# Preconditioner for large size hermitian eigenvalue problems

Basically I try to compute several smallest eigenvalues of some sparse 50k*50k eigenvalue problems using matlab.

$$Ax = \lambda Bx$$

With matlab eigs, it's not as fast as I expected. So I tried some preconditioned routine like lobpcg, however it said "The problem size is too small, relative to the block size. Try using eig or eigs instead".

Anyone can give some suggestion on how can I circumvent this with lobpcg or using some other routine?

• How slow is it, and how fast do you need it to be? – Bill Barth Sep 13 '13 at 11:56
• @Bill Barth it runs for more than 10 minutes for once (on my desktop, dual core 2.5GHz, with Matlab 2012b,64), while I expect it to be few minutes... – lorniper Sep 13 '13 at 14:29