13,947 research outputs found
On the efficient numerical solution of lattice systems with low-order couplings
We apply the Quasi Monte Carlo (QMC) and recursive numerical integration
methods to evaluate the Euclidean, discretized time path-integral for the
quantum mechanical anharmonic oscillator and a topological quantum mechanical
rotor model. For the anharmonic oscillator both methods outperform standard
Markov Chain Monte Carlo methods and show a significantly improved error
scaling. For the quantum mechanical rotor we could, however, not find a
successful way employing QMC. On the other hand, the recursive numerical
integration method works extremely well for this model and shows an at least
exponentially fast error scaling
Some Results on the Complexity of Numerical Integration
This is a survey (21 pages, 124 references) written for the MCQMC 2014
conference in Leuven, April 2014. We start with the seminal paper of Bakhvalov
(1959) and end with new results on the curse of dimension and on the complexity
of oscillatory integrals. Some small errors of earlier versions are corrected
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