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 90 articles , 1 standard article )

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  1. Segredo, Eduardo; Paechter, Ben; Segura, Carlos; González-Vila, Carlos I.: On the comparison of initialisation strategies in differential evolution for large scale optimisation (2018)
  2. Henderson, Nélio; R^ego, Marroni de Sá; Imbiriba, Janaína: Topographical global initialization for finding all solutions of nonlinear systems with constraints (2017)
  3. Léveillé, Ghislain; Hamel, Emmanuel: A compound trend renewal model for medical/professional liabilities (2017)
  4. Sak, Halis; Başoğlu, İsmail: Efficient randomized quasi-Monte Carlo methods for portfolio market risk (2017)
  5. Azzimonti, Dario; Bect, Julien; Chevalier, Clément; Ginsbourger, David: Quantifying uncertainties on excursion sets under a Gaussian random field prior (2016)
  6. Fathi-Vajargah, Behrouz; Kanafchian, Mohadeseh: Improved Markov chain Monte Carlo method for cryptanalysis substitution-transposition cipher (2016)
  7. Faure, Henri; Lemieux, Christiane: Irreducible Sobol’ sequences in prime power bases (2016)
  8. Heitsch, H.; Leövey, H.; Römisch, W.: Are quasi-Monte Carlo algorithms efficient for two-stage stochastic programs? (2016)
  9. Lai, Yongzeng; Yao, Haixiang: Simulation of multi-asset option Greeks under a special Lévy model by Malliavin calculus (2016)
  10. Goda, Takashi: Fast construction of higher order digital nets for numerical integration in weighted Sobolev spaces (2015)
  11. Leövey, H.; Römisch, W.: Quasi-Monte Carlo methods for linear two-stage stochastic programming problems (2015)
  12. Jansen, K.; Leovey, H.; Ammon, A.; Griewank, A.; Müller-Preussker, M.: Quasi-Monte Carlo methods for lattice systems: a first look (2014)
  13. Lord, Gabriel J.; Powell, Catherine E.; Shardlow, Tony: An introduction to computational stochastic PDEs (2014)
  14. Nerattini, R.; Brauchart, J.S.; Kiessling, M.K.-H.: Optimal $N$-point configurations on the sphere: “magic” numbers and Smale’s 7th problem (2014)
  15. 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)
  16. Chernov, Alexey; Reinarz, Anne: Numerical quadrature for high-dimensional singular integrals over parallelotopes (2013)
  17. Dick, Josef; Kuo, Frances Y.; Sloan, Ian H.: High-dimensional integration: The quasi-Monte Carlo way (2013)
  18. Dimov, Ivan; Georgieva, Rayna: Multidimensional sensitivity analysis of large-scale mathematical models (2013)
  19. 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)
  20. Keller, Alexander: Quasi-Monte Carlo image synthesis in a nutshell (2013)

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