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This article introduces randomized block Gram-Schmidt process (RBGS) for QR decomposition.
“Accuracy and stability of numerical algorithms”
Nicholas Higham · 2002
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“A Krylov–Schur algorithm for large eigenproblems”
Gilbert Stewart · 2002
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“Accuracy and stability of numerical algorithms”
Nicholas Higham · 2002
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“A Krylov–Schur algorithm for large eigenproblems”
Gilbert Stewart · 2002
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“On improving linear solver performance: A block variant of GMRES”
Allison Baker, John Dennis and Elizabeth Jessup · 2006
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“On improving linear solver performance: A block variant of GMRES”
Allison Baker, John Dennis and Elizabeth Jessup · 2006
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“A fast randomized algorithm for overdetermined linear least-squares regression”
Vladimir Rokhlin and Mark Tygert · 2008
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“A fast randomized algorithm for overdetermined linear least-squares regression”
Vladimir Rokhlin and Mark Tygert · 2008
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“Fast dimension reduction using Rademacher series on dual BCH codes”
Nir Ailon and Edo Liberty · 2009
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“Fast dimension reduction using Rademacher series on dual BCH codes”
Nir Ailon and Edo Liberty · 2009
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“Communication-avoiding Krylov subspace methods”
Mark Hoemmen · 2010
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“Communication-avoiding Krylov subspace methods”
Mark Hoemmen · 2010
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“Numerical methods for large eigenvalue problems: revised edition”
Yousef Saad · 2011
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“Improved analysis of the subsampled randomized Hadamard transform”
Joel Tropp · 2011
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“Numerical methods for large eigenvalue problems: revised edition”
Yousef Saad · 2011
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“Improved analysis of the subsampled randomized Hadamard transform”
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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“Communication-optimal parallel and sequential QR and LU factorizations”
James Demmel, Laura Grigori, Mark Hoemmen and Julien Langou · 2012
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“Reorthogonalized block classical Gram–Schmidt”
Jesse Barlow and Alicja Smoktunowicz · 2013
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“Reorthogonalized block classical Gram–Schmidt”
Jesse Barlow and Alicja Smoktunowicz · 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”
Takeshi Fukaya, Yuji Nakatsukasa, Yuka Yanagisawa and Yusaku Yamamoto · 2014
Cited alongside, same era.
“Sketching as a tool for numerical linear algebra”
David Woodruff · 2014
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“CholeskyQR2: a simple and communication-avoiding algorithm for computing a tall-skinny QR factorization on a large-scale parallel system”
Takeshi Fukaya, Yuji Nakatsukasa, Yuka Yanagisawa and Yusaku Yamamoto · 2014
Cited alongside, same era.
“Sketching as a tool for numerical linear algebra”
David Woodruff · 2014
Cited alongside, same era.
“Roundoff error analysis of the CholeskyQR2 algorithm”
Yusaku Yamamoto, Yuji Nakatsukasa, Yuka Yanagisawa and Takeshi Fukaya · 2015
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“Roundoff error analysis of the CholeskyQR2 algorithm”
“Stochastic Rounding and its Probabilistic Backward Error Analysis”, 2020
Michael Connolly, Nicholas Higham and Th“’eo Mary · 2020
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“Randomized numerical linear algebra: Foundations and algorithms”
Per-Gunnar Martinsson and Joel Tropp · 2020
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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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“The Stability of Block Variants of Classical Gram–Schmidt”
Erin Carson, Kathryn Lund and Miroslav Rozlozn“’k · 2021
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“Fast & Accurate Randomized Algorithms for Linear Systems and Eigenvalue Problems”
Yuji Nakatsukasa and Joel Tropp · 2021
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Yusaku Yamamoto, Yuji Nakatsukasa, Yuka Yanagisawa and Takeshi Fukaya · 2015
Cited alongside, same era.
“Enlarged Krylov subspace conjugate gradient methods for reducing communication”
Laura Grigori, Sophie Moufawad and Fr“’ed“’eric Nataf · 2016
Cited alongside, same era.
“Enlarged Krylov subspace conjugate gradient methods for reducing communication”
Laura Grigori, Sophie Moufawad and Fr“’ed“’eric Nataf · 2016
Cited alongside, same era.
“High-dimensional probability: An introduction with applications in data science”
Roman Vershynin · 2018
Cited alongside, same era.
“High-dimensional probability: An introduction with applications in data science”
Roman Vershynin · 2018
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“Randomized linear algebra for model reduction. Part I: Galerkin methods and error estimation”
Oleg Balabanov and Anthony Nouy · 2019
Cited alongside, same era.
“Block Modified Gram–Schmidt Algorithms and Their Analysis”
Jesse Barlow · 2019
Cited alongside, same era.
Katarzyna “’Swirydowicz, Julien Langou, Shreyas Ananthan, Ulrike Yang and Stephen Thomas · 2021
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“GMRES algorithms over 35 years”
Qinmeng Zou · 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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“The Stability of Block Variants of Classical Gram–Schmidt”
Erin Carson, Kathryn Lund and Miroslav Rozlozn“’k · 2021
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“Fast & Accurate Randomized Algorithms for Linear Systems and Eigenvalue Problems”
Yuji Nakatsukasa and Joel Tropp · 2021
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“Low synchronization Gram–Schmidt and generalized minimal residual algorithms”
Katarzyna “’Swirydowicz, Julien Langou, Shreyas Ananthan, Ulrike Yang and Stephen Thomas · 2021
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“GMRES algorithms over 35 years”
Qinmeng Zou · 2021
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“Randomized Cholesky QR factorizations”
Oleg Balabanov · 2022
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“Randomized Gram–Schmidt Process with Application to GMRES”
Oleg Balabanov and Laura Grigori · 2022
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“Block Gram-Schmidt algorithms and their stability properties”
Erin Carson, Kathryn Lund, Miroslav Rozlozn“’k and Stephen Thomas · 2022
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“Adaptively restarted block Krylov subspace methods with low-synchronization skeletons”
Kathryn Lund · 2022
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“Randomized Cholesky QR factorizations”
Oleg Balabanov · 2022
Closest in time.
“Randomized Gram–Schmidt Process with Application to GMRES”
Oleg Balabanov and Laura Grigori · 2022
Closest in time.
“Block Gram-Schmidt algorithms and their stability properties”
Erin Carson, Kathryn Lund, Miroslav Rozlozn“’k and Stephen Thomas · 2022
Closest in time.
“Adaptively restarted block Krylov subspace methods with low-synchronization skeletons”
Kathryn Lund · 2022
Closest in time.