Solving a sequence of eigenvalue problems using snapshot and row subsampling

A sequence of eigenvalue problems requires solving $A_i\vec{x}_i= λ_i\vec{x}_i$ where $i \in \{1, \dots, N\}$, $N \gg 1$ and (usually) $λ_i$ is the largest or smallest eigenvalue of $A_i$. Often, the matrices $A_i$ come from a discretization of a smooth map depending on a parameter $p \rightarrow A(