4
M3 - 10.1137/S1064827597319519
ER -