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Sparse LU factorization of the Cray T3D

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High-Performance Computing and Networking (HPCN-Europe 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 919))

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Abstract

The paper describes a parallel algorithm for the LU factorization of sparse matrices on distributed memory machines by using SPMD as programming model and PVM as message passing interface. We address all the difficulties arising in sparse codes, as the fill-in or the dynamic movement of data inside the matrix. The cyclic distribution has been used to evenly distribute the elements onto a mesh of processors, whereas two local storage schemes are proposed: A semi-ordered and two-dimensional linked list, which fulfils better the requirements of the algorithm, and a compressed storage by rows, which behaves better in the use of memory. The properties of the code are extensively analyzed and execution times on the CRAY T3D are presented to illustrate the overall efficiency achieved by our methods.

This work was supported by the Ministry of Education and Science (CICYT) of Spain under project TIC92-0942-C03, by the Human Capital and Mobility programme of the European Union under proyect ERB4050P1921660, and by the Training and Research on Advanced Computing Systems (TRACS) at the Edinburgh Parallel Computing Centre (EPCC)

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References

  1. R. Asenjo and E.L. Zapata. Sparse LU factorization on the Cray T3D. Technical report, Computer Architecture Dept. Univ. of Málaga, September 1994. Anonymous ftp: ftp.atc.ctima.uma.es (SpLUCray.ps).

    Google Scholar 

  2. T. A. Davis and P. C. Yew. A nondeterministic parallel algorithm for general unsymmetric sparse LU factorization. SIAM J. Matrix Anal. Appl., 11:383–402, 1990.

    Article  MathSciNet  Google Scholar 

  3. I. S. Duff and J. K. Reid. Some design features of a sparse matrix code. ACM Trans. Math. Software, 5:18–35, 1979.

    Article  Google Scholar 

  4. I. S. Duff A. M. Erisman and J. K. Reid. Direct Methods for Sparse Matrices. Oxford University Press, Oxford, U.K., 1986.

    Google Scholar 

  5. G. H. Golub and C. F. Van Loan. Matrix Computation. The Johns Hopkins University Press, Baltimore, MD, 2 edition, 1989.

    Google Scholar 

  6. I. S. Duff R. G. Grimes and J. G. Lewis. Sparse matrix test problems. ACM Trans. Math. Software, 15:1–14, 1989.

    Article  Google Scholar 

  7. A. Geist A. Beguelin J. Dongarra W. Jiang R. Manchek and V. Sunderam. PVM 3 User's Guide and Refernce Manual. Engineering Physic and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, May 1993.

    Google Scholar 

  8. H. M. Markowitz. The elimination form of the inverse and its application to linear programming. Management Sci., 3:255–269, 1957.

    MATH  MathSciNet  Google Scholar 

  9. S. Booth J. Fisher N. MacDonald P. Maccallum E. Minty and A. Simpson. Parallel Programming on the Cray T3D. Edinburgh Parallel Computing Centre, University of Edinburgh, U.K., September 1994.

    Google Scholar 

  10. R. Asenjo L. F. Romero M. Ujaldón and E. L. Zapata. Sparse block and cyclic data distributions for matrix computations. In High Performance Computing: Technology and Application. Grandinetti et al. (Eds.) Elsevier Science, (to appear).

    Google Scholar 

  11. A. F. van der Stappen R. H. Bisseling and J. G. G. van de Vorst. Parallel sparse LU decomposition on a mesh network of transputers. SIAM J. Matrix Anal. Appl., 14(3):853–879, July 1993.

    MathSciNet  Google Scholar 

  12. Z. Zlatev J. Wasniewski and K. Schaumburg. Y12M—Solution of Large and Sparse Systems of Linear Algebraic Equations. In Lecture Notes in Computer Science, number 121, pages 61–77, Berlin, 1981. Springer-Verlang.

    Google Scholar 

  13. Z. Zlatev. Computational Methods for General Sparse Matrices, Mathematics and Its Applications. 65. Kluwer Academin Publisher, Dordrecht, the Netherlands, 1991.

    Google Scholar 

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Authors and Affiliations

  1. Computer Architecture Department, University of Málaga, Plaza El Ejido S/N, 29013, Málaga, Spain

    R. Asenjo & E. L. Zapata

Authors
  1. R. Asenjo
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  2. E. L. Zapata
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Bob Hertzberger Giuseppe Serazzi

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© 1995 Springer-Verlag Berlin Heidelberg

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Asenjo, R., Zapata, E.L. (1995). Sparse LU factorization of the Cray T3D. In: Hertzberger, B., Serazzi, G. (eds) High-Performance Computing and Networking. HPCN-Europe 1995. Lecture Notes in Computer Science, vol 919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0046701

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  • DOI: https://doi.org/10.1007/BFb0046701

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59393-5

  • Online ISBN: 978-3-540-49242-9

  • eBook Packages: Springer Book Archive

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