I have some unknown numbers $x_i$ and I know only certains sums $y_i$ over them:
$\mathbf{A}\mathbf{x}=\mathbf{y}$
where this equation is underdetermined. Moreover, due to the origin of the problem I know that all $x_i>0$ are positive. I do know all $A_{ij}\in \{0,1\}$.
Do you know a way to find a solution? One "average and simple" solution would suffice.
EDIT: Some more information for that particular problem. All $x_i>0$ and $y_i>0$ and all $A_{ij}\in \{0,1\}$. There are more $x_i$ than $y_i$. And there are a lot of them, so that the method to solve it should be simple for the computer :) Something iterative would be nice.