Fast algorithm for incremental randomized SVD

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I have a list of covariance matrices $\{\Sigma_i\}$. I want to be able to take the (randomized for performance) SVD of the average of different (incremental) subsets of this list in order to perform a rolling fit. Is there an incremental or a distributed way to do this? Would it be useful to know the randomized SVD of each of the individual $\Sigma_i$?