@Article{JCM-5-316,
author = {Jiao-Xun Kuang},
title = {On the Minimum Property of the Pseudo $x$-Condition Number for a Linear Operator},
journal = {Journal of Computational Mathematics},
year = {1987},
volume = {5},
number = {4},
pages = {316--324},
abstract = {<p style="text-align: justify;">It is well known that the $x$-condition number of a linear operator is a measure of ill condition with respect to its generalized inverses and a relative error bound with respect to the generalized inverses of operator $T$ with a small perturbation operator E, namely,$$\frac{\|(T+E)^+-T^+\|}{\|T^+\|}\leq \frac{x(T)\frac{\|E\|}{\|T\|}}{1-x(T)\frac{\|E\|}{\|T\|}},$$ where $x{T}=\|T\|\dot\|T^+\|$. The problem is whether there exists a positive number $μ(T)$ independent of $E$ but dependent on $T$ such that the above relative error bound holds and $μ(T)＜x(T)$.<br/>In this paper, an answer is given to this problem.</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/9555.html}
}