Efficient algorithm for determinant of a m-diagonal NxN symmetric matrix

Question

I have to find the determinant of a symmetric square NxN matrix with M diagonals and M << N. Is there a more fast method than LU-decomposing the matrix?

Answer 1

Yes, there are special methods for band(ed) matrices that solve elimination with O(N*M^2) complexity. Arbitrary found article of Jeff Thorson