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Block Gram-Schmidt algorithms and their stability properties

  • Published:2022-04 Issue: Volume:638 Page:150-195
  • ISSN:0024-3795
  • Container-title:Linear Algebra and its Applications
  • language:en
  • Short-container-title:Linear Algebra and its Applications

Author:

Carson ErinORCID,Lund Kathryn,Rozložník Miroslav,Thomas Stephen

Funder

Academy of Sciences of the Czech Republic

US Department of Energy

Charles University

GAČR

Publisher

Elsevier BV

Subject

Discrete Mathematics and Combinatorics,Geometry and Topology,Numerical Analysis,Algebra and Number Theory

Reference65 articles.

1. The block Lanczos method for computing eigenvalues;Golub,1977

2. A Krylov-Schur algorithm for large eigenproblems;Stewart;SIAM J. Matrix Anal. Appl.,2001

3. The block conjugate gradient algorithm and related methods;O'Leary;Linear Algebra Appl.,1980

4. On improving linear solver performance: a block variant of GMRES;Baker;SIAM J. Sci. Comput.,2006

5. Communication lower bounds and optimal algorithms for numerical linear algebra;Ballard;Acta Numer.,2014

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1. Efficient GMRES+AMG on GPUs: Composite Smoothers And Mixed \(\boldsymbol{V}\)-Cycles;SIAM Journal on Scientific Computing;2024-09-03

2. Reorthogonalized Block Classical Gram–Schmidt Using Two Cholesky-Based TSQR Algorithms;SIAM Journal on Matrix Analysis and Applications;2024-08-09

3. Two-Stage Block Orthogonalization to Improve Performance of s-step GMRES;2024 IEEE International Parallel and Distributed Processing Symposium (IPDPS);2024-05-27

4. Probabilistic Rounding Error Analysis of Modified Gram–Schmidt;SIAM Journal on Matrix Analysis and Applications;2024-05-21

5. Tall-and-Skinny QR Factorization for Clusters of GPUs Using High-Performance Building Blocks;Lecture Notes in Computer Science;2024
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