  For an $n\times n$ diagonally dominant matrix $T=(t_{i,j})_{n\times n}$ with
positive elements satisfying certain bounding conditions, we propose to use a
diagonal matrix $S=(s_{i,j})_{n\times n}$ to approximate the inverse of $T$,
where $s_{i,j}=\delta_{i,j}/t_{i,i}$ and $\delta_{i,j}$ is the Kronecker delta
function. We derive an explicitly upper bound on the approximation error, which
is in the magnitude of $O(n^{-2})$. It shows that $S$ is a very good
approximation to $T^{-1}$.
