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We present the analysis of two recently proposed noise reduction techniques,Hutch++ and XTrace, both based on inexact deflation. These methods were provento have a better asymptotic convergence to the solution than the classicalGirard-Hutchinson stochastic method. We applied these methods to thecomputation of the trace of the inverse of the Dirac operator with $O(a)$improved Wilson fermions on the QCD ensemble generated by the RC$^{\star}$collaboration with $m_{\pi}\approx 400$ MeV and $V = 64\times 32^3$.Unfortunately, we see no noise reduction with a moderate number of sources, andwe attempt an explanation of why this is the case. This study was part of theeffort to evaluate isospin-breaking effects using the RM123 with C$^{\star}$boundary conditions in an unquenched set-up.

Hutch++ and XTrace to Improve Stochastic Trace Estimation