Unifying and optimizing parallel linear algebra algorithms

Two issues in linear algebra algorithms for multicomputers are addressed. First, how tounify parallel implementations of the same algorithm in a decomposition-independent way. Second, how to optimize naive parallel programs maintaining the decompositionindependence. Several matrix decompositions are viewed as instances of a more generalallocation function called subcube matrix decomposition. By this meta-decomposition, aprogramming environment characterized by general primitives that allow one to designmeta-algorithms independently of a particular decomposition. The authors apply such aframework to the parallel solution of dense matrices. This demonstrates that most of theexisting algorithms can be derived by suitably setting the primitives used in themeta-algorithm. A further application of this programming style concerns the optimization of parallel algorithms. The idea to overlap communication and computation has been extended from 1-D decompositions to 2-D decompositions. Thus, a first attempt towards a decomposition-independent definition of such optimization strategies is provided.