Computing Matrix-Matrix Addition using QR and/or SVD
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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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