@Article{JCM-25-561,
author = {Yimin Wei, Huaian Diao and Sanzheng Qiao},
title = {Condition Number for Weighted Linear Least Squares Problem},
journal = {Journal of Computational Mathematics},
year = {2007},
volume = {25},
number = {5},
pages = {561--572},
abstract = {<p style="text-align: justify;">In this paper, we investigate the condition numbers for the generalized matrix inversion and the rank deficient linear least squares problem: $\min_x \|Ax-b\|_2$, where $A$ is an $m$-by-$n$ ($m \ge n$) rank deficient matrix. We first derive an explicit expression for the condition number in the weighted Frobenius norm $\|\left[AT, \beta b\right] \|_F$ of the data $A$ and $b$, where $T$ is a positive diagonal matrix and $\beta$ is a positive scalar. We then discuss the sensitivity of the standard 2-norm condition numbers for the generalized matrix inversion and rank deficient least squares and establish relations between the condition numbers and their condition numbers called level-2 condition numbers.</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/8713.html}
}