Computing Matrix-Matrix Addition using QR and/or SVD

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Tarek Hajj Shehadi
评论： Tarek Hajj Shehadi 2021-7-5
Apologies if this sounds like an uninformed question but I was wondering if there are theoretical results that talk about the following problem:
Suppose we have two matrices and with and they can be written as the following via QR decomposition:
and
Is there a way we can get the QR decomposition of the matrix without explicitly adding and together and by only using the individual QR decomposition of both and . Specifically, I want to know if there are theoretical results that either talk about the feasibility of this algorithmically or if not? provide a justification of why it cannot be done. Also, can the same be said about the SVD of ?
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Matt J
Matt J 2021-7-4
编辑：Matt J 2021-7-4
I don't think I see how that would help you. Let's take the simple case where,
A=e*eye(2);
B=1/e*eye(2);
The QR decomposition of A+B is
Q=eye(2);
R=(e+1/e)*eye(2);
How do you use this to deal with the the case where (e+1/e) absorbs to 1/e in double float precision?

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