Abstract  In this paper we introduce a new decomposition called the pivotedQLP~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 Rvalues of $X$; those of $L$ are
called the Lvalues. Numerical examples show that the Lvalues track
the singular values of $X$ with considerable fidelity\,\,far better
than the Rvalues. At a gap in the Lvalues 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
the rows of $R$ to get a lower triangular matrix $L$. The diagonal
elements of $R$ are called the Rvalues of $X$; those of $L$ are
called the Lvalues. Numerical examples show that the Lvalues track
the singular values of $X$ with considerable fidelity\,\,far better
than the Rvalues. At a gap in the Lvalues 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 lowrank determination problems. The
interleaved algorithm also suggests a new, efficient 2norm estimator.
(Also crossreferenced as UMIACSTR9775)
