Graduate Student: Zhanye Tong
Sponsor: National Science Foundation
This research project focuses on developing parallel algorithms for
obtaining a few of the eigenpairs of a sparse generalized eigenvalue
problem. 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 sfifting strategy,
converges at least as fast as other well-known methods such as
Lanczos method and Jacobi-Davidson method, but uses far less
storage than
needed by these methods, and which 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 closely spaced eigenvalues or clusters of eigenvalues.