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@ARTICLE{Ghanem:873781,
      author       = {Ghanem, Khaldoon and Koch, Erik},
      title        = {{A}verage spectrum method for analytic continuation:
                      {E}fficient blocked-mode sampling and dependence on the
                      discretization grid},
      journal      = {Physical review / B},
      volume       = {101},
      number       = {8},
      issn         = {2469-9950},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2020-00995},
      pages        = {085111},
      year         = {2020},
      abstract     = {The average spectrum method is a promising approach for the
                      analytic continuation of imaginary time or frequency data to
                      the real axis. It determines the analytic continuation of
                      noisy data from a functional average over all admissible
                      spectral functions, weighted by how well they fit the data.
                      Its main advantage is the apparent lack of adjustable
                      parameters and smoothness constraints, using instead the
                      information on the statistical noise in the data. Its main
                      disadvantage is the enormous computational cost of
                      performing the functional integral. Here we introduce an
                      efficient implementation, based on the singular value
                      decomposition of the integral kernel, eliminating this
                      problem. It allows us to analyze the behavior of the average
                      spectrum method in detail. We find that the discretization
                      of the real-frequency grid, on which the spectral function
                      is represented, biases the results. The distribution of the
                      grid points plays the role of a default model while the
                      number of grid points acts as a regularization parameter. We
                      give a quantitative explanation for this behavior, point out
                      the crucial role of the default model and provide a
                      practical method for choosing it, making the average
                      spectrum method a reliable and efficient technique for
                      analytic continuation.},
      cin          = {JSC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511)},
      pid          = {G:(DE-HGF)POF3-511},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000512773800002},
      doi          = {10.1103/PhysRevB.101.085111},
      url          = {https://juser.fz-juelich.de/record/873781},
}