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International Conference on Large-Scale Scientific Computing

LSSC 2011: Large-Scale Scientific Computing pp 455–463Cite as

Numerical Integration Using Sequences Generating Permutations

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7116))

Abstract

In this paper we propose a new class of pseudo random number generators based on a special linear recursions modulo m. These generators produce sequences which are permutations of the elements of a ℤ m . These sequences have been developed for other applications but the analysis of their statistical properties and the experiments described in this paper show that they are appropriate for multiple integration. Here we present some results from numerical tests comparing the performance of the two proposed generators with Mersenne Twister.

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References

  1. Atanassov, E., Karaivanova, A., Gurov, T., Ivanovska, S., Durchova, M., Dimitrov, D.: Quasi-Monte Carlo integration on the grid for sensitivity studies. Earth Sci. Inform. 3, 289–296 (2010)

    Article  Google Scholar 

  2. Blum, M., Micali, S.: How to Generate Cryptographically Strong Sequences of Pseudo-Random Bits. SIAM J. Comput. 13(4), 850–864 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  3. Goldreich, O.: Pseudorandomness. Notices 46(10), 1209–1216 (1999)

    MathSciNet  MATH  Google Scholar 

  4. Kolmogorov, A.N.: Three approaches to the concept of the amount of information. Probl. Inf. Transm. 1(1), 1–7 (1965)

    MathSciNet  Google Scholar 

  5. L’Ecuyer, P.: Uniform random number generation. Annals of Operations Research 53, 77–120 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  6. L’Ecuyer, P.: Uniform random number generation. In: Henderson, S.G., Nelson, B.L. (eds.) Simulation, Handbooks in Operations Research and Management Science, ch. 3, pp. 55–81. Elsevier, Amsterdam (2006)

    Google Scholar 

  7. L’Ecuyer, P.: Pseudorandom Number Generators. In: Cont, R. (ed.) Encyclopedia of Quantitative Finance, pp. 1431–1437. John Wiley, Chichester (2010); Platen, E., Jaeckel, P. (eds.) Simulation Methods in Financial Engineering

    Google Scholar 

  8. Li, M., Vitanyi, P.: An Introduction to Kolmogorov Complexity and Its Applications. Springer, New York (1993)

    MATH  Google Scholar 

  9. Manev, N.L.: Sequences generating permutations. Applied Mathematics and Computation 216(3), 708–718 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Matsumoto, M., Nishimura, T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Transactions on Modeling and Computer Simulation (TOMACS) 8(1), 3–30 (1998)

    Article  MATH  Google Scholar 

  11. Owen, A.: The dimension distribution and quadrature test functions. Stat. Sin. 13, 1–17 (2003)

    MathSciNet  MATH  Google Scholar 

  12. Schmid, W., Uhl, A.: Techniques for parallel quasi-Monte Carlo integration with digital sequences and associated problems. Math. Comp. Sim. 55, 249–257 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Information and Communication Technologies, BAS, Acad. G. Bonchev St., Bl.25A, 1113, Sofia, Bulgaria

    Sofiya Ivanovska & A. Karaivanova

  2. Institute of Mathematics and Informatics, BAS, Acad. G. Bonchev St., Bl.8, 1113, Sofia, Bulgaria

    N. Manev

Authors
  1. Sofiya Ivanovska
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  2. A. Karaivanova
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  3. N. Manev
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Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Block 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov  & Svetozar Margenov  & 

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

    Jerzy Waśniewski

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© 2012 Springer-Verlag Berlin Heidelberg

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Ivanovska, S., Karaivanova, A., Manev, N. (2012). Numerical Integration Using Sequences Generating Permutations. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_51

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  • DOI: https://doi.org/10.1007/978-3-642-29843-1_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29842-4

  • Online ISBN: 978-3-642-29843-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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