Solution of the eigenvalue problem for a regular pencil $\lambda A_0-A_1$ with singular matrices

One considers the generalized eigenvalue problem
\begin{equation} (A_0\lambda-A_1)x=0, \end{equation}
when one or both matrices $A_0$, $A_1$ are singular and ker $\operatorname{ker}A_0\cap\operatorname{ker}A_1=\varnothing$ is the empty set. With the aid of the normalized process, the solving of problem (1) reduces to the solving of the eigenvalue problem of a constant matrix of order $r=\min(r_0,r_1)$, where $r_0$, $r_1$ are the ranks of the matrices $A_0$, $A_1$, which are determined at the normalized decomposition of the matrices. One gives an Algol program which performs the presented algorithm and testing examples.