I have this equation system, I am wondering if this is possible to solve in feasible time. And what are the methods to solve it?
We have 100 unknowns $x_i$, $i=1,2...100$
And 100 equations all of this form $j=1,2...100$
$I_j=\sum_{i\in N_j}c_i\sum_{n\in M_i} 1/(\sum_{m\in S_n} x_m)$
Here $N,M,S$ are known sets of cardinality around $5,5,20$ respectively (on average). I and c are known constants.