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 implemented i...

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Bibliographic Details
Published in:Numerical algorithms Vol. 91; no. 3; pp. 1047 - 1079
Main Authors: Dessole, Monica, Marcuzzi, Fabio
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2022
Springer Nature B.V
Subjects:
Algebra
Algorithms
Computer Science
Decomposition
Deviation
Eigenvalues
Linear algebra
Maximization
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Theory of Computation
Column pivoting
Correlation
Rank revealing
Block algorithm
QR factorization
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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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 experimental results on a wide data set of numerically singular matrices, which has become a reference in the recent literature.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-022-01291-1