Let a real circulant matrix $\textbf{A}$, and a real vector $\textbf{x}$, we have $$\textbf{Ax} \ge \textbf{0}$$
The first row of $\textbf{A}$ is denoted $(a_1 a_2 \dots a_n)$.
Is there a way to express the most precise bounds $\{l_i, u_i\}$, in function of the $\{a_j\}$, such that $∀i,x_i∈[l_i,u_i]$ ?