College of Science & Engineering
This group has three main research projects that require MSI resources:
- Numerical methods for eigenvalue problems: The researchers are developing new techniques based on polynomial and/or rational filtering, domain decomposition, and Schur complements strategies. The group is also working on generalizing those techniques into nonlinear problems like approximating the eigenvalue problem by rational functions and linearizing the resulting problem and advanced Rayleigh quotient iteration-like method. They are also developing the EigenValues Slicing Library (EVSL) library, a high-performance and robust package for solving large and difficult eigenvalue problems.
- Preconditioning methods for linear systems: This includes the group's new generalized multilevel low-rank scalable preconditioners (GeMSLR) for general complex sparse linear systems, new algorithms based on multicoloring, as well as multiple-right-hand-sides problems. The group is working on improving the convergence result of those algorithms for hard problems, as well as improving the parallel performance. The researchers are developing the GeMSLR library, a parallel generalized multilevel low-rank scalable preconditioners for general complex sparse linear systems.
- New optimization methods for machine learning: This project includes large high-dimensional tensor completion and GNN-based graph classification algorithms for large graphs.