@Article{JCM-5-4,
author = {},
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/1987-JCM-9555},
url = {https://global-sci.com/article/86194/on-the-minimum-property-of-the-pseudo-x-condition-number-for-a-linear-operator}
}