2022
DOI: 10.48550/arxiv.2203.03930
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Integral representations for higher-order Fréchet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number

Abstract: We propose an integral representation for the higher-order Fréchet derivative of analytic matrix functions f (A) which unifies known results for the first-order Fréchet derivative of general analytic matrix functions and for higher-order Fréchet derivatives of A −1 . We highlight two applications of this integral representation: On the one hand, it allows to find the exact value of the level-2 condition number (i.e., the condition number of the condition number) of f (A) for a large class of functions f when A… Show more

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