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This article proposes and analyzes several variants of the randomized Cholesky QR factorization of a matrix $X$.
“Efficient algorithms for computing a strong rank-revealing QR factorization”
Ming Gu and Stanley Eisenstat · 1996
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Nicholas Higham · 2002
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“Iterative methods for sparse linear systems”
Yousef Saad · 2003
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Ming Gu and Luiza Miranian · 2004
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Bernard Haasdonk and Mario Ohlberger · 2008
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“An algorithm for the principal component analysis of large data sets”
Nathan Halko, Per-Gunnar Martinsson, Yoel Shkolnisky and Mark Tygert · 2011
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“Numerical methods for large eigenvalue problems: revised edition”
Yousef Saad · 2011
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Joel Tropp · 2011
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“Communication-optimal parallel and sequential QR and LU factorizations”
James Demmel, Laura Grigori, Mark Hoemmen and Julien Langou · 2012
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“Fast approximation of matrix coherence and statistical leverage”
Petros Drineas, Malik Magdon-Ismail, Michael Mahoney and David Woodruff · 2012
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Steven Leon, ke Bj“”orck and Walter Gander · 2013
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“CholeskyQR2: a simple and communication-avoiding algorithm for computing a tall-skinny QR factorization on a large-scale parallel system”
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“Householder QR factorization with randomization for column pivoting (HQRRP)”
Per-Gunnar Martinsson, Gregorio Quintana“’I, Nathan Heavner and Robert van Geijn · 2017
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“Fast parallel randomized QR with column pivoting algorithms for reliable low-rank matrix approximations”
Jianwei Xiao, Ming Gu and Julien Langou · 2017
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“Randomized linear algebra for model reduction. Part I: Galerkin methods and error estimation”
Oleg Balabanov and Anthony Nouy · 2019
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“Shifted Cholesky QR for computing the QR factorization of ill-conditioned matrices”
Takeshi Fukaya, Ramaseshan Kannan, Yuji Nakatsukasa, Yusaku Yamamoto and Yuka Yanagisawa · 2020
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“Randomized numerical linear algebra: Foundations and algorithms”
Per-Gunnar Martinsson and Joel Tropp · 2020
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Per-Gunnar Martinsson · 2015
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“Performance of random sampling for computing low-rank approximations of a dense matrix on GPUs”
Th“’eo Mary, Ichitaro Yamazaki, Jakub Kurzak, Piotr Luszczek, Stanimire Tomov and Jack Dongarra · 2015
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“Roundoff error analysis of the CholeskyQR2 algorithm”
Yusaku Yamamoto, Yuji Nakatsukasa, Yuka Yanagisawa and Takeshi Fukaya · 2015
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“Mixed-precision Cholesky QR factorization and its case studies on multicore CPU with multiple GPUs”
Ichitaro Yamazaki, Stanimire Tomov and Jack Dongarra · 2015
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“Low-rank approximation and regression in input sparsity time”
Kenneth Clarkson and David Woodruff · 2017
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“Randomized QR with column pivoting”
Jed Duersch and Ming Gu · 2017
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Oleg Balabanov and Laura Grigori · 2021
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“Randomized linear algebra for model reduction. Part II: minimal residual methods and dictionary-based approximation”
Oleg Balabanov and Anthony Nouy · 2021
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“A Novel Randomized XR-Based Preconditioned CholeksyQR Algorithm”
Yuwei Fan, Yixiao Guo and Ting Lin · 2021
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“MATLAB library featuring randomized Krylov algorithms.”
Oleg Balabanov · 2022
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“Randomized Gram–Schmidt Process with Application to GMRES”
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