A Efficiently Computing Eigenvalues of a Sparse Banded Matrix

[Jimmy and Bimmy]

I have a Hamiltonian represented by a penta-diagonal matrix

The first bands are directly adjascent to the diagonals. The other two bands are N places above and below the diagonal.

Can anyone recommend an efficient algorithm or routine for finding the eigenvalues and eigenvectors?

 

[DrClaude]

LAPACK can handle banded matrices. See for instance:
http://www.netlib.org/lapack/lug/node48.html
http://www.netlib.org/lapack/lug/node124.html

 

[Jimmy and Bimmy]

LAPACK can handle banded matrices. See for instance:
http://www.netlib.org/lapack/lug/node48.html
http://www.netlib.org/lapack/lug/node124.html

Thanks for the reply.

I have been using dsyev from the lapack routine (which is for symmetric matrices). I switched to dsbev (which is for symmetric band matrices), but didn't see much improvement. This is because, even though I only have 5 bands (diagonal + 2 upper + 2 lower), the outer 2 bands are a good distance away, and lapack doesn't take advantage of spare matrices.

Someone recommended arpack, but the documentation can be hard to follow.