Generalized eigenvalue problem can be reduced to eigenvalue problem $B^{-1} A x = \lambda x$ if $B$ is non-singular matrix. Then, the standard power iteration method can be applied.
How can I use the power iteration method to find the largest eigenvalue and eigenvector of pencil $(A, B)$ if $A$ and $B$ are singular? If it is not possible to use the power iteration method, which computationally efficient method can I use to find the largest eigenvector of pencil $(A, B)$?