I am trying to solve a set of equations like the following one using singular value decomposition:
3x + 5y = 11 x + y = 3 x + 2y = 4 x - y = 1
This is a trivial example, of course; the reason why I'm trying to do this at all is that I want to apply it to working with measured data containing noise, and I was hoping that including redundancies would make the system more stable (without those redundancies a certain noise level kills the approach, but up to that point it works fine).
From what I have read about SVD it should be able to handle cases like the one above, yet when I try it (using the Fortran code given here, pp. 51), even in the absence of simulated noise, it gives me (seemingly?) nonsensical results (x = 0.59 and y = -0.66 for my example set). Several times I have checked my code for errors, but to no avail, so currently I'm wondering whether I simply cannot feed those redundancies to SVD and expect to get a meaningful result. Or can I?
I am not a mathematician, so currently I'm feeling somewhat lost. It would be great if someone on here could help me out and tell me whether the chosen approach has been doomed from the start. Thanks a lot in advance!