Hello,
I would like to try to use FEAST to solve the generalized eigenproblem (A-sB)x = 0, where A is symmetric, positive-definite, and B is symmetric (actually, it's a diagonal matrix), positive semi-definite.
I'm all setup to use my own storage for A and B, and my own tools to factorize the shifted matrix A-sB. However - and this may be a huge issue - my tools only allow me to factorize a real matrix - not a complex one.
If I understand FEAST correctly, even for the particular problem I have, I will be asked to factorize a shifted matrix where "s" is a complex variable.
Before I embark on this test, could somebody confirm for me that this is indeed the case? I ask because my matrices are huge (N > 30M), and a sparse factorization of the real matrix is already a stretch, but one I'm willing to put up with. But to double that storage because the matrix is complex will make the use of FEAST prohibitive for me.
Thanks.