Differential calculus for p-norms of complex-valued vector functions with applications
Journal of Computational and Applied Mathematics
Extension and further development of the differential calculus for matrix norms with applications
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
International Journal of Computer Mathematics
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The second logarithmic derivative $\mu^{(2)}_{\infty}[A]$ of a complex n x n matrix A in the Chebyshev norm is defined as the second right derivative of $\| \Phi(t) \|_{\infty} \,=\, \| e^{A t} \|_{\infty}$ at $t=0$, where $\| \cdot \|_{\infty}$ denotes the operator norm corresponding to the norm $\| \cdot \|_{\infty}$ in $\CC^n$. The obtained formula is illustrated by a numerical example. The result may be of interest in applications such as stability theory.