I am looking to find the largest term in determinant of Banded matrix, to approximate determinant with it? or is there another approach? Specifically i wants know approximately the determinant of following matrices(If dimension of matrix go to infinity):
$\left( \begin{array}{ccccccccccc} 0 & \text{a0} & \text{b0} & \text{c0} & 0 & 0 & 0 & 0 & \text{c1} & \text{b1} & \text{a1} \\ \text{a1} & 0 & \text{a0} & \text{b0} & \text{c0} & 0 & 0 & 0 & 0 & \text{c1} & \text{b1} \\ \text{b1} & \text{a1} & 0 & \text{a0} & \text{b0} & \text{c0} & 0 & 0 & 0 & 0 & \text{c1} \\ \text{c1} & \text{b1} & \text{a1} & 0 & \text{a0} & \text{b0} & \text{c0} & 0 & 0 & 0 & 0 \\ 0 & \text{c1} & \text{b1} & \text{a1} & 0 & \text{a0} & \text{b0} & \text{c0} & 0 & 0 & 0 \\ 0 & 0 & \text{c1} & \text{b1} & \text{a1} & 0 & \text{a0} & \text{b0} & \text{c0} & 0 & 0 \\ 0 & 0 & 0 & \text{c1} & \text{b1} & \text{a1} & 0 & \text{a0} & \text{b0} & \text{c0} & 0 \\ 0 & 0 & 0 & 0 & \text{c1} & \text{b1} & \text{a1} & 0 & \text{a0} & \text{b0} & \text{c0} \\ \text{c0} & 0 & 0 & 0 & 0 & \text{c1} & \text{b1} & \text{a1} & 0 & \text{a0} & \text{b0} \\ \text{b0} & \text{c0} & 0 & 0 & 0 & 0 & \text{c1} & \text{b1} & \text{a1} & 0 & \text{a0} \\ \text{a0} & \text{b0} & \text{c0} & 0 & 0 & 0 & 0 & \text{c1} & \text{b1} & \text{a1} & 0 \\ \end{array} \right)$