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Parallel complexity of lattice basis reduction and a floating-point parallel algorithm

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PARLE '93 Parallel Architectures and Languages Europe (PARLE 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 694))

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References

  1. W. M. Gentleman. Error analysis of QR decompositions by Givens transformations. Linear Algebra and Its Applications, 10:189–197, 1975.

    Google Scholar 

  2. C. Heckler. Parallele seminumerische Algorithmen. PhD thesis, Universität des Saarlandes, Saarbrücken, Germany, 1993. In preparation.

    Google Scholar 

  3. C. Heckler and L. Thiele. A parallel lattice basis reduction for mesh-connected processor arrays and parallel complexity. to appear.

    Google Scholar 

  4. C. Heckler and L. Thiele. On the time complexity of parallel algorithms for lattice basis reduction. Technical Report 05/1993, SFB124, Universität Saarbrücken, Germany, 1993.

    Google Scholar 

  5. A.K. Lenstra, H.W. Lenstra Jr., and L. Lovasz. Factoring polynomials with rational coefficients. Math. Ann., 261:515–534, 1982.

    Article  Google Scholar 

  6. C.P. Schnorr and M. Euchner. Lattice basis reduction: Improved practical algorithms and solving subset sum problems. In Proceedings of the FCT'91 (Gosen, Germany), LNCS 529, pages 68–85. Springer, 1991.

    Google Scholar 

  7. U. Schwiegelshohn and L. Thiele. A systolic array for cyclic-by-rows Jacobi algorithms. Journal of Parallel and Distributed Computing, 4:334–340, 1987.

    Google Scholar 

  8. G. Villard. Parallel lattice basis reduction. In International Symposium on Symbolic and Algebraic Computation, Berbeley California USA, pages 269–277. ACM Press, 1992.

    Google Scholar 

  9. J. H. Wilkinson. Rounding Errors in Algebraic Processes. Prentice-Hall, Englewood Cliffs, 1963.

    Google Scholar 

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Arndt Bode Mike Reeve Gottfried Wolf

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© 1993 Springer-Verlag Berlin Heidelberg

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Heckler, C., Thiele, L. (1993). Parallel complexity of lattice basis reduction and a floating-point parallel algorithm. In: Bode, A., Reeve, M., Wolf, G. (eds) PARLE '93 Parallel Architectures and Languages Europe. PARLE 1993. Lecture Notes in Computer Science, vol 694. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56891-3_74

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  • DOI: https://doi.org/10.1007/3-540-56891-3_74

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  • Print ISBN: 978-3-540-56891-9

  • Online ISBN: 978-3-540-47779-2

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