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 75 articles , 1 standard article )

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  1. Faure, Henri; Lemieux, Christiane: Irreducible Sobol’ sequences in prime power bases (2016)
  2. Goda, Takashi: Fast construction of higher order digital nets for numerical integration in weighted Sobolev spaces (2015)
  3. Leövey, H.; Römisch, W.: Quasi-Monte Carlo methods for linear two-stage stochastic programming problems (2015)
  4. Lord, Gabriel J.; Powell, Catherine E.; Shardlow, Tony: An introduction to computational stochastic PDEs (2014)
  5. Nerattini, R.; Brauchart, J.S.; Kiessling, M.K.-H.: Optimal $N$-point configurations on the sphere: “magic” numbers and Smale’s 7th problem (2014)
  6. 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)
  7. Chernov, Alexey; Reinarz, Anne: Numerical quadrature for high-dimensional singular integrals over parallelotopes (2013)
  8. Dick, Josef; Kuo, Frances Y.; Sloan, Ian H.: High-dimensional integration: The quasi-Monte Carlo way (2013)
  9. Fung, Hon-Kwok; Li, Leong Kwan; Yung, S.P.; Zhou, Wei: Fast evaluation of some probability integrals arisen from the valuations of discretely monitored derivative securities (2013)
  10. Keller, Alexander: Quasi-Monte Carlo image synthesis in a nutshell (2013)
  11. Omran, Mahamed G.H.; al-Sharhan, Salah; Salman, Ayed; Clerc, Maurice: Studying the effect of using low-discrepancy sequences to initialize population-based optimization algorithms (2013)
  12. Auffray, Yves; Barbillon, Pierre; Marin, Jean-Michel: Maximin design on non hypercube domains and kernel interpolation (2012)
  13. Brauchart, Johann S.; Dick, Josef: Quasi-Monte Carlo rules for numerical integration over the unit sphere $\mathbbS^2$ (2012)
  14. Challenor, Peter: Using emulators to estimate uncertainty in complex models (2012)
  15. Grünschloß, Leonhard; Raab, Matthias; Keller, Alexander: Enumerating quasi-Monte Carlo point sequences in elementary intervals (2012)
  16. Kulesza, Alex; Taskar, Ben: Determinantal point processes for machine learning (2012)
  17. Talke, Ismael S.; Borkowski, John J.: Generation of space-filling uniform designs in unit hypercubes (2012)
  18. Tarantola, Stefano; Becker, William; Zeitz, Dirk: A comparison of two sampling methods for global sensitivity analysis (2012)
  19. Zhang, Jie; Chowdhury, Souma; Messac, Achille: An adaptive hybrid surrogate model (2012)
  20. Baldeaux, Jan; Dick, Josef: A construction of polynomial lattice rules with small gain coefficients (2011)

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