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I wonder if it's possible to find the $Q$ and $R$ matrices from this QR-equation with only compute QR at one time only:

$$A = QR$$

if, the first column of $A$ got removed and then a new column got added to $A$.

I take it again: Assume that we first got our data matrix $A$ and we compute $Q$ and $R$. Then we change our data matrix $A$ by remove first column and add new data column to $A$. That means $Q$ and $R$ are going to change. Can we compute the new $Q$ and $R$ if we know the new data column of $A$ and the past $Q$ and $R$?

If you wonder what I got this question from. I got this from the paper Recursive Subspace Identification Algorithm using the Propagator Based Method, 2017.

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  • $\begingroup$ Do you mean that the first column gets removed, such that the old second column of $A$ becomes the new first column, the old third column becomes the new second column ect. and that new last column of $A$ becomes the new column, or do you mean that the first column of $A$ gets replaced with the new column? $\endgroup$ – Kwin van der Veen Jan 29 at 3:52
  • $\begingroup$ Yes! I mean this one "Do you mean that the first column gets removed, such that the old second column of A becomes the new first column, the old third column becomes the new second column ect. and that new last column of A becomes the new column". $\endgroup$ – Daniel Mårtensson Jan 29 at 12:10

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