mcuncert /

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autom4te.cache
examples
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mcuncert
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The abstract class AbsUncertaintyCalculator helps computing the numerical
integration of high dimensional integrals over [0,1)^d with estimates
on the error bounds. The main two methods used are Pseudo Monte Carlo and
Quasi-Monte Carlo (only digital nets).
Pseudo Monte Carlo uses the regular Central Limit Theorem bound while
Quasi Monte has a more technical analysis based on the Walsh-Fourier
coefficients of the integrand (assumed to be absolutely convergent).
The guarantee is based on the decay rate of these coefficients.
For more details about this error bound, please refer to the references below:

%   [1] Fred J. Hickernell and Lluis Antoni Jimenez Rugama, "Reliable adaptive
%   cubature using digital sequences," 2014. Submitted for publication:
%   arXiv:1410.8615.

%   [2] Lluis Antoni Jimenez Rugama and Fred J. Hickernell, "Adaptive
%   Multidimensional Integration Based on Rank-1 Lattices," 2014. Submitted
%   for publication: arXiv:1411.1966.

%   [3] Sou-Cheng T. Choi, Fred J. Hickernell, Yuhan Ding, Lan Jiang,
%   Lluis Antoni Jimenez Rugama, Xin Tong, Yizhi Zhang and Xuan Zhou,
%   GAIL: Guaranteed Automatic Integration Library (Version 2.1)
%   [MATLAB Software], 2015. Available from http://code.google.com/p/gail/

If you find this software useful, please cite

@article{15HicketJim,
  author =   {F. J. Hickernell and Ll. A. Jimenez Rugama},
  title =    {Reliable adaptive cubature using digital sequences.},
  journal =  {},
  volume =   {},
  number =   {},
  note =     {}},
  OPTpages = {},
  year =     {}
}

@article{15JimetHick,
  author =   {Ll. A. Jimenez Rugama and F. J. Hickernell},
  title =    {Adaptive Multidimensional Integration Based on Rank-1 Lattices}
  journal =  {},
  volume =   {},
  number =   {},
  note =     {}},
  OPTpages = {},
  year =     {}
}