Geodesic
Generalized complex step approximation to estimate the first and second order Fréchet derivative of matrix functions
Filomat, Tome 36 (2022) no. 16, p. 5603

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DOI

Applications of Fréchet derivative emerge in the sensitivity analysis of matrix functions. Our work extends the generalized complex step approximation using the complex computation f (A + e iθ hE) as a tool to matrix case, and combines it with finite difference formula to estimate the Fréchet derivative. We provide numerical results for the approximation to the first and the second order Fréchet derivative of the matrix exponential and matrix square root.
DOI : 10.2298/FIL2216603A
Classification : 65R10, 47A56
Keywords: Fréchet derivative, complex step approximation, finite difference, matrix exponential, Matrix square root 
Bahar Arslan; Awad H Al-Mohy. Generalized complex step approximation to estimate the first and second order Fréchet derivative of matrix functions. Filomat, Tome 36 (2022) no. 16, p. 5603 . doi: 10.2298/FIL2216603A
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     author = {Bahar Arslan and Awad H Al-Mohy},
     title = {Generalized complex step approximation to estimate the first and second order {Fr\'echet} derivative of matrix functions},
     journal = {Filomat},
     pages = {5603 },
     year = {2022},
     volume = {36},
     number = {16},
     doi = {10.2298/FIL2216603A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2216603A/}
}
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