Backward error analysis of the AllReduce algorithm for Householder QR decomposition

DOI10.1007/s13160-011-0053-xzbMath1260.65036OpenAlexW2099325254MaRDI QIDQ692038

Yusaku Yamamoto, Daisuke Mori

Publication date: 4 December 2012

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13160-011-0053-x

zbMATH Keywords

numerical examplesparallel computationerror analysisorthogonalizationQR decompositiontall and skinny matrices

Mathematics Subject Classification ID

Parallel numerical computation (65Y05) Direct numerical methods for linear systems and matrix inversion (65F05) Orthogonalization in numerical linear algebra (65F25)

Related Items

Adaptively restarted block Krylov subspace methods with low-synchronization skeletons ⋮ Block Gram-Schmidt algorithms and their stability properties ⋮ Rounding Error Analysis of Mixed Precision Block Householder QR Algorithms

Uses Software

• JDQR
• mctoolbox
• JDQZ
• SBR Toolbox
• ABLE

Cites Work

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• A block QMR algorithm for non-Hermitian linear systems with multiple right-hand sides
• Very large electronic structure calculations using an out-of-core filter-diagonalization method
• The block conjugate gradient algorithm and related methods
• Communication-optimal Parallel and Sequential QR and LU Factorizations
• Algorithm 807
• Templates for the Solution of Algebraic Eigenvalue Problems
• ABLE: An Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems