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

2007/04/18 by Jean‐Guillaume Dumas, Philippe Elbaz–Vincent, Dumas, Jean-Guillaume +5 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Distributed #FOS: Computer and information sciences #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #Parallel #Symbolic Computation (cs.SC) #and Cluster Computing (cs.DC)

paper · doi:10.48550/arxiv.0704.2351

openalex publication_date 2007/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 GL₇(Z).

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