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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.