Explicit Scheme, spectral radius and stability
The spectral radius is defined
as
$$
\begin{equation*}
\rho(\mathbf{A}) = \hspace{0.1cm}\mathrm{max}\left\{|\lambda|:\mathrm{det}(\mathbf{A}-\lambda\hat{I})=0\right\},
\end{equation*}
$$
which is interpreted as the smallest number such that a circle with radius centered at zero in the complex plane
contains all eigenvalues of \( \mathbf{A} \). If the matrix is positive definite, the condition in
Eq.
(8) is always satisfied.