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Solving Systems of Interval Linear Equations in Parallel Using Multithreaded Model and “Interval Extended Zero” Method

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Parallel Processing and Applied Mathematics (PPAM 2011)

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

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Abstract

In this paper, an approach to the solution of systems of interval linear equations with the use of the parallel machines is presented, based on parallel multithreaded model and “interval extended zero” method. This approach not only allows us to decrease the undesirable excess width effect, but makes it possible to avoid the inverted interval solutions too. The efficiency of this method has been already proved for non-parallel systems. Here it is shown that it can be also used to perform efficient calculations on parallel machines using the multithreaded model.

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References

  1. Agullo, E., Demmel, J., Dongarra, J., Hadri, B., Kurzak, J., Langou, J., Ltaief, H., Luszczek, P., Tomov, S.: Numerical Linear Algebra on Emerging Architectures: The PLASMA and MAGMA Projects. Journal of Physics: Conference Series 180 (2009)

    Google Scholar 

  2. Anderson, E., Bai, Z., Bischof, C., Blackford, L.S., Demmel, J.W., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D.: LAPACK Users’ Guide. SIAM (1992)

    Google Scholar 

  3. Badia, R.M., Labarta, J., Perez, J.M.: A Flexible and Portable Programming Model for SMP and Multi-cores. Tech. Report, Barcelona Supercomputing Center (2007), http://www.bsc.es/media/994.pdf

  4. Berg, D., Lewis, B.: PThreads Primer A Guide to Multithreaded Programming. Prentice Hall PTR (1996)

    Google Scholar 

  5. Blackford, L., Choi, J., Cleary, A., D’Azevedo, E., Demmel, J., Dhillon, J., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D., Whaley, R.C.: ScaLAPACK Users’ Guide. SIAM (1997)

    Google Scholar 

  6. Boost Interval Arithmetic Library, http://www.boost.org/doc/libs/1_43_0/libs/numeric/interval/doc/interval.htm

  7. Buckley, J.J.: The fuzzy mathematics of finance. Fuzzy Sets & Systems 21, 257–273 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  8. Buckley, J.J.: Solving fuzzy equations in economics and finance. Fuzzy Sets & Systems 48 (1992)

    Google Scholar 

  9. Chapman, B., Jost, G., van der Pas, R.: Using OpenMP: Portable Shared Memory Parallel Programming. MIT Press (2007)

    Google Scholar 

  10. Chen, S.H., Yang, X.W.: Interval finite element method for beam structures. Finite Elements in Analysis and Design 34, 75–88 (2000)

    Article  MATH  Google Scholar 

  11. Demmel, J.W.: Applied Numerical Linear Algebra. SIAM (1997)

    Google Scholar 

  12. Dymova, L., Pilarek, M., Wyrzykowski, R.: Solving Systems of Interval Linear Equations with Use of Modified Interval Division Procedure. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds.) PPAM 2009. LNCS, vol. 6068, pp. 427–435. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  13. Sevastjanov, P.V., Dymova, L.: Fuzzy Solution of Interval Linear Equations. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds.) PPAM 2007. LNCS, vol. 4967, pp. 1392–1399. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Dymova, L., Sevastjanov, P.: A new method for solving interval and fuzzy equations: linear case. Information Sciences 17, 925–937 (2009)

    MathSciNet  Google Scholar 

  15. Goualard, F.: Fast and Correct SIMD Algorithms for Interval Arithmetic. INRIA (2008), http://hal.archives-ouvertes.fr/docs/00/28/84/56/PDF/intervals-sse2-long-paper.pdf

  16. Knuppel, O.: Profil/BIAS v2.0, http://www.ti3.tu-harburg.de/keil/profil/Profil2.ps.gz

  17. Lambov, B.: RealLib 3 Manual, http://www.brics.dk/~barnie/RealLib/RealLib.pdf

  18. Leontief, W.: Quantitative input-output relations in the economic system of the United States. Review of Economics and Statistics 18, 100–125 (1936)

    Article  Google Scholar 

  19. Moore, R.E.: Interval Arithmetic and Automatic Error Analysis in Digital Computing. PhD thesis, Stanford University (1962)

    Google Scholar 

  20. SMP Superscalar (SMPSs) User’s Manual. Barcelona Supercomputing Center (2009), http://www.bsc.es/media/3576.pdf

  21. Wu, C.C., Chang, N.B.: Grey input-output analysis and its application for environmental cost allocation. European Journal of Operational Research 145, 175–201 (2003)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Computer and Information Sciences, Czestochowa University of Technology, Dabrowskiego 73, 42-200, Czestochowa, Poland

    Mariusz Pilarek & Roman Wyrzykowski

Authors
  1. Mariusz Pilarek
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  2. Roman Wyrzykowski
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Editor information

Editors and Affiliations

  1. Institute of Computer and Information Science, Czestochowa University of Technology, Dabrowskiego 69, 42-201, Czestochowa, Poland

    Roman Wyrzykowski  & Konrad Karczewski  & 

  2. Electrical Engineering and Computer Science Department, University of Tennessee, 1122 Volunteer Blvd, 37996-3450, Knoxville, TN, USA

    Jack Dongarra

  3. Department of Informatics and Mathematical Modeling, Technical University of Denmark, Richard Petersens Plads, Building 321, 2800, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Pilarek, M., Wyrzykowski, R. (2012). Solving Systems of Interval Linear Equations in Parallel Using Multithreaded Model and “Interval Extended Zero” Method. 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_21

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  • DOI: https://doi.org/10.1007/978-3-642-31464-3_21

  • 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)

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