Parallel Gaussian elimination on a MIMD computer

Michel Cosnard (1) , Mounir Marrakchi (2) , Yves Robert (1) , Denis Trystram

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 IMAG - Institut d'Informatique et de Mathématiques Appliquées de Grenoble

This paper introduces a graph-theoretic approach to analyse the performances of several parallel Gaussian-like triangularization algorithms on an MIMD computer. We show 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. We derive new complexity results and compare the asymptotic performances of these parallel versions.

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

Michel Cosnard, Mounir Marrakchi, Yves Robert, Denis Trystram. Parallel Gaussian elimination on a MIMD computer. Parallel Computing, 1988, 6 (3), pp.275-296. ⟨10.1016/0167-8191(88)90070-1⟩. ⟨hal-00857005⟩