Hi all, I'm trying to compute a large number of interior complex eigenvalues of a large non-Hermitian matrix. For small test problems I can use a dense matrix, and finding interior eigenvalues worked very well. However, for increasing problem sizes I cannot use this approach as my matrix is not very sparse (about 40% non zero). I need to solve problems with 64000x64000 elements. However my matrix can be very efficiently generated (it contains diagonals and two toeplitz sub matrices), so, by using MatCreateShell etc. I have created a shell matrix with very efficient matrix-vector multiply performance (using FFT for the toeplitz matrices). In this case I can solve for the largest eigenvalues of huge problems very efficiently. However, I now cannot solve for the interior eigenvalues (often closely spaced) well at all (using -eps_target).
Is there a well known solution to this? I have tried eps_harmonic etc. Note, I am not an expert in computational linalg, so I maybe being naive. Ideally I'd be able to collect all eigenvalues within a certain region, but the region based solvers (such as ciss) do not seem to be available when using a Shell Matrix, and neither is shift invert, which is what worked very well previously. Does anyone have proposed solutions or pointers to where I can find more literature on this sort of problem. Any help much appreciated! John
