The system of equations is the following:

$$
\frac{1}{\Gamma} = A\Gamma
$$

where Γ is a vector  of size n and A is a matrix of size n * n. With n > 100.
<br>*(I hope I am writing it correctly. So on the lhs we have the element-wise inverse values of &Gamma;)*

So there is a [paper](https://doi.org/10/gf5dw5) showing, that successive substitution is faster than newton-raphson if solved as mentioned above.

**I was wondering if through some kind of linear algebra change the system of equations becomes easier / faster to solve?**

<br>
I don't know it it helps, but here is how the matrix A is calculated:
$$
A = B \circ D
$$
Where B is symmetric, dense with positive and negative entries and D is dense with only positive entries and all rows are the same and their sum is 1.