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A Novel Parallel Algorithm for Gaussian Elimination of Sparse Unsymmetric Matrices

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7203)

Abstract

We describe a new algorithm for Gaussian Elimination suitable for general (unsymmetric and possibly singular) sparse matrices of any entry type, which has a natural parallel and distributed-memory formulation but degrades gracefully to sequential execution.

We present a sample MPI implementation of a program computing the rank of a sparse integer matrix using the proposed algorithm. Some preliminary performance measurements are presented and discussed, and the performance of the algorithm is compared to corresponding state-of-the-art algorithms for floating-point and integer matrices.

Keywords

  • Gaussian Elimination
  • unsymmetric sparse matrices
  • exact arithmetic

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References

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© 2012 Springer-Verlag Berlin Heidelberg

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Murri, R. (2012). A Novel Parallel Algorithm for Gaussian Elimination of Sparse Unsymmetric Matrices. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2011. Lecture Notes in Computer Science, vol 7203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31464-3_19

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  • DOI: https://doi.org/10.1007/978-3-642-31464-3_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31463-6

  • Online ISBN: 978-3-642-31464-3

  • eBook Packages: Computer ScienceComputer Science (R0)