Numerical linear algebra is the subfield that solves systems of linear equations on digital computers. These systems appear in many fields of applied science and engineering, as linear equations are the simplest and most common approximation to many more complex equations. Numerical solutions to these systems are routinely used to solve problems ranging from structural engineering to electromagnetic radiation studies. Because of their ubiquitous nature, subroutine libraries for solving these problems Has been one of the most important (and most studied) areas in computational science. This project extends one of the most widely-used of these software packages - the LAPACK project - to use new algorithms and to run on the next generation of hardware.
This project will pursue a broad range of synergistic activities to design and implement numerical linear algebra algorithms. It targets a range of dense and sparse linear systems and eigenvalue problems. The overall goal is to produce the fastest and most accurate solvers for these problems, and make them available to a broad and changing user community. Besides the existing large LAPACK user community, the software will be made available as a Grid-enabled service to the PACI, Millennium and ASCI user communities (Millennium is the Berkeley high performance computing environment). Indeed, much of the proposed research is motivated by particular applications demands from these communities. Given the size and diversity of these communities, part of the project is educational in nature, to enable users from experts to beginning students to find what they need among the wealth of tools available. Finally, the researchers are motivated to meet the opportunities and challenges of new architectures in growing use; besides the distributed environment mentioned before, they include clusters of SMPs (or "CLUMPs").
