sobol.cc

Remark on algorithm 659: Implementing Sobol’s quasirandom sequence generator. An algorithm to generate Sobol’ sequences to approximate integrals in up to 40 dimensions has been previously given by Bratley and Fox in Algorithm 659. Here, we provide more primitive polynomials and “direction numbers” so as to allow the generation of Sobol’ sequences to approximate integrals in up to 1111 dimensions. The direction numbers given generate Sobol’ sequences that satisfy Sobol’s so-called Property A.


References in zbMATH (referenced in 55 articles , 2 standard articles )

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  1. Atanassov, Emanouil; Ivanovska, Sofiya; Karaivanova, Aneta: Optimization of the direction numbers of the Sobol sequences (2021)
  2. Bigoni, Caterina; Zhang, Zhenying; Hesthaven, Jan S.: Systematic sensor placement for structural anomaly detection in the absence of damaged states (2020)
  3. Hoyt, Christopher R.; Owen, Art B.: Mean dimension of ridge functions (2020)
  4. Leövey, H.; Römisch, W.: Randomized QMC methods for mixed-integer two-stage stochastic programs with application to electricity optimization (2020)
  5. Litvinenko, Alexander; Logashenko, Dmitry; Tempone, Raul; Wittum, Gabriel; Keyes, David: Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability (2020)
  6. Marion, Pierre; Godin, Maxime; L’Ecuyer, Pierre: An algorithm to compute the (t)-value of a digital net and of its projections (2020)
  7. Polala, Arun Kumar; Ökten, Giray: Implementing de-biased estimators using mixed sequences (2020)
  8. van Appel, Jacques; McWalter, Thomas A.: Moment approximations of displaced forward-LIBOR rates with application to swaptions (2020)
  9. Zhigljavsky, Anatoly; Noonan, Jack: Covering of high-dimensional cubes and quantization (2020)
  10. Bayousef, Manal; Mascagni, Michael: A computational investigation of the optimal Halton sequence in QMC applications (2019)
  11. Bian, Qi; Nener, Brett; Wang, Xinmin: An improved NSGA-II based control allocation optimisation for aircraft longitudinal automatic landing system (2019)
  12. Faure, Henri; Lemieux, Christiane: Implementation of irreducible Sobol’ sequences in prime power bases (2019)
  13. Harase, Shin: Comparison of Sobol’ sequences in financial applications (2019)
  14. Kritzer, Peter; Leobacher, Gunther; Szölgyenyi, Michaela; Thonhauser, Stefan: Approximation methods for piecewise deterministic Markov processes and their costs (2019)
  15. Weiß, Christian; Nikolić, Zoran: An aspect of optimal regression design for LSMC (2019)
  16. Griewank, Andreas; Kuo, Frances Y.; Leövey, Hernan; Sloan, Ian H.: High dimensional integration of kinks and jumps -- smoothing by preintegration (2018)
  17. Heitzinger, Clemens; Pammer, Gudmund; Rigger, Stefan: Cubature formulas for multisymmetric functions and applications to stochastic partial differential equations (2018)
  18. Henderson, Nélio; de Sá Rêgo, Marroni; Imbiriba, Janaína; de Sá Rêgo, Márlison; Sacco, Wagner F.: Testing the topographical global initialization strategy in the framework of an unconstrained optimization method (2018)
  19. Jiménez Rugama, Lluís Antoni; Gilquin, Laurent: Reliable error estimation for Sobol’ indices (2018)
  20. Mak, Simon; Joseph, V. Roshan: Support points (2018)

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