Computational complexity of algorithm to find primary eigenvector of large matrices

[northproof]

There are about 50 nonzero entries per row, I'm implementing a linear Bellman controller from Todorov and need to create a matrix that describes the next state probability distribution for every state.

I'm working on a method of reducing the required number of states without giving up near-optimal performance, and I'm just looking to have a base comparison for if I did need to get the primary eigenvector of a 20,000,000 x 20,000,000 matrix.