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Article Dans Une Revue Linear Algebra and its Applications Année : 2012

Generalized fraction-free LU factorization for singular systems with kernel extraction

Résumé

Linear systems are usually solved with Gaussian elimination. Especially when multiple right hand sides are involved, an efficient procedure is to provide a factorization of the left hand side. When exact computations are required in an integral domain, complete fraction-free factorization and forward-backward substitutions are useful. This article deals with the case where the left hand side may be singular. In such a case, kernels are required to test a solvability condition and to derive the general form of the solutions. The complete fraction-free algorithms are therefore extended to deal with singular systems and to provide the kernels with exact computations on the same integral domain where the initial data take their entries.
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Commentaire : An example of fraction-free factorization.
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Dates et versions

hal-00678543 , version 1 (17-11-2016)

Licence

Domaine public

Identifiants

Citer

David Dureisseix. Generalized fraction-free LU factorization for singular systems with kernel extraction. Linear Algebra and its Applications, 2012, 436 (1), pp.27-40. ⟨10.1016/j.laa.2011.06.013⟩. ⟨hal-00678543⟩
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