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Position and Communication Papers of the 16th Conference on Computer Science and Intelligence Systems

Annals of Computer Science and Information Systems, Volume 26

Optimized lattice rule and adaptive approach for multidimensional integrals with applications

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DOI: http://dx.doi.org/10.15439/2021F94

Citation: Position and Communication Papers of the 16th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 26, pages 75–80 ()

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Abstract. In this work we make a comparison between optimized lattice and adaptive stochastic approaches for multidimensional integrals with different dimensions. Some of the integrals has applications in environmental safety and control theory.

References

  1. Berntsen J., Espelid T.O., Genz A. (1991) An adaptive algorithm for the approximate calculation of multiple integrals, ACM Trans. Math. Softw. 17: 437–451.
  2. Dimov I. (2008) Monte Carlo Methods for Applied Scientists, New Jersey, London, Singapore, World Scientific, 291 p., ISBN-10 981-02-2329-3.
  3. Dimov I., Karaivanova A., Georgieva R., Ivanovska S. (2003) Parallel Importance Separation and Adaptive Monte Carlo Algorithms for Multiple Integrals, Springer Lecture Notes in Computer Science, 2542, 99–107.
  4. Dimov I., Georgieva R. (2010) Monte Carlo Algorithms for Evaluating Sobol’ Sensitivity Indices. Math. Comput. Simul. 81(3): 506–514.
  5. A. Genz, Testing multidimensional integration routines. Tools, Methods and Languages for Scientific and Engineering Computation (1984) 81–94.
  6. Hua L.K. and Wang Y. (1981) Applications of Number Theory to Numerical analysis.
  7. Pencheva, V., I. Georgiev, and A. Asenov. “Evaluation of passenger waiting time in public transport by using the Monte Carlo method.” AIP Conference Proceedings. Vol. 2321. No. 1. AIP Publishing LLC, 2021.
  8. Raeva, E., & Georgiev, I. R. (2018, October). Fourier approximation for modeling limit of insurance liability. In AIP Conference Proceedings (Vol. 2025, No. 1, p. 030006). AIP Publishing LLC.
  9. I.F. Sharygin (1963) A lower estimate for the error of quadrature formulas for certain classes of functions, Zh. Vychisl. Mat. i Mat. Fiz. 3, 370–376.
  10. I.H. Sloan and P.J. Kachoyan (1987) Lattice methods for multiple integration: Theory, error analysis and examples, SIAM J. Numer. Anal. 24, 116–128.
  11. I.H. Sloan and S. Joe, Lattice Methods for Multiple Integration, Lattice methods for multiple Integration, (Oxford University Press 1994).
  12. Y. Wang and F. J. Hickernell (2000) An historical overview of lattice point sets, in Monte Carlo and Quasi-Monte Carlo Methods 2000, Proceedings of a Conference held at Hong Kong Baptist University, China.