Year: 1987
Journal of Computational Mathematics, Vol. 5 (1987), Iss. 4 : pp. 316–324
Abstract
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 $μ(T)＜x(T)$.
In this paper, an answer is given to this problem.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1987-JCM-9555
Journal of Computational Mathematics, Vol. 5 (1987), Iss. 4 : pp. 316–324
Published online: 1987-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 9