Loading...
Please wait, while we are loading the content...
Similar Documents
Applying recursive numerical integration techniques for solving high dimensional integrals
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ammon, Andreas Genz, Alan Hartung, Tobias Jansen, Karl Leovey, Hernan Volmer, Julia |
| Copyright Year | 2016 |
| 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. |
| File Format | PDF HTM / HTML |
| DOI | 10.22323/1.256.0335 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1611.08628v1.pdf |
| Alternate Webpage(s) | http://export.arxiv.org/pdf/1611.08628 |
| Alternate Webpage(s) | https://pos.sissa.it/256/335/pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
