A componentwise perturbation analysis of the QR decomposition
SIAM Journal on Matrix Analysis and Applications
On the perturbation of LU, Cholesky, and QR factorizations
SIAM Journal on Matrix Analysis and Applications
On the Perturbation of the Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
Perturbation Analyses for the QR Factorization
SIAM Journal on Matrix Analysis and Applications
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
On Floating Point Errors in Cholesky
On Floating Point Errors in Cholesky
Perturbation analysis of some matrix factorizations
Perturbation analysis of some matrix factorizations
Perturbation Theory for Factorizations of LU Type through Series Expansions
SIAM Journal on Matrix Analysis and Applications
H-LLL: using householder inside LLL
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
An LLL Algorithm with Quadratic Complexity
SIAM Journal on Computing
Perturbation analysis for the hyperbolic QR factorization
Computers & Mathematics with Applications
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This article presents rigorous normwise perturbation bounds for the Cholesky, LU, and QR factorizations with normwise or componentwise perturbations in the given matrix. The considered componentwise perturbations have the form of backward rounding errors for the standard factorization algorithms. The used approach is a combination of the classic and refined matrix equation approaches. Each of the new rigorous perturbation bounds is a small constant multiple of the corresponding first-order perturbation bound obtained by the refined matrix equation approach in the literature and can be estimated efficiently. These new bounds can be much tighter than the existing rigorous bounds obtained by the classic matrix equation approach, while the conditions for the former to hold are almost as moderate as the conditions for the latter to hold.