Dense Linear Algebra over Finite Fields: the FFLAS and FFPACK packages

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dc.creatorDumas, Jean-Guillaume
dc.creatorGiorgi, Pascal
dc.creatorPernet, Clément
dc.date2006-01-31
dc.date2009-01-14
dc.date.accessioned2026-07-07T12:29:07Z
dc.date.available2026-07-07T12:29:07Z
dc.descriptionIn the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide efficient implementations of such algorithms one need to be careful with the underlying arithmetic. It is well known that modular techniques such as the Chinese remainder algorithm or the p-adic lifting allow very good practical performance, especially when word size arithmetic are used. Therefore, finite field arithmetic becomes an important core for efficient exact linear algebra libraries. In this paper, we study high performance implementations of basic linear algebra routines over word size prime fields: specially the matrix multiplication; our goal being to provide an exact alternate to the numerical BLAS library. We show that this is made possible by a carefull combination of numerical computations and asymptotically faster algorithms. Our kernel has several symbolic linear algebra applications enabled by diverse matrix multiplication reductions: symbolic triangularization, system solving, determinant and matrix inverse implementations are thus studied.
dc.identifierhttps://arxiv.org/abs/cs/0601133
dc.identifierhttp://arxiv.org/abs/cs/0601133
dc.identifierACM Transactions on Mathematical Software 35, 3 (2009) article 19
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215766
dc.subjectSymbolic Computation
dc.titleDense Linear Algebra over Finite Fields: the FFLAS and FFPACK packages
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