Dense and iterative concurrent linear algebra in the Multicomputers Toolbox

The Multicomputer Toolbox includes sparse, dense, and iterative scalable linear algebra libraries. Dense direct, and iterative linear algebra libraries are covered in this paper, as well as the distributed data structures used to implement these algorithms; concurrent BLAS are covered elsewhere. We discuss uniform calling interfaces and functionality for linear algebra libraries. We include a detailed explanation of how the level-3 dense LU factorization works, including features that support data distribution independence with a blocked algorithm. We illustrate the data motion for this algorithm, and for a representative iterative algorithm, PCGS. We conclude that data distribution independent libraries are feasible and highly desirable. Much work remains to be done in performance tuning of these algorithms, though good portability and application-relevance have already been achieved