Recently, I have been studying some bits of numerical analysis and have managed to derive the stability function of a Runge-Kutta method. What I got is as follows
$R\left(z\right)=1+zb^{\top}\left(I-zA\right)^{-1}\overset{\rightharpoonup}{1}$
Where $I$ is the identity and $\overset{\rightharpoonup}{1}$ is a vector of ones.
I keep seeing that $R\left(\infty\right)=1-b^{\top}A^{-1}\overset{\rightharpoonup}{1}$ but I have no idea how you get from one to the other.
Any help is greatly appreciated with many thanks in advance!