Preconditioners comprise a range of techniques for transforming a system of linear equations Ax=b into a related system that is somehow ``better''. For example, a solver may take less time to compute the solution to the new system, it may compute a more accurate solution, or it may do both. Although a good preconditioner can be critical to computing an accurate solution efficiently, choosing a good preconditioner from the many that are available can be difficult.
The goal of this project is the development of tools to help users choose from large families of preconditioners one that is likely to be well-suited to their particular application; the initial focus will be on preconditioners that are based on reordering the rows and/or columns of a matrix, and those that compute an incomplete factorization of the matrix. In the process of developing these tools, the PI, undergraduate researchers, and other collaborators will work on developing better heuristics, improving theoretical knowledge about specific preconditioners, creating an extensible framework for evaluating different preconditioners, and making the results of extensive experimentation available in a user-friendly form. All work will help lead to a better understanding of the performance of specific preconditioners on sparse systems from specific applications.
As a professor at a liberal arts college, the PI's primary plans for broader impact include: supervising undergraduate and postbaccalaureate research, seeking opportunities for students to present their work outside of the local community and more generally preparing them for graduate work; outreach to groups traditionally underrepresented in computer science through mentoring and the formation of support networks; and the development, refinement, and dissemination of courses that emphasize the role of mathematics in computer science, as well as of courses that give a basic understanding of computing to students who are not computer science majors but whose education will nevertheless be enhanced by such knowledge.
