Finding eigenvalues of large, sparse matrix

Question

I am working on Fermion and Boson Hubbard Model, in which dimension of Hilbert Space are quite large (~50k). I am currently using the Lapack routine DSYEV to determine the eigenvalues & eigenfunctions of the large (50k x 50k) Hamiltonian matrix, but this takes a long time, about 8 hours on a Xeon workstation.

I would like to reduce this run time on this particular machine. I am looking at the Lanczos method and wondering if this is the best option, or if there is another choice.

Answer 1

Lanczos (or other iterative) method is used to compute extreme (small/big) eigenvalues. It is better than direct DSYEV, if you need eigenvalues and eigenfunctions much less than the system size (50k). Especially, if the matrix you have is sparse then the acceleration you will get is much better.

If you are looking for all eigenvalues and your matrix is dense then the better method is direct DSYEV.