Download e-book for iPad: Arithmetique et algorithmique en algebre lineaire exacte by Pascal G.

By Pascal G.

Summary: For a couple of many years, numerical linear algebra has visible in depth advancements in either mathematical and machine technology conception that have ended in actual average software program like BLAS or lapack. In desktop algebra the location has no longer complex as a lot, specifically a result of range of the issues and thanks to a lot of the theoretical development were performed lately. This thesis falls right into a fresh classification of labor which goals at uniforming high-performance codes from many really expert libraries right into a unmarried platform of computation. specifically, the emergence of strong and conveyable libraries like GMP or ntl for special computation has became out to be a true asset for the improvement of purposes in certain linear algebra. during this thesis, we learn the feasibility and the relevance of the re-use of specialised codes to strengthen a excessive functionality designated linear algebra library, particularly the LinBox library. We use the widely used programming mechanisms of C++ (abstract classification, template type) to supply an abstraction of the mathematical items and therefore to permit the plugin of exterior parts. Our aim is then to layout and validate, in LinBox. excessive point popular toolboxes for the implementation of algorithms in targeted linear algebra. particularly, we suggest ''exact/numeric'' hybrid computation workouts for dense matrices over finite fields which almost fit with the functionality got through numerical libraries like LAPACK. On a better point, we reuse those hybrid exercises to resolve very successfully a classical challenge of laptop algebra : fixing diophantine linear structures. for that reason, this allowed us to validate the primary of code reuse in LinBox library and extra in most cases in desktop algebra. The LinBox library is accessible at

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Additional info for Arithmetique et algorithmique en algebre lineaire exacte pour la bibliotheque LinBox

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5 NTL . . . . . . . . . . . 6 Performances et surcoˆ ut des wrappers . . 3 Extension alg´ ebrique GF (pk ) . . . . . 1 Givaro . . . . . . . . . . . 2 NTL . . . . . . . . . . . 3 LiDIA . . . . . . . . . . . 4 Performances et surcoˆ ut des wrappers . . 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28 29 31 34 38 45 45 48 48 50 51 53 59 59 60 61 63 65 28 Arithm´etique des corps finis L’algorithmique en calcul exact et plus particuli`erement en alg`ebre lin´eaire n´ecessite des calculs sur de tr`es grands entiers.

4 Performances vs g´ en´ ericit´ es L’utilisation de l’arch´etype pour l’instanciation d’un corps fini entraˆıne un surcoˆ ut dˆ u `a la manipulation abstraite des objets et des fonctions. 1. Arch´etype de donn´ees 39 a` quantifier ces diff´erents surcoˆ uts et `a observer les diff´erents impacts sur les implantations concr`etes. Nous effectuons nos tests `a la fois pour une architecture 32 bits (Pentium III 1Ghz, 512 Mo RAM) et pour une architecture 64 bits (Itanium I 733 Mhz, 1Go RAM). 3 pour l’Itanium avec dans les deux cas l’option -O3.

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Arithmetique et algorithmique en algebre lineaire exacte pour la bibliotheque LinBox by Pascal G.

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