Is there a procedure to find the eigenvalues of $\textbf{M}$?
‎
$$\begin{eqnarray}
‎\textbf{M}=\left[‎
‎\begin {array}{ccccc}‎
‎\textbf{A}   &    \textbf{B}  &        &        &\\‎
‎\textbf{B}^T &   \textbf{ A}  &    \textbf{B}  &        &\\‎
    ‎&\ddots &\ddots  & \ddots &\\‎
    ‎&       &        &        & \textbf{B}    \\‎
    ‎&       &        &  \textbf{B}^T   &  \textbf{A}
‎\end {array}‎
‎\right]‎,
‎\end{eqnarray}‎‎
$$

where $\textbf{B}^T$ is transpose of matrix $\textbf{B}$.