Fast Computation of the Rank Profile Matrix and the Generalized Bruhat Decomposition Jean-Guillaume Dumas, Clement Pernet, Ziad Sultan
Fast Computation of the Rank Profile Matrix and the Generalized Bruhat Decomposition Jean-Guillaume Dumas, Clement Pernet, Ziad Sultan To cite this version: Jean-Guillaume Dumas, Clement Pernet, Ziad Sultan. Fast Computation of the Rank Profile Matrix and the Generalized Bruhat Decomposition. Journal of Symbolic Computation, Elsevier, 2017, Special issue on ISSAC’15, 83, pp.187-210. 10.1016/j.jsc.2016.11.011. hal-01251223v1 HAL Id: hal-01251223 https://hal.archives-ouvertes.fr/hal-01251223v1 Submitted on 5 Jan 2016 (v1), last revised 14 May 2018 (v2) HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Fast Computation of the Rank Profile Matrix and the Generalized Bruhat Decomposition Jean-Guillaume Dumas Universit´eGrenoble Alpes, Laboratoire LJK, umr CNRS, BP53X, 51, av. des Math´ematiques, F38041 Grenoble, France Cl´ement Pernet Universit´eGrenoble Alpes, Laboratoire de l’Informatique du Parall´elisme, Universit´ede Lyon, France. Ziad Sultan Universit´eGrenoble Alpes, Laboratoire LJK and LIG, Inria, CNRS, Inovall´ee, 655, av. de l’Europe, F38334 St Ismier Cedex, France Abstract The row (resp. column) rank profile of a matrix describes the stair-case shape of its row (resp.
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