This award was made on a 'small' category proposal submitted in response to the ITR solicitation, NSF-02-168. This grant is funded jointly by the Divisions of Materials Research and Mathematical Sciences. It supports interdisciplinary research and education on the optimization of large-scale matrix computations, a long-standing problem in computational science with important applications to computational condensed matter and materials physics and many other fields. The research effort involves computer science, mathematics, and condensed matter physics. While much progress has been made by exploiting special properties of a matrix or the sparsity pattern of its entries, the need remains for more robust and effective methods, including preconditioning techniques to improve iterative solutions. Simulating interacting quantum systems, a powerful approach for understanding many fundamental properties of materials, is an important application of these methods. It provides motivation for this research on developing robust and efficient linear algebra solvers for quadratic form problems and for multi-length scale structured matrices. This research has a potentially high impact on the ability to predict properties of materials, such as lattice structures, magnetic properties, and lattice dynamics, through the application of theory and simulation. This award also supports education of undergraduate and graduate students and advanced training of a postdoctoral researcher. %%%
