Algorithm 659: Implementing Sobol’s quasirandom sequence generator: TOMS659 is a FORTRAN77 library which computes elements of the Sobol quasirandom sequence. A quasirandom or low discrepancy sequence, such as the Faure, Halton, Hammersley, Niederreiter or Sobol sequences, is ”less random” than a pseudorandom number sequence, but more useful for such tasks as approximation of integrals in higher dimensions, and in global optimization. This is because low discrepancy sequences tend to sample space ”more uniformly” than random numbers. Algorithms that use such sequences may have superior convergence. The original, true, correct version of ACM TOMS Algorithm 659 is available through ACM: or NETLIB:

References in zbMATH (referenced in 103 articles , 2 standard articles )

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  1. Heitzinger, Clemens; Pammer, Gudmund; Rigger, Stefan: Cubature formulas for multisymmetric functions and applications to stochastic partial differential equations (2018)
  2. Segredo, Eduardo; Paechter, Ben; Segura, Carlos; González-Vila, Carlos I.: On the comparison of initialisation strategies in differential evolution for large scale optimisation (2018)
  3. Van Appel, Jacques; Mcwalter, Thomas A.: Efficient long-dated swaption volatility approximation in the forward-LIBOR model (2018)
  4. Henderson, Nélio; R^ego, Marroni de Sá; Imbiriba, Janaína: Topographical global initialization for finding all solutions of nonlinear systems with constraints (2017)
  5. Léveillé, Ghislain; Hamel, Emmanuel: A compound trend renewal model for medical/professional liabilities (2017)
  6. Razi, M.; Pourghasemi, M.: Direct numerical simulation of deformable droplets motion with uncertain physical properties in macro and micro channels (2017)
  7. Sak, Halis; Başoğlu, İsmail: Efficient randomized quasi-Monte Carlo methods for portfolio market risk (2017)
  8. Shinozaki, Yuji: Construction of a third-order K-scheme and its application to financial models (2017)
  9. Azzimonti, Dario; Bect, Julien; Chevalier, Clément; Ginsbourger, David: Quantifying uncertainties on excursion sets under a Gaussian random field prior (2016)
  10. Chakraborty, Souvik; Chowdhury, Rajib: Sequential experimental design based generalised ANOVA (2016)
  11. Fathi-Vajargah, Behrouz; Kanafchian, Mohadeseh: Improved Markov chain Monte Carlo method for cryptanalysis substitution-transposition cipher (2016)
  12. Faure, Henri; Lemieux, Christiane: Irreducible Sobol’ sequences in prime power bases (2016)
  13. Heitsch, H.; Leövey, H.; Römisch, W.: Are quasi-Monte Carlo algorithms efficient for two-stage stochastic programs? (2016)
  14. Lai, Yongzeng; Yao, Haixiang: Simulation of multi-asset option Greeks under a special Lévy model by Malliavin calculus (2016)
  15. Goda, Takashi: Fast construction of higher order digital nets for numerical integration in weighted Sobolev spaces (2015)
  16. Leövey, H.; Römisch, W.: Quasi-Monte Carlo methods for linear two-stage stochastic programming problems (2015)
  17. Jansen, K.; Leovey, H.; Ammon, A.; Griewank, A.; Müller-Preussker, M.: Quasi-Monte Carlo methods for lattice systems: a first look (2014)
  18. Lord, Gabriel J.; Powell, Catherine E.; Shardlow, Tony: An introduction to computational stochastic PDEs (2014)
  19. Nerattini, R.; Brauchart, J. S.; Kiessling, M. K.-H.: Optimal $N$-point configurations on the sphere: “magic” numbers and Smale’s 7th problem (2014)
  20. Xu, Yongjia; Lai, Yongzeng; Yao, Haixiang: Efficient simulation of Greeks of multiasset European and Asian style options by Malliavin calculus and quasi-Monte Carlo methods (2014)

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