Noferini, Vanni (2016) A Daleckii-Krein formula for the Frechet derivative of a generalized matrix function. [MIMS Preprint]
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Abstract
We state and prove an extension of the Daleckii-Krein theorem, thus obtaining an explicit formula for the Frechet derivative of generalized matrix functions. Moreover, we prove the differentiability of generalized matrix functions of real matrices under very mild assumptions. For complex matrices, we argue that generalized matrix functions are real differentiable but generally not complex differentiable. Finally, we discuss the application of our result to the study of the condition number of generalized matrix functions. Along our way, we also derive generalized matrix functional analogues of a few classical theorems on polynomial interpolation of classical matrix functions and their derivatives.
Item Type: | MIMS Preprint |
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Uncontrolled Keywords: | generalized matrix function, Daleckii-Krein theorem, Gateaux derivative, Frechet derivative, condition number |
Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis |
Depositing User: | Dr V Noferini |
Date Deposited: | 15 Apr 2016 |
Last Modified: | 08 Nov 2017 18:18 |
URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2462 |
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- A Daleckii-Krein formula for the Frechet derivative of a generalized matrix function. (deposited 15 Apr 2016) [Currently Displayed]
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