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Sparse Gaussian Elimination modulo p: an Update

Abstract : This paper considers elimination algorithms for sparse matrices over finite fields. We mostly focus on computing the rank, because it raises the same challenges as solving linear systems, while being slightly simpler. We developed a new sparse elimination algorithm inspired by the Gilbert-Peierls sparse LU factorization, which is well-known in the numerical computation community. We benchmarked it against the usual right-looking sparse gaussian elimination and the Wiedemann algorithm using the Sparse Integer Matrix Collection of Jean-Guillaume Dumas. We obtain large speedups (1000× and more) on many cases. In particular , we are able to compute the rank of several large sparse matrices in seconds or minutes, compared to days with previous methods.
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https://hal.archives-ouvertes.fr/hal-01333670
Contributor : Charles Bouillaguet <>
Submitted on : Saturday, June 18, 2016 - 2:28:27 PM
Last modification on : Friday, November 27, 2020 - 2:20:03 PM

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  • HAL Id : hal-01333670, version 1

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Charles Bouillaguet, Claire Delaplace. Sparse Gaussian Elimination modulo p: an Update. Computer Algebra in Scientific Computing, Sep 2016, Bucharest, Romania. ⟨hal-01333670⟩

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