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Solving a linear but ill-posed linear system

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Bart Boesman
Bart Boesman on 1 Oct 2012
Hi,
I encountered some numerical problem. I Have a simple exact linear system looking like this:
[9.8117e-9 - 3.5190e-4i 0 0 0 + 3.5181e-4i [ U [ 8.4473e-7
0 0 0 0 * V = 0
0 0 0 0 A 0
0 - 3.5181e-4i 0 0 0 + 3.5191e-4i ] B ] 0 ]
Solving it by hand is very easy and gives the correct solution:
V=A=0 U=B= 1.0112207+9.275646732i
However using numerical methods to solve the system (least-squares, pseudo-inverse, svd, ...), I do not get the result that I want to obtain. I understand that the matrix is ill-defined and close to singular. However, is there a method to solve this kind of systems precisely numerically?
Thanks,
Bart

  2 Comments

Matt J
Matt J on 1 Oct 2012
What do you mean "close to singular"? The 2nd and 3rd columns of the matrix appear to be exactly zero. Why aren't we calling it exactly singular?
Matt Fig
Matt Fig on 1 Oct 2012
I can't make heads or tails of that code. How many arrays is it supposed to represent?

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