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A fast parallel algorithm to compute the rank of a matrix over an arbitrary field

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Abstract

It is shown that the rank of a matrix over an arbitrary field can be computed inO(log2 n) time using a polynomial number of processors.

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References

  1. S. Berkowitz, On computing the determinant in small parallel time using a small number of processors,Inform. Process. Lett.,18 (1984), 147–150.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Borodin, S. A. Cook andN. Pippenger, Parallel computation for well-endowed rings and space bounded probabilistic machines,Information and Control 58 (1983), 113–136.

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Borodin, J. von zur Gathen andJ. Hopcroft, Fast parallel matrix and GCD computations,Information and Control,52 (1982), 241–256.

    Article  MATH  MathSciNet  Google Scholar 

  4. L. Csánky, Fast parallel matrix inversion algorithms,SIAM J. Comput.,5 (1976).

  5. J. von zur Gathen, private communication.

  6. O. Ibarra, S. Moran andL. E. Rosier, A note on the parallel complexity of computing the rank of ordern matrices,Information Processing Letters,11 (1980), 162.

    Article  MathSciNet  Google Scholar 

  7. E. M. Luks andP. McKenzie, Fast parallel computation with permutation groups,Proc. 25 th FOCS, 1985, 505–514.

  8. P. McKenzie andS. A. Cook, The parallel complexity of the abelian permutation group membership,Proc. 24 th FOCS, 1983, 154–161.

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Also appeared in ACM Symposium on Theory of Computing, May 28–30, 1986 Berkeley, California. Research supported by Miller Fellowship, University of California, Berkeley.

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Mulmuley, K. A fast parallel algorithm to compute the rank of a matrix over an arbitrary field. Combinatorica 7, 101–104 (1987). https://doi.org/10.1007/BF02579205

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  • DOI: https://doi.org/10.1007/BF02579205

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