probml / pml2-book

Probabilistic Machine Learning: Advanced Topics
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clarified time complexity of ensemble kalman filter in sec 8.5.4 #306

Closed murphyk closed 1 month ago

murphyk commented 6 months ago

clarified time complexity of ensemble kalman filter in sec 8.5.4 to distinguish diagonal and non-diagonal F (dynamics matrix):

In summary,  for sparse (e.g., diagonal) $\vF$,
EnKF is  $O(\nhidden \nsamples + \nhidden \nsamples \nobs)$
and EKF is $O(\nhidden^2 + \nhidden^2 \nobs)$,
whereas for dense $\vF$,
EnKF is  $O(\nhidden^2 \nsamples + \nhidden \nsamples \nobs)$
and EKF is $O(\nhidden^3 + \nhidden^2 \nobs)$.