A Componentwise Perturbation Analysis of the $QR$ Decomposition

DOI10.1137/0614076zbMath0787.65014OpenAlexW2044075089MaRDI QIDQ3142617

Hongyuan Zha

Publication date: 20 December 1993

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0614076

zbMATH Keywords

perturbation analysisQR decompositionHouseholder transformationscolumn scaling

Mathematics Subject Classification ID

Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (13)

Perturbation Analysis of the QR factor R in the context of LLL lattice basis reduction ⋮ Perturbation analysis of the canonical correlations of matrix pairs ⋮ Perturbation analysis for the symplectic QR factorization ⋮ Perturbation analysis of system Hessenberg and Hessenberg-triangular forms ⋮ On the sensitivity of generators for the QR factorization of quasiseparable matrices with total nonpositivity ⋮ Imposing symmetry in augmented linear systems ⋮ Two-sided generalized hyperbolic QR factorization and its perturbation analysis ⋮ Rounding-error and perturbation bounds for the indefinite QR factorization ⋮ Perturbation analysis for the hyperbolic QR factorization ⋮ On the perturbation of the Q‐factor of the QR factorization ⋮ An improved Toeplitz algorithm for polynomial matrix null-space computation ⋮ Mixed and componentwise condition numbers for matrix decompositions ⋮ Conditioning of Leverage Scores and Computation by QR Decomposition

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