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\begin{document}
\title{Perturbation Analyses for the Cholesky Factorization with 
Backward Rounding Errors}
\author{Xiao-Wen Chang\\
School of Computer Science, McGill University \\
      Montreal, Quebec, Canada H3A 2A7}
\date{}
\maketitle
This paper gives perturbation analyses for the Cholesky factorization 
$A=R^TR$ of a real symmetric positive definite matrix $A$, with the form 
of perturbations we could expect from the equivalent backward error in 
$A$ resulting from numerically stable computations on finite precision 
floating point computers. First-order and rigorous perturbation bounds are 
obtained. The analyses more accurately reflect the true sensitivity of the 
problem than previous such results. Both numerical results and an analysis 
show the standard method of pivoting usually improves the condition of the
problem. A useful upper bound on the condition of the problem is derived.
\end{document}

Xiao-Wen Chang
