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\title{On Optimal Backward Perturbation Bounds}
\author{Ji-guang Sun\\
Department of Computer Science, Umea University \\
S-901 87 Umea, Sweden}
\date{}
\maketitle
In general, a computed solution to a problem solves many perturbed 
problems. The optimal backward perturbation bound for the problem 
with respect to the computed solution is a measure of the nearness 
between the perturbed problems and the original problem. 
An explicit expression of the optimal backward perturbation bound 
may provide a very convenient way of testing the stability of 
practical algorithms. This paper surveys some new results on optimal 
backward perturbation bounds for linear systems, underdetermined 
systems, and linear least squares problems. 
\end{document}
