Currently, I am working with a (non-symmetric) discretization matrix $A$ coming from a convection-diffusion problem without elimination of boundary conditions. Regarding the SOR algorithm, I have to express the number of iterations until convergence as a function of the matrix size $N$. Looking for literature on the internet, I found that this number of iterations is directly related to the spectral radius of iteration matrix, $\rho(B_{SOR})$.
However, this is where I get stuck. I see the relationship between the spectral radius and the eigenvalues of the matrix. But I can't seem to find any relationship between $\rho(B_{SOR})$ and matrix size $N$. Can anyone please help with finding this relation?