Conference proceeding
Solving triangular linear systems in parallel using substitution
Proceedings.Seventh IEEE Symposium on Parallel and Distributed Processing, (7th), pp 553-560
1995
Abstract
Working within the LogP model, we present parallel triangular solvers which use forward/backward substitution and show that they are optimal. We begin by deriving several lower bounds on execution time for solving triangular linear systems. Specifically, we derive lower bounds in which it is assumed that the number of data items per processor is bounded, a general lower bound, and lower bounds for specific data layouts commonly used for this problem. Furthermore, algorithms are provided which have running times within a constant factor of the lower bounds described. One interesting result is that the popular 2-dimensional block matrix layout necessarily results in significantly longer running times than simpler one-dimensional schemes. Finally, we present a generalization of the lower bounds to banded triangular linear systems.
Metrics
1 Record Views
Details
- Title
- Solving triangular linear systems in parallel using substitution
- Creators
- E.E. Santos - University of California, Berkeley
- Publication Details
- Proceedings.Seventh IEEE Symposium on Parallel and Distributed Processing, (7th), pp 553-560
- Publisher
- IEEE
- Number of pages
- 8
- Resource Type
- Conference proceeding
- Language
- English
- Academic Unit
- School of Engineering
- Scopus ID
- 2-s2.0-0029507455
- Other Identifier
- 991022207146704721