Improved rigorous perturbation bounds for the LU and QR factorizations

DOI10.1002/nla.1998zbMath1374.65032arXiv1405.0179OpenAlexW2113465019WikidataQ114235437 ScholiaQ114235437MaRDI QIDQ5739745

Hanyu Li, Yi-Min Wei

Publication date: 19 July 2016

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.0179

zbMATH Keywords

numerical examplesLU factorizationBanach fixed point theoremQR factorizationLyapunov majorant functionrigorous perturbation bound

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical computation of matrix norms, conditioning, scaling (65F35) Direct numerical methods for linear systems and matrix inversion (65F05) Orthogonalization in numerical linear algebra (65F25)

Related Items

Multiplicative perturbation bounds for the block Cholesky downdating problem ⋮ Componentwise perturbation analysis for the generalized Schur decomposition ⋮ Sensitivity analysis for the generalized Cholesky block downdating problem ⋮ Structured condition numbers for some matrix factorizations of structured matrices ⋮ Multiplicative perturbation analysis for the generalized Cholesky block downdating problem ⋮ Perturbation analysis for the Takagi vector matrix ⋮ Sensitivity analysis for the generalized Cholesky factorization ⋮ New rigorous perturbation bounds for the Cholesky-like factorization of skew-symmetric matrix ⋮ Mixed and componentwise condition numbers for matrix decompositions ⋮ Improved rigorous multiplicative perturbation bounds for the generalized Cholesky factorization and the Cholesky-like factorization ⋮ Perturbation analysis for the QX factorization for centrosymmetric matrices ⋮ Sensitivity analysis for the block Cholesky downdating problem

Uses Software

• LAPACK
• Matlab
• mctoolbox
• CSparse

Cites Work

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• Perturbation theory for the LDU factorization and accurate computations for diagonally dominant matrices
• Perturbation bounds for the Cholesky and QR factorizations
• Perturbation bounds for the \(LDL^ H\) and LU decompositions
• On the sensitivity of the LU factorization
• Matrix factorizations and their perturbations
• On perturbation bounds for the QR factorization
• Cholesky-like factorizations of skew-symmetric matrices
• On the perturbation of LU and Cholesky factors
• Perturbation Analysis of the QR factor R in the context of LLL lattice basis reduction
• Improved Backward Error Bounds for LU and Cholesky Factorizations
• A New Perturbation Bound for the LDU Factorization of Diagonally Dominant Matrices
• Sensitivity analysis for the SR decomposition
• Rigorous Perturbation Bounds of Some Matrix Factorizations
• On the Perturbation of LU, Cholesky, and QR Factorizations
• Direct Methods for Sparse Linear Systems
• A Survey of Condition Number Estimation for Triangular Matrices
• Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
• Perturbation Bounds for the $QR$ Factorization of a Matrix
• Perturbation Analyses for the QR Factorization
• Perturbation Analyses for the Cholesky Downdating Problem
• Accuracy and Stability of Numerical Algorithms
• THE METHOD OF SPLITTING OPERATORS AND LYAPUNOV MAJORANTS IN PERTURBATION LINEAR ALGEBRA AND CONTROL
• Perturbation Theory for Factorizations of LU Type through Series Expansions
• New perturbation analyses for the Cholesky factorization