This paper develops and analyzes a new algorithm for QR decomposition with
column pivoting (QRCP) of rectangular matrices with large row counts. The
algorithm combines methods from randomized numerical linear algebra in a
particularly careful way in order to accelerate both pivot decisions for the
input matrix and the process of decomposing the pivoted matrix into the QR
form. The source of the latter acceleration is a use of randomized
preconditioning and CholeskyQR. Comprehensive analysis is provided in both
exact and finite-precision arithmetic to characterize the algorithm's
rank-revealing properties and its numerical stability granted probabilistic
assumptions of the sketching operator. An implementation of the proposed
algorithm is described and made available inside the open-source RandLAPACK
library, which itself relies on RandBLAS - also available in open-source
format. Experiments with this implementation on an Intel Xeon Gold 6248R CPU
demonstrate order-of-magnitude speedups relative to LAPACK's standard function
for QRCP, and comparable performance to a specialized algorithm for unpivoted
QR of tall matrices, which lacks the strong rank-revealing properties of the
proposed method.Comment: v1: 26 pages in the body, 10 pages in the appendices, 10 figures. v2:
performance experiments now use a larger sketch size for CQRRP