Here is the situation.
You have a black box x, whose values are not known to you, but you can choose values for A and generate the corresponding b value using Ax=b. There is some noise in the system so it is not possible to get an exact solution.
What is an efficient way to select values for A, to approximate a solution for x, using least squares approximation (or some other approximation algorithm if it would work better for this problem)?
So, it's like a least squares approximation with active feedback. Are there any algorithms for this?
I've tried doing some google searching and found nothing, it's a situation where I don't even know what keywords to search for, so any information to lead me in the right direction would be helpful.
Thank you!