TY - JOUR
T1 - On Stable Perturbations of the Stiffly Weighted Pseudoinverse and Weighted Least Squares Problem
JO - Journal of Computational Mathematics
VL - 5
SP - 527
EP - 536
PY - 2005
DA - 2005/10
SN - 23
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8837.html
KW - Stiffly
KW - Weighted pseudoinverse
KW - Weighted least squares
KW - Perturbation
KW - Stability
AB - In this paper we study perturbations of the stiffly weighted pseudoinverse $ (W^{1\over 2}A)^\dag W^{1\over 2}$ and the related stiffly weighted least squares problem, where both the matrices $A$ and $W$ are given with $W$ positive diagonal and severely stiff. We show that the perturbations to the stiffly weighted pseudoinverse and the related stiffly weighted least squares problem are stable, if and only if the perturbed matrices $\widehat A=A+\delta A$ satisfy several row rank preserving conditions.