Frolov cubature points in $[0,1]^d$

The table at the bottom allows to download the Frolov cubature points for dimensions between 2 and 10 and points numbers up to 1.000.000.

• Each file contains approximately $N=2^{\text{level}}$ points.

• The text-files follow the format:

  # Comments
  {dimension} d
  {number of points} N
  {integration weight} w
  {x_1} {x_2} ... {x_d}
  

• For reference, please cite:
  C. Kacwin, J. Oettershagen, M. Ullrich and T. Ullrich. Numerical performance of optimized Frolov lattices in tensor product reproducing kernel Sobolev spaces. ArXiv e-prints, 2017. [pdf]

• If larger point numbers or dimensionalities are needed please contact one of the authors.

Software examples

• C++ example code: Download tar gz archive
• Python example code: Download Python skript
• Python and Matlab scripts for a quick start will be available soon.

A zip archieve with all files for level 1..20 and dimension 2..10 can be downloaded here (about 1 GB).