I need to compute in an efficient way the determinant of a complex symmetric banded matrix. The matrix is composed by the central diagonal and three upper diagonals, and three subdiagonals of course. Nowadays I am using LU decomposition for general complex matrices. I am using the LAPACK library. What is the best algorithm to compute the determinant of this kind of matrix?? Can anyone suggest a better algorithm or give me some clue and advice to go in the right direction please?? Thanks! Antonio.