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A Efficiently Computing Eigenvalues of a Sparse Banded Matrix

  1. Nov 17, 2016 #1
    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?
  2. jcsd
  3. Nov 17, 2016 #2


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    Staff: Mentor

  4. Nov 17, 2016 #3
    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.
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