Multilevel Monte Carlo for trace estimation

by Andreas Frommer

Tuesday 18 Oct 2022, 16:00 → 17:00 Europe/Zurich

online (CERN)

The idea of multilevel Monte-Carlo is to represent a to-be-estimated random variable by a sum of new random variables, where for each summand the variance is low when it is expensive to evaluate and (possibly) high when it is cheap to evaluate.

We apply this idea to the estimation of the trace of the inverse, taking each summand as a difference of two successive multigrid approximations of the inverse. We also discuss how other approaches for the trace of the inverse fit into the multilevel Monte Carlo approach.

We present some numerical examples for the Schwinger model and preliminary results for the Wilson-Dirac matrix in lattice QCD.