Book Chapter10.1007/BFB0024794
An Optimal Parallel Algorithm for Gaussian Elimination
Mounir Marrakchi
- 26 Aug 1996
- pp 907-910
TL;DR: The 2-steps graph which occurs in the parallelization of Gaussian elimination with partial pivoting is presented and an optimal parallel algorithm with two processors is presented.
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Abstract: This paper presents the 2-steps graph which occurs in the parallelization of Gaussian elimination with partial pivoting. We compute the task deadlines and the lower bound of processors popt (n) for executing the task graph in minimal time (n is the size of the considered matrix). Finally, we present an optimal parallel algorithm with two processors.
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References
Solving Linear Algebraic Equations on an MIMD Computer
TL;DR: Two pracUcal parallel algorithms for solving systems of dense linear equations on an MIMD computer are presented, based on Gaussian elunmation and Givens transformations, which are numerically stable and have been tested on the Denelcor HEP machine.
177
Parallel Gaussian elimination on an MIMD computer
Michel Cosnard,Mounir Marrakchi,Yves Robert,Denis Trystram +3 more
- 01 Mar 1988
TL;DR: It is shown that the SAXPY, GAXPY and DOT algorithms of Dongarra, Gustavson and Karp, as well as parallel versions of the LDMt, LDLt, Doolittle and Cholesky algorithms, can be classified into four task graph models.
118
Gaussian elimination with partial pivoting on an MIMD computer
TL;DR: A parallel algorithm for an MIMD computer that runs in time n 2 − 1 and needs 0.3536 … n processors in order to perform a Gaussian elimination with partial pivoting on an n × n matrix is presented.
13
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