A note about power-boundedness of interval matrices (Q913452)

\textit{J. Garloff} [J. Comput. Appl. Math. 14, 353-360 (1986; Zbl 0593.65022)] stated a theorem on the boundedness of the sequence \(\{k^{- \alpha}[A]^ k\}^{\infty}_{k=1}\), where [A] is an \(n\times n\) interval matrix with powers \([A]^ k:=[A]^{k-1}\cdot [A]\) and where \(\alpha\geq 0\). In the present paper, this theorem is proved in a different way. Furthermore, criteria are derived guaranteeing that the sequence \(\{\| k^{-\alpha}|\) \([A]^ k| \|^{1/k}\}^{\infty}_{k=1}\) (\(|.|\) absolute value, \(\|.\|\) any monotone matrix norm) converges to the spectral radius of \(| [A]|\).