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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.

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    It all depends: how many $\,x_i's\,,\,y_i's\,$ are there? Are there some zero or negative $\,y_i's\,$? This kind of problems can be easily (more or less) solved by means of matrix theory within linear algebra.2012-12-14
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    You have to regularize the problem. For instance, by imposing an $L_2$ norm (determine $x$'s such that the sum of their squares is minimal).2012-12-14
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    @Johannes: For that particular problem I'm not sure what the most sensible real-world regularization is. Maybe all $x_i$ should be concentrated maybe spread. I actually think making them rather spread and equal would be better. But any suggestion for an easy algorithm will do for now.2012-12-14

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