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A randomized Gram-Schmidt algorithm is developed for orthonormalization of high-dimensional vectors or QR factorization.
“Solving linear least squares problems by Gram–Schmidt orthogonalization”
Ake Bj“”orck · 1967
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“Solving linear least squares problems by Gram–Schmidt orthogonalization”
Ake Bj“”orck · 1967
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“Round off error analysis for Gram–Schmidt method and solution of linear least squares problems”
Nabih Abdelmalek · 1971
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“Round off error analysis for Gram–Schmidt method and solution of linear least squares problems”
Nabih Abdelmalek · 1971
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“Numerical aspects of Gram-Schmidt orthogonalization of vectors”
Axel Ruhe · 1983
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“Numerical aspects of Gram-Schmidt orthogonalization of vectors”
Axel Ruhe · 1983
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“An efficient parallel algorithm for extreme eigenvalues of sparse nonsymmetric matrices”
Sun Kim and AT Chrortopoulos · 1992
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“An efficient parallel algorithm for extreme eigenvalues of sparse nonsymmetric matrices”
Sun Kim and AT Chrortopoulos · 1992
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“Efficiency and scalability of two parallel QR factorization algorithms”
J Malard and CC Paige · 1994
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“Efficiency and scalability of two parallel QR factorization algorithms”
J Malard and CC Paige · 1994
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“Numerical stability of GMRES”
Jitka Drkosov“’a, Anne Greenbaum, M Rozlozn“’k and Zdenek Strakos · 1995
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“Numerical stability of GMRES”
Jitka Drkosov“’a, Anne Greenbaum, M Rozlozn“’k and Zdenek Strakos · 1995
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“Numerical stability of the GMRES method”
Miroslav Rozlozn“’k · 1996
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“Numerical stability of the GMRES method”
Miroslav Rozlozn“’k · 1996
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“Numerical behaviour of the modified Gram-Schmidt GMRES implementation”
Anne Greenbaum, Miroslav Rozloznik and Zdenek Strakos · 1997
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“Numerical behaviour of the modified Gram-Schmidt GMRES implementation”
Anne Greenbaum, Miroslav Rozloznik and Zdenek Strakos · 1997
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“Accuracy and stability of numerical algorithms”
Nicholas Higham · 2002
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“Accuracy and stability of numerical algorithms”
Nicholas Higham · 2002
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“Database-friendly random projections: Johnson-Lindenstrauss with binary coins”
Dimitris Achlioptas · 2003
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“Database-friendly random projections: Johnson-Lindenstrauss with binary coins”
Dimitris Achlioptas · 2003
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“Inexact Krylov subspace methods for linear systems”
Jasper Van Den and Gerard Sleijpen · 2004
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“Inexact Krylov subspace methods for linear systems”
Jasper Van Den and Gerard Sleijpen · 2004
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“Improved Gram–Schmidt type downdating methods”
Jesse Barlow, Alicja Smoktunowicz and Hasan Erbay · 2005
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“The loss of orthogonality in the Gram–Schmidt orthogonalization process”
Luc Giraud, Julien Langou and Miroslav Rozloznik · 2005
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“Rounding error analysis of the classical Gram–Schmidt orthogonalization process”
Luc Giraud, Julien Langou, Miroslav Rozlozn“’k and Jasper van Eshof · 2005
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“Improved Gram–Schmidt type downdating methods”
Jesse Barlow, Alicja Smoktunowicz and Hasan Erbay · 2005
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“The loss of orthogonality in the Gram–Schmidt orthogonalization process”
Luc Giraud, Julien Langou and Miroslav Rozloznik · 2005
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“Rounding error analysis of the classical Gram–Schmidt orthogonalization process”
Luc Giraud, Julien Langou, Miroslav Rozlozn“’k and Jasper van Eshof · 2005
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“Modified Gram-Schmidt (MGS), least squares, and backward stability of MGS-GMRES”
Christopher Paige, Miroslav Rozlozn“’k and Zdenvek Strakos · 2006
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“Improved approximation algorithms for large matrices via random projections”
Ichitaro Yamazaki, Stanimire Tomov, Tingxing Dong and Jack Dongarra · 2014
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“Lecture notes in Advanced Probability”
David Pollard · 2017
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“Lecture notes in Advanced Probability”
David Pollard · 2017
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“High-dimensional probability: An introduction with applications in data science”
Roman Vershynin · 2018
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“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”
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Tamas Sarlos · 2006
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“A note on the error analysis of classical Gram–Schmidt”
Alicja Smoktunowicz, Jesse Barlow and Julien Langou · 2006
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“Modified Gram-Schmidt (MGS), least squares, and backward stability of MGS-GMRES”
Christopher Paige, Miroslav Rozlozn“’k and Zdenvek Strakos · 2006
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“Improved approximation algorithms for large matrices via random projections”
Tamas Sarlos · 2006
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“A note on the error analysis of classical Gram–Schmidt”
Alicja Smoktunowicz, Jesse Barlow and Julien Langou · 2006
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“Convergence in backward error of relaxed GMRES”
Luc Giraud, Serge Gratton and Julien Langou · 2007
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“Recent computational developments in Krylov subspace methods for linear systems”
Valeria Simoncini and Daniel Szyld · 2007
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Nicholas Higham and Theo Mary · 2019
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Oleg Balabanov and Anthony Nouy · 2019
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Serge Gratton, Ehouarn Simon, David Titley-Peloquin and Philippe Toint · 2019
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“A new approach to probabilistic rounding error analysis”
Nicholas Higham and Theo Mary · 2019
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“Probabilistic error analysis for inner products”
Ilse Ipsen and Hua Zhou · 2019
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