Algorithmes parallèles efficaces pour le calcul formel : algèbre linéaire creuse et extensions algébriques

Abstract : In every field of scientific and industrial research, the extension of the use of computer science has resulted in an increasing need for computing power. It is thus vital to use these computing resources in parallel. In this thesis we seek to compute the canonical form of very large sparse matrices with integer coefficients, the Smith normal form. By "very large", we mean a million indeterminates and a million equations, i.e. thousand billion of variables. Nowadays, such systems are usually not even storable. However, we are interested in systems for which many of these variables are identical and zero; in this case we talk about sparse systems. We want to solve these systems in an exact way, i.e. we work with integers or in smaller algebraic structures where all the basic arithmetic operations are still valid, finite fields. The rebuilding of the whole solution from the smaller solutions is then relatively easy.
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Modélisation et simulation. Institut National Polytechnique de Grenoble - INPG, 2000. Français
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Contributor : Dumas Jean-Guillaume <>
Submitted on : Thursday, April 17, 2003 - 11:11:28 AM
Last modification on : Monday, March 21, 2016 - 5:32:44 PM
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Jean-Guillaume Dumas. Algorithmes parallèles efficaces pour le calcul formel : algèbre linéaire creuse et extensions algébriques. Modélisation et simulation. Institut National Polytechnique de Grenoble - INPG, 2000. Français. <tel-00002742v2>

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