Given a set of $n$ complex numbers $a_i$ and error magnitude $\epsilon_i$ with $|a_i| > \epsilon_i$. We define the error disk $D(\epsilon_i) = \{ z \mid |z| \leq \epsilon_i\}$. We have the set
$$ F = \sum_{i=1}^n \frac{1}{a_i + D(\epsilon_i)} $$ Now, I would like to find a minimum $\delta$ such that $$ G = D(\delta) + \sum_{i=1}^n \frac{1}{a_i} $$ and $F \subset G$. Sorry, for the awkward notation, I guess there is a much better to conceptualize this. Please enlighten me.