Let $A=(a_{ij})$ be an $n\times n$ positive matrix: $ a_{{ij}}>0$ for $1\leq i,j\leq n$. According to the statement of Perron–Frobenius theorem, one of the claims is $$\lim _{{k\rightarrow \infty }}A^{k}/r^{k}=vw^{T}\,,\quad \tag{1}$$ where the left and right eigenvectors for A are normalized so that $w^Tv = 1$. The positive real number $r$ is called the Perron root.
I would like to know whether there exist some algorithm to estimate the eigenvectors in Eq. (1) e what are they.
Thanks in advance.