Volume 256 - 34th annual International Symposium on Lattice Field Theory (LATTICE2016) - Theoretical Developments
Applying recursive numerical integration techniques for solving high dimensional integrals
A. Ammon, A. Genz, T. Hartung, K. Jansen, H. Leövey, J. Volmer*
*corresponding author
Full text: pdf
Pre-published on: February 17, 2017
Published on: March 24, 2017
Abstract
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. It is therefore highly
desirable to have alternative methods at hand which show an improved
error scaling. One candidate for such an alternative integration
technique is the method of recursive numerical integration (RNI). 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. We
present the application of such an algorithm to the topological rotor
and the anharmonic oscillator and compare the error scaling to MCMC
results. In particular, we demonstrate that the RNI technique shows an
error scaling in the number of integration points $m$ that is at least exponential.
DOI: https://doi.org/10.22323/1.256.0335
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