Alternatives to ARPACK?
- To: mathgroup at smc.vnet.net
- Subject: [mg107993] Alternatives to ARPACK?
- From: Matin Inck <matin.inck at gmail.com>
- Date: Thu, 4 Mar 2010 05:32:08 -0500 (EST)
Hi guys
My system is currently described by a dense 2500x2500 matrix, which
contains many zero entries. Diagonalizing this matrix using
Eigensystem takes about 2 minutes, which seems like a long time, and I
assume it has got something to do with the fact that the eigenvalues
are degenerate. In order to investigate my system further, I need to
generate a larger matrix (say 3600x3600), but my computer runs out of
memory when I try to diagonalize it in this case (Mathematica
complaints about no memory).
I have two questions.
1) If I want the full spectrum of the matrix, what options do I have?
2) It might be possible that I can do with only a small part of the
spectrum of my matrix. In this case what I would use is following
piece of code, where =E2=80=9CHamiltonian=E2=80=9D is the name of the matrix:
Eigensystem[SparseArray[Hamiltonian], 50, Method=EF=82=AE{"Arnoldi",
"Shift"=EF=82=AE0.25}]
Just to be absolutely sure: Does this give me the 50 eigenvalues (and
corresponding eigenvectors) closest to 0.25? Also, I believe I read
somewhere that for each time an eigenvector/value is found using this
method, there is a loss of precision. Can you confirm this?
Any help would be much appreciated.
Best,
Matin.