Non-Asymptotic Analysis of Ensemble Kalman Updates: Effective Dimension and Localization

@article{Ghattas2022NonAsymptoticAO,
  title={Non-Asymptotic Analysis of Ensemble Kalman Updates: Effective Dimension and Localization},
  author={Omar Al Ghattas and Daniel Sanz-Alonso},
  journal={ArXiv},
  year={2022},
  volume={abs/2208.03246}
}
Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data. Ensemble Kalman methods often perform well with a small ensemble size, which is essential in applications where generating each particle is costly. This paper develops a non-asymptotic analysis of ensemble Kalman updates that rigorously explains why a small ensemble size suffices if the prior covariance has moderate effective dimension due to fast… 

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