Graduate Student: Z. Tong
Sponsor: NSF
This research project focuses on developing parallel algorithms for obtaining a few of the eigenpairs of sparse generalized eigenvalue problems. The problems under consideration are too large for the traditional QR-type schemes, or solvers that use expanding subspaces. The algorithm currently under development is based on the trace minimization algorithm (previous work of the PI) which, with a good shifting strategy, converges at least as fast as other well-known methods such as the Lanczos method and Jacobi-Davidson methods. Our algorithm, however, uses far less storage than needed by other schemes, and is more suitable for parallel architectures. The major challenge in this research is to design an efficient and robust shifting strategy that overcomes problems associated with poorly separated eigenvalues or clusters of eigenvalues.