Deviation Maximization for Rank-Revealing QR Factorizations

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 implemen...

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Bibliographic Details
Published inarXiv.org
Main Authors Dessole, Monica, Marcuzzi, Fabio
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.06.2021
Subjects
Algorithms
Computer Science - Numerical Analysis
Deviation
Mathematics - Numerical Analysis
Maximization
Optimization
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2106.03138