XTrace: Making the most of every sample in stochastic trace estimation

  title={XTrace: Making the most of every sample in stochastic trace estimation},
  author={Ethan N. Epperly and Joel A. Tropp and Robert J. Webber},
The implicit trace estimation problem asks for an approximation of the trace of a square matrix, accessed via matrix-vector products (matvecs). This paper designs new randomized algorithms, XTrace and XNysTrace, for the trace estimation problem by exploiting both variance reduction and the exchangeability principle. For a fixed budget of matvecs, numerical experiments show that the new methods can achieve errors that are orders of magnitude smaller than existing algorithms, such as the Girard… 
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