Unifying and optimizing parallel linear algebra algorithms
- 1 January 1993
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Parallel and Distributed Systems
- Vol. 4 (12) , 1382-1397
- https://doi.org/10.1109/71.250119
Abstract
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.Keywords
This publication has 13 references indexed in Scilit:
- Compiling Fortran D for MIMD distributed-memory machinesCommunications of the ACM, 1992
- $LU$ Factorization Algorithms on Distributed-Memory Multiprocessor ArchitecturesSIAM Journal on Scientific and Statistical Computing, 1988
- The ijk forms of factorization methods I. Vector computersParallel Computing, 1988
- Parallel Solution of Triangular Systems on Distributed-Memory MultiprocessorsSIAM Journal on Scientific and Statistical Computing, 1988
- A Parallel Triangular Solver for a Distributed-Memory MultiprocessorSIAM Journal on Scientific and Statistical Computing, 1988
- Introduction to Parallel and Vector Solution of Linear SystemsPublished by Springer Nature ,1988
- Gaussian elimination on message passing architecturePublished by Springer Nature ,1988
- Parallel solution of triangular systems of equationsParallel Computing, 1988
- Gaussian elimination with partial pivoting and load balancing on a multiprocessorParallel Computing, 1987
- Data-flow algorithms for parallel matrix computationCommunications of the ACM, 1985