Hierarchically Blocked Algorithms and Optimized Kernels for Dense Matrix Computations on Memory-Tiered High-Performance Computing Systems

The overall goal in this research program, funded by the Swedish Research Council (VR), is to develop new theory, methods, and algorithms and to produce high-quality, reusable software that deliver close to practical peak performance on today`s evolving deep memory HPC multicore architectures. This is essential, since otherwise users cannot do their computations in reasonable time or with the accuracy and resolution required.

We propose new techniques for efficient utilization of all levels of the memory system and efficient utilization of all functional units of the advanced CPU. Recent results include the development of innovative recursive algorithms for linear algebra computations. The fundamental principles of recursion lead to automatic and variable blocking for deep memory hierarchies.

This work also includes development of software tools and environments for design of parallel algorithms and applications. The research group participates in international collaboration regarding high-performance software libraries (e.g., LAPACK, ScaLAPACK, SLICOT).

The research program is structured as follows: (1) Square and Recursive Blocked Algorithms and Hybrid Data Structures for MAtrix Computations; (2) Blocked and Parallel Matrix Equation Solvers; (3) Blocked and Parallel Two-sided Reductions to Condensed Forms; and (4) Blocked and Parallel Reduction to Schur Forms; (5) HPC Software and Tools. The deliverables also include an essential set of high-performance software and tools in support for scientists and engineers to enable their applications.

Team members

Publications and Theses

Publication list from 2002 - 2009 (pdf version)