Noferini, Vanni (2016) A formula for the Frechet derivative of a generalized matrix function. SIAM Journal of Matrix Analysis and Applications (2016.2). ISSN 17499097 (In Press)
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Abstract
We state and prove an extension of the DaleckiiKrein 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:  Article 

Uncontrolled Keywords:  generalized matrix function, DaleckiiKrein 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:  24 Apr 2017 
Last Modified:  20 Oct 2017 14:13 
URI:  https://eprints.maths.manchester.ac.uk/id/eprint/2544 
Available Versions of this Item

A DaleckiiKrein formula for the Frechet derivative of a
generalized matrix function. (deposited 15 Apr 2016)

A DaleckiiKrein formula for the Frechet derivative of a
generalized matrix function. (deposited 10 May 2016)
 A formula for the Frechet derivative of a generalized matrix function. (deposited 24 Apr 2017) [Currently Displayed]

A DaleckiiKrein formula for the Frechet derivative of a
generalized matrix function. (deposited 10 May 2016)
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