Higher-Order Quasi-Monte Carlo

A collection of resources for HOQMC, in particular for interlaced polynomial lattice rules.

Email

We consider weights of the SPOD form

with $\delta(i,j) = 1$ if $i=j$ and 0 else, where the sequence $\beta_j$ is given for $\zeta=2,3,4$ by the “standard parametrization”

These sequences are then $p$-summable with $p=1/\zeta+\varepsilon$, which yields the choice $\alpha=\zeta$ for the interlacing factor.

IDstandard_spod
Generated2015-08-05
Weight TypeSPOD_TZ

Publications using these vectors

  1. Dick, J., Kuo, F.Y., Le Gia, Q.T., and Schwab, C. 2014. Multi-level higher order QMC Galerkin discretization for affine parametric operator equations. Report 2014-14 Seminar for Applied Mathematics, ETH Zürich. (link)
  2. 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)

Generating Vectors

$\alpha=2$
$\boldsymbol{\alpha}$$\boldsymbol{C}$$\boldsymbol{\zeta}$$\boldsymbol{\theta}$Links
20.120.2.tar.gz, .tar.bz2, .zip
20.120.5.tar.gz, .tar.bz2, .zip
$\boldsymbol{\alpha}$$\boldsymbol{C}$$\boldsymbol{\zeta}$$\boldsymbol{\theta}$Links
2120.2.tar.gz, .tar.bz2, .zip
2120.5.tar.gz, .tar.bz2, .zip
$\alpha=3$
$\boldsymbol{\alpha}$$\boldsymbol{C}$$\boldsymbol{\zeta}$$\boldsymbol{\theta}$Links
30.130.2.tar.gz, .tar.bz2, .zip
30.130.5.tar.gz, .tar.bz2, .zip
$\boldsymbol{\alpha}$$\boldsymbol{C}$$\boldsymbol{\zeta}$$\boldsymbol{\theta}$Links
3130.2.tar.gz, .tar.bz2, .zip
3130.5.tar.gz, .tar.bz2, .zip
$\alpha=4$
$\boldsymbol{\alpha}$$\boldsymbol{C}$$\boldsymbol{\zeta}$$\boldsymbol{\theta}$Links
40.140.2.tar.gz, .tar.bz2, .zip
40.140.5.tar.gz, .tar.bz2, .zip
$\boldsymbol{\alpha}$$\boldsymbol{C}$$\boldsymbol{\zeta}$$\boldsymbol{\theta}$Links
4140.2.tar.gz, .tar.bz2, .zip
4140.5.tar.gz, .tar.bz2, .zip