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Description: |
It is well-known that the sensitivity of the matrix pth root (and primary matrix functions in general) to small perturbations in the data is measured by a condition number based on the norm of the Fréchet derivative. In this talk we show that computing the Fréchet derivative of the matrix pth root is equivalent to solve a sequence of p Sylvester equations. This provides the theoretical support to design an algorithm for the effective computation of the Fréchet derivative. Some numerical experiments will be carried out to illustrate the results and basic facts about matrix pth roots, Fréchet derivatives, Kronecker products and Sylvester equations will be revisited.
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