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Monte Carlo and Quasi-Monte Carlo Methods 2006 pp 495–510Cite as

Zinterhof Sequences in GRID-Based Numerical Integration

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Summary

The appropriateness of Zinterhof sequences to be used in GRID-based QMC integration is discussed. Theoretical considerations as well as experimental investigations are conducted comparing and assessing different strategies for an efficient and reliable usage. The high robustness and ease of construction exhibited by those sequences qualifies them as excellent QMC point set candidates for heterogeneous environments like the GRID.

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References

  1. B.C. Bromley. Quasirandom number generators for parallel Monte Carlo algorithms. Journal of Parallel and Distributed Computing, 38:101–104, 1996.

    Article  Google Scholar 

  2. L. Cucos and E. deDoncker. Distributed QMC algorithms: new strategies for and performance evaluation. In Proceedings of the High Performance Computing Symposium 2002 (HPC’02)/Advanced Simulation Techniques Conference, pages 155–159, 2002.

    Google Scholar 

  3. M. Drmota and R.F. Tichy. Sequences, discrepancies and applications, volume 1651 of Lect. Notes in Math. Springer-Verlag, 1997.

    Google Scholar 

  4. E. deDoncker, R. Zanny, M. Ciobanu, and Y. Guan. Asynchronous quasi-Monte Carlo methods. In Proceedings of the High Performance Computing Symposium 2000 (HPC’00), pages 130–135, 2000.

    Google Scholar 

  5. K. Entacher, T. Schell, W. Ch. Schmid, and A. Uhl. Defects in parallel Monte Carlo and quasi-Monte Carlo integration using the leap-frog technique. Parallel Algorithms and Applications, 18(1–2):27–47, 2003.

    MathSciNet  Google Scholar 

  6. J. H. Halton. On the efficiency of certain quasi-random sequences of points in evaluating multi-dimension integrals. Numer. Math., 2:84–90, 1960. Berichtigung, ibid., (1960), p. 196.

    Article  MathSciNet  Google Scholar 

  7. H. Hofbauer, A. Uhl, and P. Zinterhof. Quasi Monte Carlo Integration in GRID Environments: Further Leaping Effects. Parallel Processing Letters, 16(3):285–311, 2006.

    Article  MathSciNet  Google Scholar 

  8. H. Hofbauer, A. Uhl, and P. Zinterhof. Parameterization of Zinterhof Sequences for GRID-based QMC Integration. In J. Volkert, T. Fahringer, D. Kranzlmüller, and W. Schreiner, editors, Proceedings of the 2nd Austrian Grid Symposium, volume 221 of books@ocg.at, pages 91–105, Innsbruck, Austria, 2007. Austrian Computer Society.

    Google Scholar 

  9. A.R. Krommer and C.W. Überhuber. Numerical Integration on Advanced Computer Systems, volume 848 of Lecture Notes in Computer Science. Springer, Berlin, 1994.

    Google Scholar 

  10. H. L. Keng and W. Yuan. Applications of Number Theory to Numerical Analysis. Springer Verlag, Science Press, 1981.

    MATH  Google Scholar 

  11. S. Li, K. Kaugars, and E. deDoncker. Grid-based numerical integration and visualization. In Sixth International Conference on Computational Intelligence and Multimedia Applications (ICCIMA’05), pages 260–265. IEEE Computer Society Press, 2005.

    Google Scholar 

  12. Y. Li and M. Mascagni. Grid-based Quasi-Monte Carlo applications. Monte Carlo Methods and Appl., 11(1):39–55, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  13. G. L. Mullen, A. Mahalanabis, and H. Niederreiter. Tables of (t, m, s)-net and (t, s)-sequence parameters. In Harald Niederreiter and P. J.-S. Shiue, editors, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, volume Lecture Notes in Statistics of 106, pages 58–86. Springer-Verlag, 1995.

    Google Scholar 

  14. H. Niederreiter. Random Number Generation and Quasi-Monte Carlo Methods, volume 62 of CBMS-NSF Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), 1992.

    Google Scholar 

  15. G. Ökten and A. Srinivasan. Parallel quasi-Monte Carlo methods on a heterogeneous cluster. In K. T. Fang, F. J. Hickernell, and H. Niederreiter, editors, Monte Carlo and Quasi-Monte Carlo Methods 2000, pages 406–421. pub-springer, 2002.

    Google Scholar 

  16. R. Schürer and W. Ch. Schmid. Mint - the database of optimal (t, m, s)-net parameters. online: http://mint.sbg.ac.at/.

  17. W. Ch. Schmid and A. Uhl. Techniques for parallel quasi-Monte Carlo integration with digital sequences and associated problems. Mathematics and Computers in Simulation, 55:249–257, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  18. R. Schürer and A. Uhl. An evaluation of adaptive numerical integration algorithms on parallel systems. Parallel Algorithms and Applications, 18(1–2):13–26, 2003.

    MathSciNet  Google Scholar 

  19. P. Zinterhof. Einige zahlentheoretische Methoden zur numerischen Quadratur und Interpolation. Sitzungsberichte der Osterreichischen Akademie der Wissenschaften, math.-nat.wiss. Klasse Abt. II, 177:51–77, 1969.

    MATH  MathSciNet  Google Scholar 

  20. P. Zinterhof. Ü ber einige Abschätzungen bei der Approximation von Funktionen mit Gleichverteilungsmethoden. Sitzungsber. Österr. Akad. Wiss. Math.-Natur. Kl. II, 185:121–132, 1976.

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Sciences, Salzburg University, Austria

    Heinz Hofbauer, Andreas Uhl & Peter Zinterhof

Authors
  1. Heinz Hofbauer
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  2. Andreas Uhl
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  3. Peter Zinterhof
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Ulm University, Albert-Einstein-Allee 11, 89069, Ulm, Germany

    Alexander Keller

  2. Department of Computer Science, University of Kaiserslautern, 67653, Kaiserslautern, Germany

    Stefan Heinrich

  3. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Republic of Singapore

    Harald Niederreiter

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Hofbauer, H., Uhl, A., Zinterhof, P. (2008). Zinterhof Sequences in GRID-Based Numerical Integration. In: Keller, A., Heinrich, S., Niederreiter, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74496-2_28

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