On the existence and computation of rank-revealing LU factorizations
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Publication:1587285
DOI10.1016/S0024-3795(00)00120-8zbMath0962.65023WikidataQ114122594 ScholiaQ114122594MaRDI QIDQ1587285
Publication date: 31 May 2001
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
algorithmsGaussian eliminationsingular valuesSchur complementsrank revealing LU factorizationblock pivoting
Numerical solutions to overdetermined systems, pseudoinverses (65F20) Direct numerical methods for linear systems and matrix inversion (65F05)
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Uses Software
Cites Work
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- A volume associated with \(m{\times}n\) matrices
- Rank revealing \(LU\) factorizations
- A theory of pseudoskeleton approximations
- Improved bound for rank revealing LU factorizations
- Manifestations of the Schur complement
- Bounds on singular values revealed by QR factorizations
- On the Existence and Computation of LU-Factorizations with Small Pivots
- Matrix Analysis
- Rank-Revealing QR Factorizations and the Singular Value Decomposition
- Computing rank-revealing QR factorizations of dense matrices
- Algorithm 782
- On Rank-Revealing Factorisations
- Efficient Algorithms for Computing a Strong Rank-Revealing QR Factorization
- The least squares problem and pseudo-inverses
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