Parasitic roots of BDF and Tendler's formulas

The parasitic roots $\lambda_i$ of a multistep method are the roots, which are not 1. In below table the root 1 is indexed with 0. The roots are for the matrix polynomial $$ \rho(\lambda) = A_m \lambda^m + A_{m-1} \lambda^{m-1} + \cdots + A_1 \lambda + A_0 $$ for the multistep method $$ \sum\limits_{i=0}^{m} A_i Y_{k+i} = h \sum\limits_{i=0}^{m} B_i Y'_{k+i}. $$ Tendler's formulas can be found in…