On the processing time of a parallel linear system solver
The speed-up obtained by the use of multiprocessor systems is of major importance for numerical applications involving the solution of large dense systems of linear equations. We are interested here in the performance evaluation of an algorithm for the parallel solution of linear systems. The structure of the algorithm's task graph is representative of a class of recently proposed parallel linear system solvers. We develop a probabilistic model for two different parallel execution schemes depending on the synchronization policy adopted. The analytical solution of the model provides the mean algorithm execution time and therefore the speed-up and efficiency obtained with respect to the single processor environment.
KeywordsParallel Algorithm Precedence Constraint Secondary Process Computation Graph Task Graph
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- D.Heller, "A Survey of Parallel Algorithms in Numerical Linear Algebra", SIAM Rev.20 (1978).Google Scholar
- D.J.Evans, M.Hatzopoulos, "A Parallel Linear System Solver", Intern. J. Comput. Math.7 (1979).Google Scholar
- B.Plateau, A.Staphylopatis, "Modeling of the Parallel Resolution of a Numerical Problem on a Locally Distributed Computing System", ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, Seattle, WA, Aug. 1982.Google Scholar
- P.Heidelberger, K.S.Trivedi, "Queueing Network Models for Parallel Processing with Asynchronous Tasks", IEEE Trans. on Computers, Vol. C-31, No.11, Nov. 1982.Google Scholar
- E.Gelenbe, A.Lichnewsky, A.Staphylopatis, "Experience with the Parallel Solution of Partial Differential Equations on a Distributed Computing System", IEEE Trans. on Computers, Vol. C-31, No.12, Dec. 1982.Google Scholar
- G.Fayolle, P.J.B.King, I.Mitrani, "On the Execution of Programs by Many Processors", PERFORMANCE '83, A.K.Agrawala and S.K.Tripathi (editors), North-Holland, 1983.Google Scholar
- L.M.Adams, T.W.Crockett, "Modeling Algorithm Execution Time on Processor Arrays", IEEE Computer, July 1984.Google Scholar
- Ph. Mussi, Ph. Nain, "Evaluation of Parallel Execution of Program Tree Structures", ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, Cambridge, Mass., Aug. 1984Google Scholar
- M.Hatzopoulos, N.M.Missirlis, "Advantages for Solving Linear Systems in an Asynchronous Environment", Journal of Computational and Applied Math. 12 & 13, 1985.Google Scholar