# The 34th International Symposium on Lattice Field Theory (Lattice 2016)

24-30 July 2016
Highfield Campus, University of Southampton
Europe/London timezone

## Applying recursive numerical integration techniques for solving high dimensional integrals

26 Jul 2016, 15:00
20m
Building 67 Room 1003 (Highfield Campus, University of Southampton)

### Building 67 Room 1003

#### Highfield Campus, University of Southampton

Talk Theoretical Developments

### Speaker

Ms Julia Volmer (DESY Zeuthen)

### Description

The error scaling for Markov Chain - Monte Carlo techniques (MC-MC) with $N$ samples behaves like $\frac{1}{\sqrt{N}}$. This scaling makes it often very time intensive to reduce the error of calculated 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 Gauss quadrature with Legendre polynomials and apply it iteratively to integrate over observable and Boltzmann weight. In this talk we will present the application of such an algorithm to the topological rotor and the anharmonic oscillator and compare the error scaling to MC-MC results. In particular, we demonstrate that the RNI technique shows an error scaling in $N$ that is at least exponential.

### Primary author

Ms Julia Volmer (DESY Zeuthen)

### Co-authors

Prof. Alan Genz (Washington State University) Dr Andreas Ammon (OAKLABS GmbH) Dr Hernan Leövey (Humboldt-Universität zu Berlin) Dr Karl Jansen (DESY Zeuthen) Dr Tobias Hartung (King's College London)

### Presentation Materials

 Slides
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