Solving a linear but ill-posed linear system

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Bart Boesman 2012-10-1

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https://ww2.mathworks.cn/matlabcentral/answers/49571-solving-a-linear-but-ill-posed-linear-system

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