Dear PETSc-Dev, I am trying to solve some eigenvalue and singular value decomposition problems using SLEPc and I wanted to get a little advice on how to proceed.
My problems are moderate sized (maximum size of ~30K X 30K for eigenvalues; and ~10K x 10K for SVD) and quite sparse (<7 non-zero entries per row, independent of size). However, I need the FULL eigenspectrum (eigenvalues and eigenvectors), which as I understand requires that a dense 30K x 30K matrix end up being generated. There are many repeated eigenvalues in the full spectrum, if that is of use. It also of type EPS_NHEP (ie non-Hermitian standard eigenvalue problem). For the SVD I am only interested in the null space of the matrix (so the "zero" singular values and their associated vectors). I am running into numerical stability issues when the matrices get larger than ~250x250 for the eigenvalue problems; and ~400x400 for the SVD problems. I am currently using the SVDLANCZOS solver for SVD problem; and the EPSKRYLOVSCHUR solver (since I need the whole spectrum) for the eigenvalue problem. Questions: 1) Are there other algorithms I can try that might be more stable? 2) Any other suggestions for improving numerical stability? 3) Is it worthwhile to use a non-sparse (dense) solver library (something like Elemental?) since I need to construct the entire eigenspace anyways? I am happy to provide more details, specific examples of instability, etc. if necessary. Thanks, Chris Eldred -- Chris Eldred DOE Computational Science Graduate Fellow Graduate Student, Atmospheric Science, Colorado State University B.S. Applied Computational Physics, Carnegie Mellon University, 2009 [email protected] / [email protected]
