Standard Product Weights
Product weights with $\beta_j=\theta j^{-\zeta}$.
Generating Vector Repository
These QMC rules can achieve an order of convergence higher than one for functions fulfilling suitable derivative bounds, independent of the dimension. For more information, see [Dick et al. 2014] for the theoretical development and [Gantner and Schwab 2014] for some computational results. For a more complete list of relevant references, see the Literature page.
For a specification of the format of the generating vector files, see the format page. Generating vectors are available for up to $s=256$ dimensions and $N=2^{15}$ points. If you require more dimensions and/or points, please contact us. If you experience any problems applying these generating vectors, please do not hesitate to contact us.
References
- Dick, J., Kuo, F.Y., Le Gia, Q.T., Nuyens, D., and Schwab, C. 2014. Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs. SIAM J. Numer. Anal. 52, 6, 2676–2702. (link)
- Gantner, R.N. and Schwab, C. 2014. Computational Higher-Order Quasi-Monte Carlo Integration. Tech. Report 2014-25, Seminar for Applied Mathematics, ETH Zürich (to appear in Proc. MCQMC14). (link, pdf)
Product Weights
SPOD Weights
Standard SPOD Weights
SPOD weights with $\beta_j=\theta j^{-\zeta}$.
SPOD Weights for 2d Diffusion Equation
SPOD weights for 2d KL expansion in a square domain.
Related Links
HOQMC Literature
List of relevant literature.
Generating Vector Format
Documentation of generating vector file format.