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@INPROCEEDINGS{Frommer:1049919,
      author       = {Frommer, Andreas and Jimenez-Merchan, Jose and Ramirez
                      Hidalgo, Gustavo and Urrea-Niño, Juan Andrés},
      title        = {{V}ariance {R}eduction in {T}race {E}stimation for
                      {L}attice {QCD} {U}sing {M}ultigrid {M}ultilevel {M}onte
                      {C}arlo},
      publisher    = {Sissa Medialab Trieste, Italy},
      reportid     = {FZJ-2025-05673},
      pages        = {279},
      year         = {2025},
      comment      = {Proceedings of The 41st International Symposium on Lattice
                      Field Theory — PoS(LATTICE2024)},
      booktitle     = {Proceedings of The 41st International
                       Symposium on Lattice Field Theory —
                       PoS(LATTICE2024)},
      abstract     = {race estimation is a significant challenge in lattice QCD
                      simulations. The Hutchinson method's accuracy scales with
                      the square root of the sample size, resulting in high
                      computational costs for precise estimates. Variance
                      reduction techniques, such as deflating the lowest eigen or
                      singular vectors of the matrix, are employed to alleviate
                      this issue.This study explores Multigrid Multilevel Monte
                      Carlo (MGMLMC) to reduce the computational cost of
                      constructing the deflation subspace while maintaining
                      efficient application of the deflation projectors and
                      improving variance reduction. In MGMLMC, spectral deflation
                      is accomplished using a projector derived from the multigrid
                      prolongator $P$ used in solving linear systems involving the
                      Wilson-Dirac operator. By utilizing the low-mode spectral
                      information inherent in $P$, this approach significantly
                      lowers memory requirements while achieving up to a
                      three-fold variance reduction compared to inexact deflation,
                      which relies on a few iterations of the inverse block power
                      method to derive the deflation subspace.We investigate the
                      efficacy of MGMLMC for computing $tr(B(t)D^{−1}(t,t))$,
                      where $B(t)$ acts on spin, color, and space indices, for
                      example, a combination of gamma matrices and gauge covariant
                      spatial derivatives.},
      month         = {Jul},
      date          = {2024-07-28},
      organization  = {The 41st International Symposium on
                       Lattice Field Theory, Liverpool (UK),
                       28 Jul 2024 - 3 Aug 2024},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511) / DFG project
                      G:(GEPRIS)451886959 - FOR 5269: Zukünftige Methoden für
                      Studien von eingeschlossenen Gluonen in QCD (451886959)},
      pid          = {G:(DE-HGF)POF4-5111 / G:(GEPRIS)451886959},
      typ          = {PUB:(DE-HGF)8 / PUB:(DE-HGF)7},
      doi          = {https://doi.org/10.22323/1.466.0279},
      url          = {https://juser.fz-juelich.de/record/1049919},
}