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Mathematics > K-Theory and Homology

arXiv:0704.2351 (math)
[Submitted on 18 Apr 2007 (v1), last revised 24 Apr 2007 (this version, v2)]

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

Authors:Jean-Guillaume Dumas (LMC - IMAG), Philippe Elbaz-Vincent (I3M), Pascal Giorgi (LP2A), Anna Urbanska (LMC - IMAG)
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Abstract: This paper deals with the computation of the rank and of 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).
Subjects: K-Theory and Homology (math.KT); Distributed, Parallel, and Cluster Computing (cs.DC); Symbolic Computation (cs.SC); Number Theory (math.NT)
Cite as: arXiv:0704.2351 [math.KT]
  (or arXiv:0704.2351v2 [math.KT] for this version)
  https://doi.org/10.48550/arXiv.0704.2351

Submission history

From: Giorgi Pascal [view email]
[v1] Wed, 18 Apr 2007 14:29:28 UTC (50 KB)
[v2] Tue, 24 Apr 2007 15:28:48 UTC (46 KB)
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