Deviation Maximization for Rank-Revealing QR Factorizations

TL;DR

This paper introduces Deviation Maximization, a new column selection strategy for rank-revealing QR factorizations, offering similar accuracy to existing methods but with improved computational efficiency.

Contribution

The paper proposes QRDM, a novel QR factorization algorithm using Deviation Maximization, providing an effective alternative to the traditional QP3 method with enhanced speed.

Findings

QRDM achieves comparable rank-revealing quality to QP3.

QRDM demonstrates faster execution times in numerical tests.

The method performs well on a wide set of numerically singular matrices.

Abstract

In this paper we introduce a new column selection strategy, named here ``Deviation Maximization", and apply it to compute rank-revealing QR factorizations as an alternative to the well known block version of the QR factorization with the column pivoting method, called QP3 and currently implemented in LAPACK's xgeqp3 routine. We show that the resulting algorithm, named QRDM, has similar rank-revealing properties of QP3 and better execution times. We present numerical test results on a wide data set of numerically singular matrices, which has become a reference in the recent literature.