Parallel computation of the rank of large sparse matrices from algebraic K-theory

Authors:
Jean-Guillaume Dumas;Philippe Elbaz-Vincent;Pascal Giorgi;Anna Urbánska
Affiliations:
Université Joseph Fourier, Grenoble, France;Université Montpellier II, FRANCE;Université de Perpignan Via Domitia, Perpignan France;Université Joseph Fourier, Grenoble, France
Venue:
Proceedings of the 2007 international workshop on Parallel symbolic computation
Year:
2007

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Abstract

This paper deals with the computation of the rank and some integer Smith forms of a series of sparse matrices arising in algebraic K-theory. The number of non zero entries in the considered matrices ranges from 8 to 37 millions. The largest rank computation took more than 35 days on 50 processors. We report on the actual algorithms we used to build the matrices, their link to the motivic cohomology and the linear algebra and parallelizations required to perform such huge computations. In particular, these results are part of the first computation of the cohomology of the linear group GL 7(Z).