Computing Matrix-Matrix Addition using QR and/or SVD

1 view (last 30 days)
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 ?
  4 Comments
Matt J
Matt J on 4 Jul 2021
Edited: Matt J on 4 Jul 2021
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?
Tarek Hajj Shehadi
Tarek Hajj Shehadi on 5 Jul 2021
Thank you very much Matt, I will accept your counter example.

Sign in to comment.

Answers (0)

Categories

Find more on Eigenvalues in Help Center and File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!