A Componentwise Perturbation Analysis of the $QR$ Decomposition
Hong Yuan Zha · SIAM Journal on Matrix Analysis and Applications · 1993
A first-order componentwise perturbation analysis of the $QR$ decomposition is presented. In contrast to the traditional normwise perturbation analysis, the bounds derived are invariant under column scaling of the underlying matrix. As an application, an assessment of the accuracy of the computed $QR$ decomposition using Householder transformations is given.