### 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)