Applying recursive numerical integration techniques for solving high dimensional integrals

  title={Applying recursive numerical integration techniques for solving high dimensional integrals},
  author={A. Ammon and A. Genz and T. Hartung and K. Jansen and H. Leovey and J. Volmer},
  journal={arXiv: High Energy Physics - Lattice},
The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with $N$ samples behaves like $1/\sqrt{N}$. This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in lattice QCD. [...] Key Method The basic idea of this method is to use an efficient low-dimensional quadrature rule (usually of Gaussian type) and apply it iteratively to integrate over high-dimensional observables and Boltzmann weights.Expand

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  • Phys. Comm. 198
  • 2016
  • Inference 136
  • 2006
Cambridge Monographs on Mathematical Physics
  • Cambridge University Press
  • 1994