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Is there a method to find QR factorization for ill conditioned matrix... here the matrix (eye($3$) and geographical $xyz$ coordinate) $n*7$ matrix

1 0 0 0 -4.2495e+06 1.0366e+06 4.6289e+06 0 1 0 4.2495e+06 0.0 -4.6289e+06 1.0366e+06 0 0 1 -1.0366e+06 4.6289e+06 0 4.2495e+06 1 0 0 0 -4.2495e+06 1.0371e+06 4.6287e+06 0 1 0 4.2495e+06 0 -4.6287e+06 1.0371e+06 0 0 1 -1.0371e+06 4.6287e+06 0 4.2495e+06 1 0 0 0 -4.2495e+06 1.0376e+06 4.6286e+06 0 1 0 4.2495e+06 0 -4.6286e+06 1.0376e+06 0 0 1 -1.0376e+06 4.6286e+06 0 4.2495e+06

structure of the matrix : identity $3\times 3$ terms with $10^6$.

Thank you.

amWhy
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claudio
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Sep 07 '21 at 15:37
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    This seems like a hard problem in general after glancing at wikipedia and the definition of conditioning. I did find this paper on ArXiV attempting to address it (but I have not read the paper): https://arxiv.org/abs/1809.11085 – Sidharth Ghoshal Sep 07 '21 at 17:09
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    i think your question will get a lot of downvotes the way its posted because you are asking about a specific case, you should instead ask the question "how to find the QR decomposition of an ill conditioned matrix" and then show what your attempts have been to solve the problem. If you are interested I can help you edit your question to make it more suitable for the math.stackexchange community – Sidharth Ghoshal Sep 07 '21 at 17:10
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    This link also appears to contain useful information for your title: https://www.cs.cornell.edu/~bindel/class/cs3220-s12/notes/lec11.pdf – Sidharth Ghoshal Sep 07 '21 at 17:13

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