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?