Assume we have a family of $N$ continuous functions $f_i(x)\in C_\infty$ along domain $D$.
Define a set of constants $c_i \in \mathbb{R}$ and define the functions $g_i(x)$ so each $g_i(x)$. \begin{equation} g_i(x) = f_i(x) + c_i \end{equation} The mean of the functions $g_i$ at $x$ is denoted $\mu_g(x)$
\begin{equation} \mu_g(x) = \frac{1}{N} \sum_{i=1}^{N} (g_i(x)) \end{equation}
We define the variance of $g_i(x)$ using the following: \begin{equation} Var_g(x) = \frac{1}{N} \sum_{i=1}^{N} (g_i(x) - \mu_g(x))^2 \end{equation} Our goal is to find the set of constants $c_i$ to minimise the quantity. \begin{equation} \max_{x \in D} \{ (Var_g(x)) \} \end{equation}
What is a reasonable strategy for finding the set of $c_i$'s?
