I have a problem in which I need to diagonalize matrices with many thousands of complex elements three times. I know that the matrices are hermitian and sparse. Specifically, they consist of 9 bands either side of the diagonal. I am currently using LAPACK with reasonable time using the hermitian matrix routines, however I feel that there must be a faster way as there are so many zero entries in the matrices. I have searched for packages online but not found anything for this specific problem. Does anyone have any recommendations?