Reorthogonalized block classical Gram-Schmidt

DOI10.1007/s00211-012-0496-2zbMath1269.65042arXiv1108.4209OpenAlexW2064122889MaRDI QIDQ1939650

Alicja Smoktunowicz, Jesse L. Barlow

Publication date: 5 March 2013

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.4209

zbMATH Keywords

numerical stability\(QR\) factorizationreorthogonalizationBLAS-3 compatible algorithmblock Gram-Schmidt algorithm

Mathematics Subject Classification ID

Numerical computation of matrix norms, conditioning, scaling (65F35) Orthogonalization in numerical linear algebra (65F25)

Related Items

GMRES algorithms over 35 years ⋮ Numerical stability of orthogonalization methods with a non-standard inner product ⋮ Block classical Gram–Schmidt-based block updating in low-rank matrix approximation ⋮ The Stability of Block Variants of Classical Gram--Schmidt ⋮ Numerical solution of 2 × 2 block linear systems by block Gram–Schmidt methods ⋮ Block Updating/Downdating Algorithms for Regularised Least Squares Problems and Applications to Linear Discriminant Analysis ⋮ Block Gram-Schmidt algorithms and their stability properties ⋮ Block Modified Gram--Schmidt Algorithms and Their Analysis ⋮ Mixed-Precision Cholesky QR Factorization and Its Case Studies on Multicore CPU with Multiple GPUs ⋮ Cholesky-Like Factorization of Symmetric Indefinite Matrices and Orthogonalization with Respect to Bilinear Forms

Uses Software

• BLAS
• mctoolbox

Cites Work

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• Numerics of Gram-Schmidt orthogonalization
• Numerical behaviour of the modified Gram-Schmidt GMRES implementation
• Rounding error analysis of the classical Gram-Schmidt orthogonalization process
• Improved Gram-Schmidt type downdating methods
• Stability Analysis and Improvement of the Block Gram–Schmidt Algorithm
• Matrix Analysis
• Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
• A set of level 3 basic linear algebra subprograms
• Accuracy and Stability of Numerical Algorithms
• A Block Orthogonalization Procedure with Constant Synchronization Requirements
• Block Gram–Schmidt Orthogonalization
• Modified Gram-Schmidt (MGS), Least Squares, and Backward Stability of MGS-GMRES
• Experiments on Gram-Schmidt Orthogonalization
• Round off error analysis for Gram-Schmidt method and solution of linear least squares problems

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