ALGORITHMS: Collaborative Research: New Contributions to the Theory and Practice of Programming Linear Algebra Libraries

University Of Texas At Austin, Austin TX

Investigators

Abstract

While many of the insights are readily demonstrated for dense linear algebra operations, there are natal extensions that impact sparse direct methods. It is the goal of the proposed project to pursue a unified approach to all of these insights in an effort to put software architectures of linear algebra libraries for this domain of operations on a solid scientific footing. We will undertake a one year pilot project that will demonstrate the following: (1) The systematic approach can be used to derive highly efficient kernels for specialized dense linear algebra operations that are encountered in sparse direct methods; (2) The abstract program interface that has been demonstrated to allow high-performance implementation of dense linear algebra operations will be extended to apply to sparse matrices that are viewed as hierarchical matrices; (3) We will lay the foundation for a mathematical description of sparse matrices as hierarchical matrices which we believe will allow the derivation methods to be extended to operations on hierarchical matrices.